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There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Arnold`, `Bob`, `Eric`, `Peter`
- Each person has a unique hobby: `painting`, `photography`, `cooking`, `gardening`, `knitting`
- Each person has a unique birthday month: `jan`, `sept`, `mar`, `feb`, `april`
- People have unique favorite sports: `swimming`, `basketball`, `tennis`, `baseball`, `soccer`
- Each person has an occupation: `engineer`, `lawyer`, `teacher`, `doctor`, `artist`
- Each person has a unique level of education: `bachelor`, `master`, `high school`, `doctorate`, `associate`
## Clues:
1. The person with a high school diploma is directly left of the person whose birthday is in February.
2. The person who loves soccer is directly left of the photography enthusiast.
3. Arnold is the person whose birthday is in January.
4. The person who is a doctor is the person who loves baseball.
5. The person who is an artist is somewhere to the left of Bob.
6. The photography enthusiast is somewhere to the right of the person with an associate's degree.
7. The photography enthusiast is directly left of the person who paints as a hobby.
8. Eric is in the fifth house.
9. The person whose birthday is in February is directly left of the person who loves tennis.
10. The person who loves baseball is somewhere to the right of the person whose birthday is in January.
11. The person who is an engineer is not in the first house.
12. Alice is not in the second house.
13. The person who enjoys gardening is somewhere to the left of the person whose birthday is in September.
14. The person who loves swimming is not in the first house.
15. The person who is a teacher is Bob.
16. Arnold is the person who enjoys knitting.
17. The person who is an artist is the person whose birthday is in March.
18. Arnold is the person with a master's degree.
19. The person whose birthday is in March is directly left of the person who is a doctor.
20. The person whose birthday is in September is the person with a bachelor's degree.
What is the value of attribute FavoriteSport for the person whose attribute Occupation is teacher? Please reason step by step, and put your final answer within \boxed{}
|
swimming
|
0/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Alice`, `Peter`
- The mothers' names in different houses are unique: `Holly`, `Kailyn`, `Aniya`, `Janelle`
- Each person has a unique birthday month: `april`, `feb`, `sept`, `jan`
- Each person lives in a unique style of house: `ranch`, `colonial`, `victorian`, `craftsman`
## Clues:
1. Peter is the person whose birthday is in February.
2. The person whose birthday is in February is not in the fourth house.
3. The person whose birthday is in January is somewhere to the right of the person in a ranch-style home.
4. The person whose birthday is in January is directly left of Eric.
5. The person in a ranch-style home is the person whose birthday is in April.
6. The person whose mother's name is Janelle is the person whose birthday is in September.
7. The person in a ranch-style home and The person whose mother's name is Kailyn are next to each other.
8. Arnold is The person whose mother's name is Holly.
9. The person whose mother's name is Kailyn is directly left of the person residing in a Victorian house.
10. The person whose birthday is in January is the person in a Craftsman-style house.
What is the value of attribute House for the person whose attribute HouseStyle is ranch? Please reason step by step, and put your final answer within \boxed{}
|
2
|
1/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Carol`, `Bob`, `Peter`, `Arnold`, `Alice`
- Everyone has something unique for lunch: `stew`, `stir fry`, `soup`, `grilled cheese`, `pizza`, `spaghetti`
- Each person has a unique favorite drink: `root beer`, `milk`, `boba tea`, `water`, `coffee`, `tea`
- People have unique heights: `super tall`, `short`, `tall`, `very short`, `very tall`, `average`
- Each person has a unique birthday month: `sept`, `feb`, `may`, `mar`, `jan`, `april`
## Clues:
1. The person whose birthday is in January is Peter.
2. The person who loves eating grilled cheese is the person whose birthday is in May.
3. The person whose birthday is in April is the person who loves stir fry.
4. The person who loves the stew is the one who only drinks water.
5. The person whose birthday is in September is not in the fourth house.
6. The person who likes milk is somewhere to the left of the person who loves stir fry.
7. The coffee drinker is in the fifth house.
8. The person who loves eating grilled cheese is directly left of the one who only drinks water.
9. The person whose birthday is in May is directly left of Arnold.
10. The root beer lover is somewhere to the left of Alice.
11. There are two houses between Eric and the person who is a pizza lover.
12. The person who loves the spaghetti eater is the person who is very short.
13. The person who is super tall is the tea drinker.
14. The person who is tall is not in the third house.
15. Peter is directly left of the person who is a pizza lover.
16. The person who likes milk is somewhere to the right of the one who only drinks water.
17. The person who is very short is the coffee drinker.
18. The person who is super tall is Bob.
19. The person who is super tall and the person whose birthday is in March are next to each other.
20. Carol is somewhere to the left of the person who has an average height.
21. The person who is very tall is the person who loves the stew.
22. There is one house between the person who loves eating grilled cheese and Peter.
What is the value of attribute Height for the person whose attribute Birthday is mar? Please reason step by step, and put your final answer within \boxed{}
|
very short
|
0/8
|
Problem 4. A clock shows exactly one o'clock. A mosquito and a fly are sitting at the same distance from the center on the hour and minute hands, respectively. When the hands coincide, the insects swap places. How many times greater is the distance that the mosquito has traveled in half a day compared to the distance the fly has traveled in the same time?
|
\dfrac{83}{73}
|
0/8
|
1. Find all pairs $(r, s)$ of real numbers such that the zeros of the polynomials
$$
f(x)=x^{2}-2 r x+r
$$
and
$$
g(x)=27 x^{3}-27 r x^{2}+s x-r^{6}
$$
are all real and nonnegative.
|
(0, 0)
|
1/8
|
Let $X$ be a non-empty and finite set, $A_1,...,A_k$ $k$ subsets of $X$ , satisying:
(1) $|A_i|\leq 3,i=1,2,...,k$ (2) Any element of $X$ is an element of at least $4$ sets among $A_1,....,A_k$ .
Show that one can select $[\frac{3k}{7}] $ sets from $A_1,...,A_k$ such that their union is $X$ .
|
\left\lfloor \frac{3k}{7} \right\rfloor
|
2/8
|
3.21. The planes $A B C_{1}$ and $A_{1} B_{1} C$ divide the triangular prism $A B C A_{1} B_{1} C_{1}$ into four parts. Find the ratio of the volumes of these parts.
|
1:3:3:5
|
0/8
|
One. (35 points) The lines $l_{1}$ and $l_{2}$ are tangent to a circle at points $A$ and $B$, respectively. On lines $l_{1}$ and $l_{2}$, take 1993 points $A_{1}, A_{2}, \cdots, A_{1993}$ and $B_{1}, B_{2}, \cdots, B_{1993}$, such that $A A_{i}=(i+1) B B_{i} (i=1, 2, \cdots, 1993)$. If the extension of $A_{i} B_{i}$ intersects the extension of $A B$ at point $M_{i} (i=1, 2, \cdots, 1993)$, find:
$$
\frac{A_{1} B_{1}}{A_{1} M_{1}} \cdot \frac{A_{2} B_{2}}{A_{2} M_{2}} \cdot \cdots \cdot \frac{A_{1993} B_{1993}}{A_{1993} M_{1993}}=?
$$
|
\dfrac{1}{1994}
|
4/8
|
Example 3 Choose 1 young man and 1 young woman from each of the four groups to perform a circle dance, with the rule that men and women must alternate, and two people from the same group cannot be adjacent. How many different team formation variations are there?
|
12
|
3/8
|
Given a set $A$ which contains $n$ elements. For any two distinct subsets $A_{1}$, $A_{2}$ of the given set $A$, we fix the number of elements of $A_1 \cap A_2$. Find the sum of all the numbers obtained in the described way.
|
n \cdot (2^{2n - 3} - 2^{n - 2})
|
2/8
|
# 9. Problem 9.10
In a convex 10-gon \(A_{1} A_{2} \ldots A_{10}\), all sides and all diagonals connecting vertices every other one (i.e., \(A_{1} A_{3}, A_{2} A_{4}\), etc.) are drawn, except for the side \(A_{1} A_{10}\) and the diagonals \(A_{1} A_{9}, A_{2} A_{10}\).
We call a path leading from \(A_{1}\) to \(A_{10}\) a non-self-intersecting broken line (i.e., one in which non-adjacent segments do not have common points) with endpoints \(A_{1}\) and \(A_{10}\), each segment of which coincides with one of the drawn sides or diagonals. Find the number of such paths.
|
55
|
1/8
|
Let $1 \leq k \leq n$ be integers. How many $k$-element subsets of the set $\{1,2, \ldots, n\}$ can be chosen such that any two of them consist of the $k$ smallest elements of their union?
|
n - k + 1
|
0/8
|
Little João always lies on Tuesdays, Thursdays, and Saturdays, and on the rest of the days of the week, he always tells the truth. One day, Little Pedro meets João and the following dialogue occurs.
- Little Pedro asks: What day is it today?
- João answers: Saturday.
- Little Pedro asks: And what day will it be tomorrow?
- João answers: Wednesday.
On what day of the week did Little Pedro meet João?
|
Thursday
|
5/8
|
Let $F$ be a family of subsets of the set $\{1, 2, \cdots, n\}$, satisfying: (1) If $A \in F$, then $|A|=3$; (2) If $A \in F$ and $B \in F$ with $A \neq B$, then $|A \cap B| \leqslant 1$. Define $f(n) = \max |F|$. Prove that for $n \geqslant 3$, $\frac{1}{6}\left(n^{2}-4n\right) \leq f(n) \leq \frac{1}{6}\left(n^{2}-n\right)$.
|
\frac{1}{6}\left(n^{2}-4n\right) \leq f(n) \leq \frac{1}{6}\left(n^{2}-n\right)
|
0/8
|
5. Given in isosceles $\triangle A B C$, $A C=B C=\sqrt{5}$, points $D, E, F$ are on sides $A B, B C, C A$ respectively, and $A D=D B=E F=1$. If $\overrightarrow{D E} \cdot \overrightarrow{D F} \leqslant \frac{25}{16}$, then the range of $\overrightarrow{E F} \cdot \overrightarrow{B A}$ is $\qquad$ .
|
\left[ \dfrac{4}{3}, 2 \right]
|
0/8
|
6. Three boys and 20 girls stood in a row. Each child counted the number of girls who were to the left of them, the number of boys who were to the right of them, and added the results. What is the maximum number of different sums that the children could have obtained? (Provide an example of how such a number could be obtained and prove that a greater number of different sums is not possible.)
|
20
|
2/8
|
1B. If for the non-zero real numbers $a, b$ and $c$ the equalities $a^{2}+a=b^{2}, b^{2}+b=c^{2}$ and $c^{2}+c=a^{2}$ hold, determine the value of the expression $(a-b)(b-c)(c-a)$.
|
1
|
4/8
|
13.287. Two dairy factories together should process an equal amount of a certain number of liters of milk. The second workshop started working on the task $a$ working days later, but processed $m$ liters of milk more daily than the first. After another $5a/9$ working days from the start of the joint work of these workshops, $1/3$ of the entire task remained uncompleted. How many working days were required to complete the task, if the work was completed simultaneously and each workshop processed half of the assigned amount of liters of milk?
|
2a
|
3/8
|
In a tournament, each participant plays a match against each other participant. The winner of a match earns 1 point, the loser 0, and if the match is a draw, both players earn half a point. At the end of the tournament, the participants are ranked according to their score (if multiple participants have the same score, their order is chosen randomly). Each participant won half of their points in their matches against the last ten participants (in the ranking). How many people participated in this tournament?
|
25
|
3/8
|
10. In 2021, the difference between the digits of any two adjacent positions does not exceed 2 (subtracting the smaller number from the larger one). If all four-digit numbers where the difference between the digits of any two adjacent positions does not exceed 2 are arranged in ascending order, then 2021 is the $\qquad$th number in this sequence.
|
84
|
3/8
|
## Task 1 - 240811
At a school, a waste collection campaign is being conducted in grades 5 to 10. During the subsequent evaluation for a competition between the grade levels, the following is observed:
The students of grade 9 collected waste worth $42 \mathrm{M}$; the students of grade 10 collected the same amount. The grade 8 students achieved twice as much as the combined efforts of grades 9 and 10. The students of grade 5 reached $21 \%$ of the total school result; grade 6 contributed $30 \%$ of the total school result, and grade 7 achieved $2 \%$ less of the total school result than grade 6.
What is the total result of the school according to these findings?
|
1200
|
5/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
- People have unique favorite music genres: `rock`, `jazz`, `pop`, `classical`
- Everyone has a favorite smoothie: `dragonfruit`, `watermelon`, `desert`, `cherry`
- People have unique hair colors: `red`, `black`, `brown`, `blonde`
- People have unique favorite book genres: `science fiction`, `fantasy`, `romance`, `mystery`
## Clues:
1. The person who has red hair is not in the third house.
2. There is one house between Eric and the person who likes Cherry smoothies.
3. The person who loves science fiction books is Peter.
4. The person who loves fantasy books is Alice.
5. The Dragonfruit smoothie lover is the person who loves pop music.
6. The Dragonfruit smoothie lover is the person who has red hair.
7. The Watermelon smoothie lover is somewhere to the right of the person who loves classical music.
8. The person who has black hair is the person who likes Cherry smoothies.
9. There is one house between the person who loves pop music and the person who loves fantasy books.
10. The person who loves romance books is somewhere to the right of the person who loves jazz music.
11. The person who has red hair is directly left of the person who has black hair.
12. The person who has brown hair and the Dragonfruit smoothie lover are next to each other.
13. The person who loves science fiction books is the Dragonfruit smoothie lover.
What is the value of attribute HairColor for the person whose attribute MusicGenre is pop? Please reason step by step, and put your final answer within \boxed{}
|
red
|
2/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Peter`, `Eric`
- People have unique favorite sports: `soccer`, `tennis`, `basketball`
- Each person has a unique birthday month: `april`, `sept`, `jan`
- Each person prefers a unique type of vacation: `city`, `beach`, `mountain`
- People have unique heights: `average`, `short`, `very short`
- They all have a unique favorite flower: `lilies`, `carnations`, `daffodils`
## Clues:
1. The person who is very short is the person who prefers city breaks.
2. The person whose birthday is in January is Peter.
3. The person whose birthday is in January is directly left of the person who loves a carnations arrangement.
4. The person who loves beach vacations is somewhere to the right of the person who loves a bouquet of daffodils.
5. Eric is the person who loves basketball.
6. The person who is short is the person whose birthday is in April.
7. The person who enjoys mountain retreats is the person who loves a carnations arrangement.
8. Eric is the person who is short.
9. The person who loves tennis is the person who loves a carnations arrangement.
What is the value of attribute Height for the person whose attribute Birthday is jan? Please reason step by step, and put your final answer within \boxed{}
|
very short
|
1/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Bob`, `Peter`
- Everyone has a favorite smoothie: `watermelon`, `cherry`, `dragonfruit`, `lime`, `desert`
- People have unique favorite music genres: `hip hop`, `classical`, `rock`, `pop`, `jazz`
- Everyone has something unique for lunch: `grilled cheese`, `pizza`, `spaghetti`, `stir fry`, `stew`
- Each person has a unique favorite drink: `tea`, `root beer`, `milk`, `water`, `coffee`
## Clues:
1. The coffee drinker is not in the first house.
2. The person who loves jazz music is the Desert smoothie lover.
3. The Watermelon smoothie lover is in the fourth house.
4. The coffee drinker is directly left of Peter.
5. The one who only drinks water is the person who loves hip-hop music.
6. The Dragonfruit smoothie lover is directly left of the one who only drinks water.
7. The Desert smoothie lover is in the fifth house.
8. The person who loves stir fry is somewhere to the right of Bob.
9. The person who is a pizza lover is the person who likes Cherry smoothies.
10. The person who loves classical music is the person who loves the stew.
11. The one who only drinks water is Bob.
12. The root beer lover is the Dragonfruit smoothie lover.
13. There is one house between Arnold and the person who likes Cherry smoothies.
14. The person who loves the spaghetti eater is in the fifth house.
15. The person who likes milk is in the fifth house.
16. The person who likes Cherry smoothies is Bob.
17. The Dragonfruit smoothie lover is the person who loves the stew.
18. Eric and Peter are next to each other.
19. The person who loves rock music is not in the first house.
What is the value of attribute House for the person whose attribute Food is stew? Please reason step by step, and put your final answer within \boxed{}
|
2
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Bob`, `Peter`, `Alice`
- Everyone has something unique for lunch: `spaghetti`, `stew`, `grilled cheese`, `stir fry`, `pizza`
- Each person has a favorite color: `red`, `green`, `white`, `blue`, `yellow`
## Clues:
1. The person who loves blue is somewhere to the left of the person who is a pizza lover.
2. Bob is somewhere to the left of the person who loves white.
3. Alice is directly left of the person who loves the stew.
4. The person who loves stir fry is in the fourth house.
5. The person who loves white is Peter.
6. The person who loves the spaghetti eater is Bob.
7. The person whose favorite color is green is Alice.
8. The person who loves blue is in the third house.
9. The person who loves yellow is somewhere to the right of the person who loves stir fry.
10. Alice is in the first house.
11. The person who loves yellow is Arnold.
What is the value of attribute Color for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}
|
white
|
1/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Bob`, `Carol`, `Peter`, `Eric`, `Alice`
- People have unique favorite music genres: `classical`, `hip hop`, `jazz`, `pop`, `rock`, `country`
- Everyone has something unique for lunch: `soup`, `stir fry`, `grilled cheese`, `spaghetti`, `stew`, `pizza`
- Each person lives in a unique style of house: `craftsman`, `ranch`, `mediterranean`, `modern`, `colonial`, `victorian`
- Each person has a unique birthday month: `feb`, `sept`, `april`, `may`, `jan`, `mar`
- People have unique hair colors: `red`, `black`, `blonde`, `brown`, `gray`, `auburn`
## Clues:
1. The person whose birthday is in April is Bob.
2. The person residing in a Victorian house is the person who loves stir fry.
3. There are two houses between the person who loves jazz music and the person who has auburn hair.
4. The person who loves the stew is in the second house.
5. The person who loves stir fry is the person whose birthday is in February.
6. The person who loves classical music is in the fifth house.
7. The person who loves jazz music is Alice.
8. The person living in a colonial-style house is in the fifth house.
9. The person who has gray hair is the person who loves the stew.
10. The person whose birthday is in March is the person who has red hair.
11. The person who loves country music is directly left of the person whose birthday is in September.
12. The person whose birthday is in May is somewhere to the left of the person who loves country music.
13. The person in a ranch-style home is the person who loves the soup.
14. The person whose birthday is in January is the person who loves the stew.
15. The person who has blonde hair is the person in a Mediterranean-style villa.
16. Arnold is somewhere to the right of the person whose birthday is in April.
17. The person whose birthday is in February is the person who loves hip-hop music.
18. The person who has blonde hair is somewhere to the left of Eric.
19. The person residing in a Victorian house is Carol.
20. The person who has black hair is the person in a ranch-style home.
21. The person in a modern-style house is not in the second house.
22. The person who loves the spaghetti eater is somewhere to the left of the person who loves country music.
23. The person who is a pizza lover is Bob.
24. The person who loves pop music is somewhere to the left of the person whose birthday is in September.
What is the value of attribute Food for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{}
|
stir fry
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Eric`, `Peter`, `Bob`, `Arnold`
- The mothers' names in different houses are unique: `Penny`, `Holly`, `Janelle`, `Aniya`, `Kailyn`
- Each mother is accompanied by their child: `Samantha`, `Fred`, `Timothy`, `Meredith`, `Bella`
- People have unique favorite book genres: `mystery`, `fantasy`, `biography`, `science fiction`, `romance`
## Clues:
1. The person who loves mystery books is somewhere to the left of the person who is the mother of Timothy.
2. The person whose mother's name is Janelle is in the third house.
3. The person who loves science fiction books is directly left of the person's child is named Bella.
4. Arnold is somewhere to the right of the person's child is named Meredith.
5. The person's child is named Fred is Peter.
6. Alice is directly left of Eric.
7. The person whose mother's name is Aniya is in the second house.
8. The person's child is named Fred is not in the fifth house.
9. The person who loves romance books is Alice.
10. The person whose mother's name is Janelle is directly left of the person who is the mother of Timothy.
11. The person whose mother's name is Aniya is somewhere to the left of The person whose mother's name is Kailyn.
12. The person who loves science fiction books is Bob.
13. The person whose mother's name is Janelle is somewhere to the left of the person who loves fantasy books.
14. The person who loves fantasy books is somewhere to the left of The person whose mother's name is Penny.
What is the value of attribute House for the person whose attribute Children is Bella? Please reason step by step, and put your final answer within \boxed{}
|
3
|
0/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Eric`, `Alice`, `Arnold`
- Each person has a unique level of education: `bachelor`, `high school`, `associate`, `master`
- People have unique favorite music genres: `jazz`, `rock`, `pop`, `classical`
- Each person has a favorite color: `green`, `red`, `yellow`, `white`
- They all have a unique favorite flower: `lilies`, `carnations`, `daffodils`, `roses`
## Clues:
1. The person with a bachelor's degree is the person who loves a bouquet of daffodils.
2. The person who loves a carnations arrangement is not in the first house.
3. The person with a master's degree is Alice.
4. The person with a master's degree is directly left of the person who loves classical music.
5. Eric is not in the second house.
6. Arnold is not in the third house.
7. The person who loves yellow is directly left of the person who loves the rose bouquet.
8. The person who loves pop music is in the second house.
9. The person with an associate's degree is not in the fourth house.
10. The person who loves a carnations arrangement is not in the fourth house.
11. The person whose favorite color is red is directly left of the person who loves white.
12. The person whose favorite color is red is the person who loves rock music.
13. Arnold is the person who loves yellow.
14. The person who loves a bouquet of daffodils is the person who loves yellow.
What is the value of attribute MusicGenre for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}
|
jazz
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Arnold`, `Eric`, `Peter`, `Carol`, `Alice`
- Each person has a unique hobby: `cooking`, `woodworking`, `gardening`, `knitting`, `photography`, `painting`
## Clues:
1. Alice is directly left of Bob.
2. The photography enthusiast is not in the fourth house.
3. The person who paints as a hobby and the woodworking hobbyist are next to each other.
4. The person who loves cooking is somewhere to the left of the person who enjoys knitting.
5. The woodworking hobbyist is not in the fourth house.
6. Arnold is in the fifth house.
7. There are two houses between Peter and the person who enjoys knitting.
8. The person who loves cooking is in the third house.
9. Bob is not in the third house.
10. There is one house between the woodworking hobbyist and Carol.
What is the value of attribute House for the person whose attribute Hobby is gardening? Please reason step by step, and put your final answer within \boxed{}
|
4
|
2/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Arnold`, `Peter`, `Alice`, `Eric`
- Each person has a unique favorite drink: `milk`, `root beer`, `coffee`, `water`, `tea`
- Each person has a unique type of pet: `dog`, `bird`, `hamster`, `cat`, `fish`
- Each mother is accompanied by their child: `Timothy`, `Meredith`, `Fred`, `Bella`, `Samantha`
- The mothers' names in different houses are unique: `Kailyn`, `Penny`, `Aniya`, `Janelle`, `Holly`
- People have unique favorite sports: `tennis`, `soccer`, `swimming`, `baseball`, `basketball`
## Clues:
1. The tea drinker is the person who loves tennis.
2. The person whose mother's name is Aniya is Arnold.
3. The person whose mother's name is Janelle is somewhere to the right of the person who loves swimming.
4. The person whose mother's name is Janelle is the person's child is named Bella.
5. The person's child is named Samantha is the person who likes milk.
6. The coffee drinker is not in the fifth house.
7. Bob is the person's child is named Bella.
8. The person who loves swimming and the person who loves basketball are next to each other.
9. The person who is the mother of Timothy is somewhere to the left of the person who owns a dog.
10. The person whose mother's name is Kailyn is in the fifth house.
11. The root beer lover is Alice.
12. The person whose mother's name is Holly is directly left of the root beer lover.
13. The person who likes milk is not in the second house.
14. There is one house between the person who has a cat and the person who loves baseball.
15. The person whose mother's name is Penny is somewhere to the right of the person who loves tennis.
16. The person's child is named Fred is the person who keeps a pet bird.
17. The person who likes milk is directly left of the person with a pet hamster.
18. The person who keeps a pet bird is Alice.
19. There are two houses between Eric and The person whose mother's name is Aniya.
What is the value of attribute Mother for the person whose attribute FavoriteSport is basketball? Please reason step by step, and put your final answer within \boxed{}
|
Janelle
|
0/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Peter`
- Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`
- Each person has a unique favorite drink: `tea`, `water`, `milk`
- People have unique favorite sports: `tennis`, `soccer`, `basketball`
- The people are of nationalities: `dane`, `swede`, `brit`
- Each person has a unique type of pet: `fish`, `dog`, `cat`
## Clues:
1. The one who only drinks water is the person partial to Pall Mall.
2. Peter is the Dane.
3. The one who only drinks water is the person who loves soccer.
4. The person who smokes Blue Master is Arnold.
5. The Dane is the person with an aquarium of fish.
6. The Swedish person is the person who loves basketball.
7. The person who owns a dog is not in the first house.
8. The person with an aquarium of fish is not in the second house.
9. The Dane is not in the first house.
10. The tea drinker is in the third house.
11. The person who likes milk is in the first house.
What is the value of attribute Nationality for the person whose attribute Drink is milk? Please reason step by step, and put your final answer within \boxed{}
|
swede
|
1/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Peter`, `Eric`, `Bob`, `Alice`, `Arnold`
- Each person prefers a unique type of vacation: `cruise`, `mountain`, `city`, `camping`, `cultural`, `beach`
- Each person has a unique hobby: `knitting`, `photography`, `cooking`, `painting`, `gardening`, `woodworking`
- Everyone has something unique for lunch: `stew`, `pizza`, `spaghetti`, `grilled cheese`, `stir fry`, `soup`
- People own unique car models: `chevrolet silverado`, `honda civic`, `toyota camry`, `ford f150`, `tesla model 3`, `bmw 3 series`
- They all have a unique favorite flower: `tulips`, `daffodils`, `carnations`, `lilies`, `iris`, `roses`
## Clues:
1. Arnold is the person who enjoys camping trips.
2. The photography enthusiast is the person who loves the soup.
3. Carol is the person who loves eating grilled cheese.
4. The person who owns a Honda Civic is the person who loves a carnations arrangement.
5. The person who loves beach vacations is not in the first house.
6. The person who enjoys gardening is the person who owns a Toyota Camry.
7. There is one house between the person who loves the boquet of iris and the person who loves the vase of tulips.
8. The person who prefers city breaks is the person who loves the stew.
9. The person who loves a bouquet of daffodils is Carol.
10. The person who prefers city breaks is Eric.
11. Carol is the person who loves cooking.
12. Eric is directly left of the photography enthusiast.
13. The person who loves the rose bouquet is Bob.
14. There is one house between Arnold and the person who likes going on cruises.
15. The person who owns a Tesla Model 3 and the person who enjoys mountain retreats are next to each other.
16. The person who loves the rose bouquet is the person who owns a Toyota Camry.
17. The person who owns a BMW 3 Series is somewhere to the right of the person who loves cooking.
18. The woodworking hobbyist is not in the third house.
19. The person who owns a Ford F-150 is the person who enjoys mountain retreats.
20. The person who is a pizza lover is not in the second house.
21. The person who loves the vase of tulips is not in the fourth house.
22. The person who loves the spaghetti eater is somewhere to the left of the person who enjoys knitting.
23. Peter is somewhere to the right of the photography enthusiast.
24. The person who owns a Honda Civic is the person who is a pizza lover.
25. The person who loves cooking is in the fifth house.
26. The person who likes going on cruises is the person who enjoys knitting.
What is the value of attribute Hobby for the person whose attribute Vacation is city? Please reason step by step, and put your final answer within \boxed{}
|
painting
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Arnold`, `Carol`, `Peter`, `Eric`, `Bob`
- Each person has a unique type of pet: `cat`, `bird`, `fish`, `dog`, `hamster`, `rabbit`
- People have unique heights: `super tall`, `average`, `tall`, `very short`, `very tall`, `short`
- People have unique favorite sports: `baseball`, `tennis`, `soccer`, `swimming`, `basketball`, `volleyball`
## Clues:
1. There is one house between the person who has an average height and the person who is short.
2. The person with an aquarium of fish is in the fifth house.
3. The person who has a cat is the person who is tall.
4. The person who is very tall is the person who loves soccer.
5. Peter is in the first house.
6. The person who loves tennis is in the sixth house.
7. Carol is somewhere to the right of the person who is very tall.
8. The person who loves volleyball is directly left of the person who loves soccer.
9. The person who loves baseball is directly left of the person who is super tall.
10. Carol and Bob are next to each other.
11. The person who is super tall is not in the sixth house.
12. The person who is short is not in the fourth house.
13. There is one house between the person who loves swimming and Bob.
14. The person who loves basketball is somewhere to the left of the person who owns a dog.
15. The person who owns a rabbit is somewhere to the left of the person who is short.
16. The person who keeps a pet bird is the person who is short.
17. Arnold is not in the second house.
18. Bob is directly left of Eric.
19. The person who owns a rabbit and the person who is very tall are next to each other.
What is the value of attribute FavoriteSport for the person whose attribute Pet is dog? Please reason step by step, and put your final answer within \boxed{}
|
tennis
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Bob`, `Arnold`, `Alice`, `Peter`, `Eric`
- The people are of nationalities: `swede`, `german`, `dane`, `brit`, `chinese`, `norwegian`
- Each person has a unique type of pet: `bird`, `cat`, `dog`, `rabbit`, `fish`, `hamster`
- Each person has a favorite color: `red`, `green`, `purple`, `yellow`, `white`, `blue`
## Clues:
1. The person who has a cat is the British person.
2. The person with a pet hamster is in the fourth house.
3. The person who owns a rabbit is the person who loves purple.
4. Arnold is the person who loves white.
5. The Dane is somewhere to the left of the person who owns a dog.
6. Carol and Peter are next to each other.
7. The Swedish person is somewhere to the right of the person whose favorite color is green.
8. The person who loves blue is the person with a pet hamster.
9. There are two houses between the person whose favorite color is red and Bob.
10. The person who keeps a pet bird is in the second house.
11. Carol is in the first house.
12. The person who loves yellow and the German are next to each other.
13. Alice is the person who loves yellow.
14. The Dane is the person who loves yellow.
15. Bob is the Norwegian.
16. Alice is directly left of the person who loves white.
What is the value of attribute Nationality for the person whose attribute Pet is rabbit? Please reason step by step, and put your final answer within \boxed{}
|
swede
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Bob`, `Peter`
- Each person prefers a unique type of vacation: `mountain`, `city`, `cruise`, `beach`, `camping`
- Each person has a unique level of education: `doctorate`, `high school`, `bachelor`, `associate`, `master`
- Each person has a favorite color: `blue`, `red`, `white`, `yellow`, `green`
- People use unique phone models: `google pixel 6`, `iphone 13`, `oneplus 9`, `huawei p50`, `samsung galaxy s21`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `stew`
## Clues:
1. The person who loves the stew is not in the first house.
2. There are two houses between the person who loves stir fry and the person with an associate's degree.
3. The person who enjoys mountain retreats is the person with a bachelor's degree.
4. The person with a doctorate is somewhere to the right of Bob.
5. The person who uses a Samsung Galaxy S21 is in the third house.
6. Eric is the person with a doctorate.
7. The person with a doctorate is in the third house.
8. The person who loves stir fry is the person with a bachelor's degree.
9. The person with a doctorate is the person who is a pizza lover.
10. The person whose favorite color is green is somewhere to the right of Peter.
11. The person who enjoys camping trips is the person who uses an iPhone 13.
12. The person who likes going on cruises is Alice.
13. There is one house between the person with a high school diploma and the person who uses a Samsung Galaxy S21.
14. The person who uses a Google Pixel 6 is Arnold.
15. The person who uses a OnePlus 9 is somewhere to the right of the person who uses a Huawei P50.
16. Arnold is the person who loves eating grilled cheese.
17. The person who loves eating grilled cheese is not in the fourth house.
18. There are two houses between the person with a bachelor's degree and the person whose favorite color is red.
19. The person who loves beach vacations is somewhere to the right of the person who prefers city breaks.
20. The person whose favorite color is green is not in the second house.
21. The person who loves blue is somewhere to the right of Peter.
22. There is one house between the person who enjoys camping trips and the person who loves yellow.
What is the value of attribute PhoneModel for the person whose attribute Food is spaghetti? Please reason step by step, and put your final answer within \boxed{}
|
iphone 13
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Peter`, `Eric`, `Arnold`, `Alice`
- Each person has a favorite color: `blue`, `red`, `green`, `yellow`, `white`
- Everyone has a unique favorite cigar: `dunhill`, `prince`, `pall mall`, `blends`, `blue master`
- People have unique hair colors: `blonde`, `brown`, `red`, `gray`, `black`
- Each person has a unique favorite drink: `tea`, `milk`, `coffee`, `water`, `root beer`
- The people are of nationalities: `dane`, `swede`, `german`, `brit`, `norwegian`
## Clues:
1. The Norwegian is directly left of the Prince smoker.
2. The person who loves yellow is somewhere to the right of the tea drinker.
3. The person who has blonde hair is the Norwegian.
4. The root beer lover is somewhere to the left of the Dane.
5. There is one house between the person whose favorite color is red and the person who has black hair.
6. The German is in the third house.
7. The person who loves blue is not in the fourth house.
8. The person whose favorite color is red and the Dunhill smoker are next to each other.
9. The root beer lover is directly left of the German.
10. The Norwegian is Eric.
11. The British person is the person who likes milk.
12. Peter is the person who smokes many unique blends.
13. The coffee drinker is directly left of the Swedish person.
14. The person who smokes Blue Master is somewhere to the left of the person who smokes many unique blends.
15. The person who has gray hair is directly left of the person who has red hair.
16. The person who loves blue is somewhere to the right of the one who only drinks water.
17. Arnold is the person who has brown hair.
18. The person who has gray hair is not in the third house.
19. The coffee drinker is the person whose favorite color is green.
20. The Dunhill smoker is Alice.
What is the value of attribute Drink for the person whose attribute Nationality is german? Please reason step by step, and put your final answer within \boxed{}
|
tea
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Carol`, `Peter`, `Eric`, `Bob`, `Alice`
- Each person lives in a unique style of house: `ranch`, `colonial`, `modern`, `craftsman`, `mediterranean`, `victorian`
- Everyone has something unique for lunch: `pizza`, `stew`, `spaghetti`, `grilled cheese`, `stir fry`, `soup`
- Each person prefers a unique type of vacation: `cultural`, `cruise`, `mountain`, `camping`, `city`, `beach`
- People have unique heights: `average`, `very tall`, `very short`, `short`, `tall`, `super tall`
- Everyone has a unique favorite cigar: `yellow monster`, `prince`, `dunhill`, `pall mall`, `blue master`, `blends`
## Clues:
1. Alice is in the fifth house.
2. The person who loves stir fry is the person living in a colonial-style house.
3. Alice is the person who loves the spaghetti eater.
4. Arnold is the person who loves the stew.
5. There is one house between the person who has an average height and Peter.
6. The person in a Craftsman-style house is not in the third house.
7. The person who has an average height is the person who loves stir fry.
8. The person who loves beach vacations is the person in a ranch-style home.
9. Eric is in the fourth house.
10. There is one house between the person living in a colonial-style house and the person who enjoys camping trips.
11. The person who enjoys mountain retreats is the person who smokes Yellow Monster.
12. The person who enjoys mountain retreats is the person who is very tall.
13. The person who enjoys mountain retreats and the Dunhill smoker are next to each other.
14. The person who loves the spaghetti eater is the person residing in a Victorian house.
15. The person who is tall is the person who loves beach vacations.
16. The person who is tall is somewhere to the left of the person residing in a Victorian house.
17. The person who loves stir fry is directly left of Bob.
18. The person in a modern-style house is somewhere to the left of Alice.
19. The person in a Craftsman-style house is somewhere to the left of the person who is short.
20. The person who loves stir fry is somewhere to the left of the Prince smoker.
21. There are two houses between the person who loves eating grilled cheese and the person who is super tall.
22. The person in a ranch-style home is the person who smokes Blue Master.
23. The person who smokes many unique blends is directly left of the person who smokes Blue Master.
24. The person who goes on cultural tours is the person who is a pizza lover.
25. The person who is a pizza lover is somewhere to the left of the person who likes going on cruises.
What is the value of attribute HouseStyle for the person whose attribute Cigar is dunhill? Please reason step by step, and put your final answer within \boxed{}
|
mediterranean
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Peter`, `Eric`, `Arnold`, `Alice`
- The people keep unique animals: `dog`, `fish`, `bird`, `horse`, `cat`
- The people are of nationalities: `dane`, `swede`, `brit`, `german`, `norwegian`
- Each mother is accompanied by their child: `Meredith`, `Bella`, `Timothy`, `Samantha`, `Fred`
- Each person has a unique type of pet: `bird`, `fish`, `hamster`, `cat`, `dog`
## Clues:
1. The dog owner is not in the third house.
2. The person who keeps a pet bird is in the fourth house.
3. The German is Eric.
4. Bob is somewhere to the left of the person's child is named Fred.
5. The person with a pet hamster is Arnold.
6. The British person is the dog owner.
7. The person's child is named Meredith is not in the third house.
8. The fish enthusiast is the person's child is named Samantha.
9. The person who is the mother of Timothy is the German.
10. The person who has a cat is in the fifth house.
11. Peter is not in the fourth house.
12. The Swedish person and the person's child is named Samantha are next to each other.
13. The Swedish person is Peter.
14. The Dane is in the second house.
15. Eric and the cat lover are next to each other.
16. The German is in the first house.
17. The person with an aquarium of fish is somewhere to the right of the bird keeper.
What is the value of attribute House for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
1
|
1/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Alice`, `Arnold`, `Bob`, `Carol`
- Each person has a unique hobby: `cooking`, `knitting`, `painting`, `gardening`, `woodworking`, `photography`
- Everyone has a favorite smoothie: `lime`, `cherry`, `desert`, `blueberry`, `watermelon`, `dragonfruit`
- The people are of nationalities: `chinese`, `dane`, `german`, `norwegian`, `swede`, `brit`
- People have unique favorite music genres: `hip hop`, `country`, `rock`, `jazz`, `classical`, `pop`
## Clues:
1. The person who loves rock music is Bob.
2. The person who enjoys knitting is the German.
3. The woodworking hobbyist is in the sixth house.
4. The person who loves rock music is directly left of the woodworking hobbyist.
5. There is one house between the Watermelon smoothie lover and the person who loves hip-hop music.
6. The Chinese is the Watermelon smoothie lover.
7. The Desert smoothie lover is the Norwegian.
8. The person who drinks Blueberry smoothies is not in the sixth house.
9. The person who loves pop music is somewhere to the left of the person who enjoys gardening.
10. Carol is somewhere to the left of the Swedish person.
11. Peter is somewhere to the right of the person who loves pop music.
12. The Norwegian is somewhere to the right of the Dragonfruit smoothie lover.
13. The German is the person who loves country music.
14. The person who paints as a hobby is directly left of the person who loves hip-hop music.
15. The Dane is Arnold.
16. The person who loves jazz music is the Chinese.
17. The British person is not in the third house.
18. The Swedish person is the person who loves pop music.
19. The person who drinks Lime smoothies is the photography enthusiast.
20. The person who loves hip-hop music is directly left of Alice.
21. The Dane is the woodworking hobbyist.
What is the value of attribute House for the person whose attribute Nationality is chinese? Please reason step by step, and put your final answer within \boxed{}
|
1
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Carol`, `Peter`, `Eric`, `Bob`, `Alice`
- Each person lives in a unique style of house: `ranch`, `colonial`, `modern`, `craftsman`, `mediterranean`, `victorian`
- Everyone has something unique for lunch: `pizza`, `stew`, `spaghetti`, `grilled cheese`, `stir fry`, `soup`
- Each person prefers a unique type of vacation: `cultural`, `cruise`, `mountain`, `camping`, `city`, `beach`
- People have unique heights: `average`, `very tall`, `very short`, `short`, `tall`, `super tall`
- Everyone has a unique favorite cigar: `yellow monster`, `prince`, `dunhill`, `pall mall`, `blue master`, `blends`
## Clues:
1. Alice is in the fifth house.
2. The person who loves stir fry is the person living in a colonial-style house.
3. Alice is the person who loves the spaghetti eater.
4. Arnold is the person who loves the stew.
5. There is one house between the person who has an average height and Peter.
6. The person in a Craftsman-style house is not in the third house.
7. The person who has an average height is the person who loves stir fry.
8. The person who loves beach vacations is the person in a ranch-style home.
9. Eric is in the fourth house.
10. There is one house between the person living in a colonial-style house and the person who enjoys camping trips.
11. The person who enjoys mountain retreats is the person who smokes Yellow Monster.
12. The person who enjoys mountain retreats is the person who is very tall.
13. The person who enjoys mountain retreats and the Dunhill smoker are next to each other.
14. The person who loves the spaghetti eater is the person residing in a Victorian house.
15. The person who is tall is the person who loves beach vacations.
16. The person who is tall is somewhere to the left of the person residing in a Victorian house.
17. The person who loves stir fry is directly left of Bob.
18. The person in a modern-style house is somewhere to the left of Alice.
19. The person in a Craftsman-style house is somewhere to the left of the person who is short.
20. The person who loves stir fry is somewhere to the left of the Prince smoker.
21. There are two houses between the person who loves eating grilled cheese and the person who is super tall.
22. The person in a ranch-style home is the person who smokes Blue Master.
23. The person who smokes many unique blends is directly left of the person who smokes Blue Master.
24. The person who goes on cultural tours is the person who is a pizza lover.
25. The person who is a pizza lover is somewhere to the left of the person who likes going on cruises.
What is the value of attribute Height for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
tall
|
0/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Arnold`, `Peter`
- Each person has a unique favorite drink: `milk`, `water`, `coffee`, `tea`
- They all have a unique favorite flower: `lilies`, `roses`, `daffodils`, `carnations`
- People have unique favorite sports: `tennis`, `basketball`, `soccer`, `swimming`
- Each person has an occupation: `doctor`, `teacher`, `artist`, `engineer`
- Each mother is accompanied by their child: `Fred`, `Samantha`, `Bella`, `Meredith`
## Clues:
1. The person who loves basketball is somewhere to the left of the person who is an engineer.
2. Eric is the person who loves a carnations arrangement.
3. The person who loves the rose bouquet is somewhere to the left of Peter.
4. The person who is a doctor is the person who loves tennis.
5. The person's child is named Bella is directly left of the person's child is named Samantha.
6. The person who is an artist is not in the third house.
7. The person who loves the rose bouquet is in the second house.
8. The person who loves a bouquet of daffodils and the person who loves tennis are next to each other.
9. The person who loves a bouquet of daffodils is the person who is a teacher.
10. The person who loves the rose bouquet is the person who likes milk.
11. The person's child is named Samantha is Alice.
12. The person who loves tennis is directly left of the one who only drinks water.
13. The person who loves a carnations arrangement is in the fourth house.
14. Arnold is somewhere to the left of the person who is an artist.
15. The person's child is named Fred is not in the fourth house.
16. The coffee drinker is the person who loves swimming.
What is the value of attribute FavoriteSport for the person whose attribute Drink is coffee? Please reason step by step, and put your final answer within \boxed{}
|
swimming
|
0/8
|
Determine all rational numbers $a$ for which the matrix
$$
\left(\begin{array}{cccc}
a & -a & -1 & 0 \\
a & -a & 0 & -1 \\
1 & 0 & a & -a \\
0 & 1 & a & -a
\end{array}\right)
$$
is the square of a matrix with all rational entries. Provide the integer value of $a$ that satisfies the condition.
|
0
|
2/8
|
For $R>1$ let $\mathcal{D}_{R}=\left\{(a, b) \in \mathbb{Z}^{2}: 0<a^{2}+b^{2}<R\right\}$. Compute
$$
\lim _{R \rightarrow \infty} \sum_{(a, b) \in \mathcal{D}_{R}} \frac{(-1)^{a+b}}{a^{2}+b^{2}}
$$
The original answer is in the format $m\pi \log n$. Please provide the integer value of m and n.
|
1
|
1/8
|
Let $p$ be a prime number and let $k$ be a positive integer. Suppose that the numbers $a_{i}=i^{k}+i$ for $i=0,1, \\ldots, p-1$ form a complete residue system modulo $p$. What is the set of possible remainders of $a_{2}$ upon division by $p$? Please provide the sum of all possible remainders.
|
5
|
1/8
|
We throw a dice (which selects one of the numbers $1,2, \ldots, 6$ with equal probability) $n$ times. What is the probability that the sum of the values is divisible by 5? What is the value of the probability when n = 1/6?
|
0
|
0/8
|
Five unit squares are arranged in the coordinate plane as shown, with the lower left corner at the origin. The slanted line, extending from $(c,0)$ to $(3,3)$, divides the entire region into two regions of equal area. The original answer is in $\frac{k}{m}$ format, where $\frac{k}{m}$ is in simplest form. Please find the value of $k + m$.
|
5
|
0/8
|
Points \(A\) and \(C\) lie on a circle centered at \(O\), each of \(\overline{BA}\) and \(\overline{BC}\) are tangent to the circle, and \(\triangle ABC\) is equilateral. The circle intersects \(\overline{BO}\) at \(D\). The original answer is in the form \(\frac{k}{m}\). Please find the value of \(k + m\).
|
3
|
4/8
|
Trapezoid \(ABCD\) has \(AD \parallel BC\), \(BD = 1\), \(\angle DBA = 23^\circ\), and \(\angle BDC = 46^\circ\). The ratio \(BC: AD\) is \(9: 5\). What is the value of \(CD\)? The original answer is in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is a fully simplified fraction. Please provide the value of \(k + m\).
|
9
|
0/8
|
Find all values of $b$ for which the equations $1988x^2 + bx + 8891 = 0$ and $8891x^2 + bx + 1988 = 0$ have a common root.
Enter all the possible values of $b,$ separated by commas.
|
10879
|
1/8
|
Three circles $C_i$ are given in the plane: $C_1$ has diameter $AB$ of length $1$; $C_2$ is concentric and has diameter $k$ ($1 < k < 3$); $C_3$ has center $A$ and diameter $2k$. We regard $k$ as fixed. Consider all straight line segments $XY$ which have one endpoint $X$ on $C_2$, one endpoint $Y$ on $C_3$, and contain the point $B$. For what ratio $\frac{XB}{BY}$ will the segment $XY$ have minimal length?
|
1
|
3/8
|
There are $128$ numbered seats arranged around a circle in a palaestra. The first person to enter the place would sit on seat number $1$. Since a contagious disease is infecting the people of the city, each person who enters the palaestra would sit on a seat whose distance is the longest to the nearest occupied seat. If there are several such seats, the newly entered person would sit on the seat with the smallest number. What is the number of the seat on which the $39$th person sits?
|
27
|
0/8
|
Let $r$ be a nonzero real number. The values of $z$ which satisfy the equation
\[ r^4z^4 + (10r^6-2r^2)z^2-16r^5z+(9r^8+10r^4+1) = 0 \]
are plotted on the complex plane (i.e., using the real part of each root as the x-coordinate and the imaginary part as the y-coordinate). Show that the area of the convex quadrilateral with these points as vertices is independent of $r$, and find this area.
|
8
|
3/8
|
For each positive integer $n$, let $S_n$ denote the set of positive integers $k$ such that $n^k - 1$ is divisible by $2006$. Define the function $P(n)$ by the rule:
$$P(n) = \begin{cases} \min(s)_{s \in S_n} & \text{if } S_n \neq \emptyset, \\ 0 & \text{otherwise}. \end{cases}$$
Let $d$ be the least upper bound of $\{P(1), P(2), P(3), \ldots\}$, and let $m$ be the number of integers $i$ such that $1 \leq i \leq 2006$ and $P(i) = d$. Compute the value of $d + m$.
|
912
|
5/8
|
Alfred and Bonnie play a game where they take turns tossing a fair coin. The winner of the game is the first person to obtain a head. Alfred and Bonnie play this game multiple times with the rule that the loser of a game goes first in the next game. Suppose Alfred goes first in the first game, and the probability that he wins the sixth game is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What are the last three digits of $m + n$?
|
93
|
3/8
|
While there do not exist pairwise distinct real numbers $a,b,c$ satisfying $a^2+b^2+c^2 = ab+bc+ca$, there do exist complex numbers with that property. Let $a,b,c$ be complex numbers such that $a^2+b^2+c^2 = ab+bc+ca$ and $|a+b+c| = 21$. Given that $|a-b| = 2\sqrt{3}$, $|a| = 3\sqrt{3}$, compute $|b|^2+|c|^2$.
|
132
|
2/8
|
Wu starts with exactly one coin. Each year, Wu flips every coin he has at once. For each heads he flips, Wu receives a coin, and for each tails he flips, Wu loses a coin. He continues this process each year until he has $0$ coins, at which point he stops. The probability that Wu will stop after exactly five years can be expressed as $\frac{a}{2^b}$, where $a$ and $b$ are positive integers with $a$ being odd. Find $a+b$.
|
71622400
|
0/8
|
An acute triangle $ABC$ has side lengths $a$, $b$, $c$ such that $a$, $b$, $c$ form an arithmetic sequence. Given that the area of triangle $ABC$ is an integer, what is the smallest value of its perimeter?
|
42
|
3/8
|
Farmer James invents a new currency such that for every positive integer $n \leq 6$, there exists an $n$-coin worth $n!$ cents. Furthermore, he has exactly $n$ copies of each $n$-coin. An integer $k$ is said to be *nice* if Farmer James can make $k$ cents using at least one copy of each type of coin. How many positive integers less than 2018 are nice?
|
210
|
1/8
|
A board with dimensions $2018 \times 2018$ is divided into unit cells of size $1 \times 1$. In some cells of the board, black chips are placed, and in others, white chips are placed (each cell contains at most one chip).
First, we remove all black chips from columns that contain white chips. Then, we remove all white chips from rows that contain black chips.
Let $W$ be the number of remaining white chips, and $B$ be the number of remaining black chips on the board. Define $A = \min\{W, B\}$. Determine the maximum value of $A$.
|
1018081
|
4/8
|
10. There are two sets of square paper pieces of the same size and the same number, one set black and one set white. Xiao Zhang first uses the white paper pieces to form a rectangle without any gaps in the middle, then uses the black paper pieces to surround the already formed white rectangle to create a larger rectangle, and then continues with white paper pieces. This process is repeated, and after Xiao Zhang has used the black paper pieces 5 times, the black and white paper pieces are exactly used up. Therefore, the black paper pieces are at least $\qquad$ pieces.
|
350
|
0/8
|
Bakayev E.V.
A secret base is surrounded by a transparent winding fence in the shape of a non-convex polygon, with a swamp outside. A straight power line consisting of 36 poles runs through the swamp, some of which are outside the base, and some are inside. (The power line does not pass through the vertices of the fence.) A spy walks around the base along the fence from the outside, keeping the fence always to his right. Each time he reaches the power line, he counts how many poles are to his left (he can see all of them). By the time the spy has walked around the entire fence, he has counted a total of 2015 poles. How many poles are inside the base?
|
1
|
2/8
|
5. There are two methods to increase the concentration of saltwater, one is to evaporate the water, and the other is to add salt. Now, 200 grams of 10% saltwater is divided into two portions. To one portion, 5 grams of salt is added; from the other portion, 5 grams of water is evaporated. As a result, the concentration of the two portions of saltwater is still equal. In the two portions of saltwater initially divided, the smaller portion originally had $\qquad$ grams.
|
25
|
5/8
|
Problem 4. Let $n$ be a non-zero natural number; consider the set $M=\{1,2, \ldots, 2 n+1\}$.
Determine in how many ways the set $M$ can be partitioned into three non-empty subsets $A, B, C$ $(A \cup B \cup C=M, A \cap B=B \cap C=C \cap A=\emptyset)$ such that the following conditions are simultaneously satisfied:
(i) for any $a \in A$ and any $b \in B$, the remainder of the division of $a$ by $b$ belongs to the set $C$;
(ii) for any $c \in C$, there exist $a \in A$ and $b \in B$ such that $c$ is the remainder of the division of $a$ by $b$.
|
n
|
0/8
|
A semicircle with diameter $d$ is contained in a square whose sides have length 8. Given the maximum value of $d$ is $m - \sqrt{n},$ find $m+n.$
Please give the answer directly without any intermediate steps.
|
544
|
3/8
|
Let \( A, B, C, \) and \( D \) be four points on a circle \(\Gamma\) such that chords \([A B]\) and \([C D]\) intersect at a point \(E\) inside \(\Gamma\), and let \(P\) be an arbitrary point on \([B E]\). The tangent \( t \) to the circumcircle of \(D E P\) at \(E\) intersects \((A C)\) at \(F\).
Demonstrate that \(\widehat{E F C} = \widehat{B D P}\).
|
\widehat{EFC} = \widehat{BDP}
|
2/8
|
6. Given real numbers $x, y$ satisfy $x^{2}-x y-2 y^{2}=1$. Then the minimum value of $2 x^{2}+y^{2}$ is $\qquad$ .
|
\dfrac{2(1 + \sqrt{3})}{3}
|
5/8
|
Jack has a large number of tiles, each of which is in the shape of a right-angled triangle with side lengths \(3 \text{ cm}, 4 \text{ cm}\) and \(5 \text{ cm}\). Is it possible for Jack to combine a number of these tiles, without gaps or overlap, to form a rectangle of size \(2016 \text{ cm} \times 2021 \text{ cm}\)?
|
\text{Yes}
|
4/8
|
In triangle \(ABC\), an inscribed circle with radius \(R\) touches side \(AC\) at point \(D\), side \(AB\) at point \(E\), and side \(BC\) at point \(F\). Given that \(AD = R\) and \(DC = a\), find the area of triangle \(BEF\).
|
\dfrac{R^2 (a + R)^3}{2 (a - R) (a^2 + R^2)}
|
0/8
|
Positive integers $a_0<a_1<\dots<a_n$, are to be chosen so that $a_j-a_i$ is not a prime for any $i,j$ with $0 \le i <j \le n$. For each $n \ge 1$, determine the smallest possible value of $a_n$.
|
4n +1
|
1/8
|
Example 6. Let $a=\sqrt{17}, b=\mathrm{i} \sqrt{19}$. Find the maximum value of $\frac{|a-z|}{|b-z|}$, where $z$ is any complex number with modulus 1.
(2015, Harvard-MIT Mathematics Tournament)
|
\dfrac{4}{3}
|
1/8
|
Let \(a, b, c > 0\) and \(ab + bc + ca = 1\). Prove that \(\sqrt{a^3 + a} + \sqrt{b^3 + b} + \sqrt{c^3 + c} \geq 2\sqrt{a + b + c}\).
|
\sqrt{a^3 + a} + \sqrt{b^3 + b} + \sqrt{c^3 + c} \geq 2\sqrt{a + b + c}
|
1/8
|
Task 1. We have 1000 balls in 40 different colors, with exactly 25 balls of each color. Determine the smallest value of $n$ with the following property: if you randomly arrange the 1000 balls in a circle, there will always be $n$ balls next to each other where at least 20 different colors occur.
|
452
|
0/8
|
4. Natural numbers $a$, $b$, and $c$, greater than 2022, are such that $a+b$ is divisible by $c-2022$, $a+c$ is divisible by $b-2022$, and $b+c$ is divisible by $a-2022$. What is the greatest value that the number $a+b+c$ can take? (S. Berlov)
|
171870
|
1/8
|
1. Dima wrote a sequence of zeros and ones in his notebook. Then he noticed that a one follows a zero 16 times, a one follows 01 seven times, and a zero follows 01 eight times. What could be the last two digits on the board? (In your answer, indicate all options and prove that there are no others).
|
01
|
5/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Alice`, `Eric`
- People have unique favorite book genres: `romance`, `mystery`, `fantasy`, `science fiction`
- People have unique heights: `tall`, `very short`, `short`, `average`
- Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `desert`, `watermelon`
- Each person has a favorite color: `red`, `green`, `yellow`, `white`
## Clues:
1. Arnold is not in the fourth house.
2. Peter is the person who loves mystery books.
3. The person who likes Cherry smoothies is somewhere to the right of the Desert smoothie lover.
4. The person who loves science fiction books is directly left of Eric.
5. The Desert smoothie lover is the person who is very short.
6. The person who loves white is the person who loves mystery books.
7. The person who loves fantasy books is the person who loves yellow.
8. The Desert smoothie lover is somewhere to the right of the person who is short.
9. The Dragonfruit smoothie lover and the person whose favorite color is green are next to each other.
10. The Dragonfruit smoothie lover is the person who loves mystery books.
11. The person who loves yellow is in the second house.
12. The person who likes Cherry smoothies is not in the third house.
13. The person who has an average height is the person who likes Cherry smoothies.
What is the value of attribute Height for the person whose attribute Smoothie is watermelon? Please reason step by step, and put your final answer within \boxed{}
|
short
|
0/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Eric`, `Alice`, `Arnold`
- Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`, `Samantha`
- People have unique hair colors: `red`, `brown`, `black`, `blonde`
- They all have a unique favorite flower: `carnations`, `roses`, `daffodils`, `lilies`
- The people keep unique animals: `cat`, `bird`, `fish`, `horse`
## Clues:
1. Alice is somewhere to the right of the person who has red hair.
2. The person who loves a bouquet of daffodils is directly left of Arnold.
3. The fish enthusiast is the person's child is named Samantha.
4. Alice is directly left of the bird keeper.
5. The cat lover is the person who loves the rose bouquet.
6. The person who loves a carnations arrangement is somewhere to the right of the person who has brown hair.
7. The person who loves a bouquet of daffodils is directly left of the bird keeper.
8. Eric is the person's child is named Meredith.
9. There are two houses between the person who has red hair and the person who has black hair.
10. Eric is in the fourth house.
11. The person's child is named Bella is the person who loves a bouquet of daffodils.
What is the value of attribute House for the person whose attribute Children is Meredith? Please reason step by step, and put your final answer within \boxed{}
|
4
|
3/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Peter`, `Alice`, `Carol`, `Bob`
- People have unique favorite book genres: `mystery`, `biography`, `science fiction`, `romance`, `fantasy`, `historical fiction`
- Each person has a unique favorite drink: `water`, `milk`, `boba tea`, `coffee`, `tea`, `root beer`
- People have unique hair colors: `blonde`, `red`, `gray`, `black`, `auburn`, `brown`
- Each person has a unique birthday month: `may`, `mar`, `sept`, `jan`, `april`, `feb`
## Clues:
1. The person who likes milk is the person who has gray hair.
2. Alice is somewhere to the right of the person who has auburn hair.
3. The person whose birthday is in September is not in the sixth house.
4. The tea drinker is somewhere to the left of the person who has auburn hair.
5. Carol is the person who loves biography books.
6. The person who likes milk is in the fourth house.
7. The person who has auburn hair is directly left of Eric.
8. The boba tea drinker is the person who has brown hair.
9. The person whose birthday is in February is the person who has gray hair.
10. Carol is the person who has blonde hair.
11. The person who loves fantasy books is somewhere to the left of Bob.
12. The person who has blonde hair is the person whose birthday is in April.
13. Peter is the coffee drinker.
14. The person who loves historical fiction books is somewhere to the right of the person who loves science fiction books.
15. The person who loves science fiction books is Bob.
16. The root beer lover is not in the first house.
17. There is one house between the person whose birthday is in May and Peter.
18. The person who has black hair is in the second house.
19. The person whose birthday is in February is the person who loves historical fiction books.
20. Arnold is the person whose birthday is in March.
21. The root beer lover is somewhere to the left of the person whose birthday is in May.
22. The person who loves mystery books is in the sixth house.
What is the value of attribute BookGenre for the person whose attribute Birthday is jan? Please reason step by step, and put your final answer within \boxed{}
|
mystery
|
0/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Eric`, `Peter`
- People have unique favorite book genres: `science fiction`, `mystery`, `romance`
- Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`
- People have unique hair colors: `black`, `blonde`, `brown`
- Each person has a unique level of education: `high school`, `associate`, `bachelor`
- They all have a unique favorite flower: `daffodils`, `lilies`, `carnations`
## Clues:
1. The person who loves the boquet of lilies is directly left of the person who loves romance books.
2. Peter is the person with a high school diploma.
3. The person who loves the boquet of lilies is the person who has brown hair.
4. The person's child is named Bella is Arnold.
5. The person who loves science fiction books is the person's child is named Fred.
6. The person's child is named Fred is the person who loves the boquet of lilies.
7. The person who has black hair is the person with an associate's degree.
8. The person's child is named Meredith is not in the first house.
9. The person with a high school diploma is the person who loves a carnations arrangement.
10. Peter is not in the third house.
What is the value of attribute Children for the person whose attribute BookGenre is romance? Please reason step by step, and put your final answer within \boxed{}
|
Meredith
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Alice`, `Peter`, `Bob`
- The people are of nationalities: `german`, `norwegian`, `brit`, `dane`, `swede`
- People have unique favorite sports: `swimming`, `soccer`, `baseball`, `basketball`, `tennis`
- People have unique hair colors: `blonde`, `brown`, `red`, `black`, `gray`
## Clues:
1. Arnold is the person who loves baseball.
2. The Swedish person is somewhere to the left of Arnold.
3. There are two houses between the person who loves basketball and the person who has black hair.
4. The Norwegian is in the fourth house.
5. Peter is the person who has black hair.
6. The person who has red hair is in the second house.
7. Bob is the German.
8. The person who has blonde hair is not in the third house.
9. The person who loves swimming is the person who has red hair.
10. The German is not in the first house.
11. The person who loves basketball is directly left of the Dane.
12. The person who loves soccer is directly left of Arnold.
13. Alice is the person who has gray hair.
What is the value of attribute House for the person whose attribute FavoriteSport is basketball? Please reason step by step, and put your final answer within \boxed{}
|
1
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Carol`, `Eric`, `Peter`, `Bob`, `Arnold`
- People have unique favorite music genres: `classical`, `hip hop`, `jazz`, `pop`, `rock`, `country`
- The mothers' names in different houses are unique: `Sarah`, `Penny`, `Aniya`, `Janelle`, `Kailyn`, `Holly`
- Each mother is accompanied by their child: `Alice`, `Fred`, `Timothy`, `Bella`, `Samantha`, `Meredith`
- People have unique heights: `very short`, `tall`, `short`, `very tall`, `super tall`, `average`
- The people keep unique animals: `bird`, `dog`, `horse`, `rabbit`, `cat`, `fish`
## Clues:
1. The person who loves pop music is the cat lover.
2. The rabbit owner is directly left of The person whose mother's name is Aniya.
3. The person whose mother's name is Holly is directly left of Carol.
4. The person whose mother's name is Holly is the person's child is named Alice.
5. The person whose mother's name is Holly is the person who loves classical music.
6. The person who loves jazz music is The person whose mother's name is Sarah.
7. The person's child is named Meredith is somewhere to the right of The person whose mother's name is Aniya.
8. The person who is super tall is The person whose mother's name is Holly.
9. The person who is the mother of Timothy is Bob.
10. The person who is very short is somewhere to the left of The person whose mother's name is Aniya.
11. Eric is the fish enthusiast.
12. The person's child is named Samantha is somewhere to the right of the person who is very tall.
13. The person who loves rock music is The person whose mother's name is Janelle.
14. There is one house between the person who keeps horses and the person's child is named Meredith.
15. The person's child is named Bella is somewhere to the right of Peter.
16. The fish enthusiast is somewhere to the left of the bird keeper.
17. The fish enthusiast is somewhere to the right of the person's child is named Alice.
18. There is one house between the person's child is named Bella and the person who loves rock music.
19. The person who is short is the cat lover.
20. Alice is directly left of the person who loves classical music.
21. The person's child is named Bella is The person whose mother's name is Aniya.
22. There are two houses between The person whose mother's name is Penny and the person who is short.
23. The person who loves hip-hop music is in the first house.
24. Carol is the person who is tall.
What is the value of attribute House for the person whose attribute Children is Timothy? Please reason step by step, and put your final answer within \boxed{}
|
4
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Eric`, `Carol`, `Bob`, `Arnold`, `Peter`
- People have unique favorite music genres: `hip hop`, `jazz`, `country`, `classical`, `rock`, `pop`
- People use unique phone models: `iphone 13`, `oneplus 9`, `xiaomi mi 11`, `huawei p50`, `samsung galaxy s21`, `google pixel 6`
- People have unique favorite book genres: `biography`, `historical fiction`, `fantasy`, `romance`, `science fiction`, `mystery`
## Clues:
1. Arnold is not in the sixth house.
2. There are two houses between the person who loves country music and the person who loves hip-hop music.
3. The person who loves romance books is Carol.
4. The person who loves biography books is somewhere to the left of the person who loves rock music.
5. The person who loves mystery books is somewhere to the right of Peter.
6. The person who loves romance books is the person who loves classical music.
7. The person who loves mystery books is directly left of the person who loves fantasy books.
8. Bob is the person who loves pop music.
9. The person who loves jazz music is somewhere to the left of the person who loves pop music.
10. Arnold is somewhere to the right of the person who loves hip-hop music.
11. The person who loves hip-hop music and the person who uses a OnePlus 9 are next to each other.
12. The person who loves science fiction books is the person who uses a Xiaomi Mi 11.
13. The person who loves classical music is in the second house.
14. The person who uses a Xiaomi Mi 11 is directly left of Eric.
15. The person who loves historical fiction books is somewhere to the left of the person who loves classical music.
16. The person who uses a Huawei P50 is Peter.
17. The person who uses a Samsung Galaxy S21 is in the fourth house.
18. The person who uses a Samsung Galaxy S21 is somewhere to the right of the person who uses an iPhone 13.
What is the value of attribute House for the person whose attribute PhoneModel is oneplus 9? Please reason step by step, and put your final answer within \boxed{}
|
5
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Arnold`, `Bob`, `Alice`, `Peter`, `Eric`
- People use unique phone models: `samsung galaxy s21`, `oneplus 9`, `google pixel 6`, `iphone 13`, `xiaomi mi 11`, `huawei p50`
- Each person has a unique type of pet: `dog`, `cat`, `fish`, `rabbit`, `hamster`, `bird`
- They all have a unique favorite flower: `daffodils`, `tulips`, `carnations`, `lilies`, `iris`, `roses`
- People own unique car models: `toyota camry`, `chevrolet silverado`, `bmw 3 series`, `tesla model 3`, `honda civic`, `ford f150`
## Clues:
1. There is one house between the person who owns a Tesla Model 3 and the person who uses a OnePlus 9.
2. There are two houses between the person who owns a dog and the person who owns a Honda Civic.
3. There is one house between the person who uses an iPhone 13 and the person who uses a Xiaomi Mi 11.
4. The person who loves the vase of tulips is somewhere to the right of the person who loves a bouquet of daffodils.
5. The person who owns a Chevrolet Silverado is directly left of the person who loves the rose bouquet.
6. Alice is the person who owns a dog.
7. There are two houses between the person who uses a Google Pixel 6 and the person who uses a Huawei P50.
8. There are two houses between the person who owns a Ford F-150 and the person who loves the boquet of lilies.
9. The person who uses a Google Pixel 6 is somewhere to the left of the person who has a cat.
10. The person who loves a bouquet of daffodils is not in the first house.
11. There is one house between the person with a pet hamster and the person who has a cat.
12. The person who uses a OnePlus 9 is Peter.
13. The person who uses a Xiaomi Mi 11 is the person who has a cat.
14. The person who loves the boquet of lilies is Eric.
15. The person who owns a Tesla Model 3 and the person who uses a Google Pixel 6 are next to each other.
16. The person who owns a rabbit is not in the second house.
17. The person who loves a carnations arrangement is in the second house.
18. The person who loves the boquet of lilies is somewhere to the right of the person who owns a Honda Civic.
19. There are two houses between Arnold and the person who owns a Chevrolet Silverado.
20. There are two houses between Peter and Bob.
21. The person who keeps a pet bird is in the fifth house.
22. The person who owns a Toyota Camry is the person who has a cat.
What is the value of attribute Flower for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}
|
iris
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Bob`, `Alice`, `Arnold`, `Eric`, `Peter`
- People use unique phone models: `samsung galaxy s21`, `google pixel 6`, `iphone 13`, `huawei p50`, `oneplus 9`, `xiaomi mi 11`
- The people are of nationalities: `swede`, `chinese`, `norwegian`, `dane`, `german`, `brit`
- Each person has a favorite color: `blue`, `red`, `yellow`, `green`, `white`, `purple`
## Clues:
1. Carol is not in the third house.
2. There is one house between the Dane and the British person.
3. Carol is the person whose favorite color is green.
4. Arnold is directly left of Alice.
5. Alice is the German.
6. The person who uses a OnePlus 9 is the person who loves purple.
7. The person who uses a Huawei P50 is not in the third house.
8. The person who uses a Samsung Galaxy S21 is in the fifth house.
9. The person who loves white is somewhere to the right of the person whose favorite color is red.
10. The person who uses a Samsung Galaxy S21 is Bob.
11. The Dane is the person who loves yellow.
12. The person who uses a Samsung Galaxy S21 is somewhere to the left of Peter.
13. The person who loves blue is Peter.
14. Peter is the British person.
15. The person who uses a Samsung Galaxy S21 is directly left of the person who uses an iPhone 13.
16. The Norwegian is the person who loves purple.
17. The person who uses a Xiaomi Mi 11 is the Chinese.
What is the value of attribute House for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}
|
5
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Arnold`, `Carol`, `Peter`, `Bob`, `Eric`
- People use unique phone models: `huawei p50`, `samsung galaxy s21`, `iphone 13`, `xiaomi mi 11`, `google pixel 6`, `oneplus 9`
- Each person has a unique hobby: `photography`, `painting`, `gardening`, `woodworking`, `cooking`, `knitting`
## Clues:
1. The woodworking hobbyist is somewhere to the left of Bob.
2. The person who paints as a hobby is in the fifth house.
3. Arnold is directly left of the person who uses a Google Pixel 6.
4. The person who uses a Samsung Galaxy S21 is Arnold.
5. Carol is somewhere to the right of the person who uses a Samsung Galaxy S21.
6. The person who uses a Google Pixel 6 is directly left of the person who uses a OnePlus 9.
7. The person who uses a OnePlus 9 is somewhere to the right of Eric.
8. There are two houses between the person who loves cooking and Peter.
9. The person who enjoys knitting is Eric.
10. Peter is the person who paints as a hobby.
11. The person who enjoys gardening is somewhere to the right of Bob.
12. There is one house between Bob and the person who uses a Huawei P50.
13. The person who uses a Xiaomi Mi 11 is not in the first house.
14. Alice is in the sixth house.
What is the value of attribute PhoneModel for the person whose attribute Hobby is cooking? Please reason step by step, and put your final answer within \boxed{}
|
samsung galaxy s21
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Eric`, `Alice`, `Carol`, `Bob`, `Arnold`
- The people keep unique animals: `horse`, `fish`, `cat`, `bird`, `dog`, `rabbit`
- Each person has a unique birthday month: `sept`, `mar`, `jan`, `feb`, `april`, `may`
- The mothers' names in different houses are unique: `Holly`, `Sarah`, `Penny`, `Kailyn`, `Aniya`, `Janelle`
- Each person prefers a unique type of vacation: `beach`, `cruise`, `cultural`, `camping`, `city`, `mountain`
## Clues:
1. The person whose birthday is in February is the fish enthusiast.
2. The person whose birthday is in May is somewhere to the right of The person whose mother's name is Penny.
3. The person who loves beach vacations is Peter.
4. The person whose mother's name is Janelle is Carol.
5. The rabbit owner is Bob.
6. The rabbit owner is the person whose birthday is in May.
7. The person whose mother's name is Kailyn is in the fourth house.
8. The person who enjoys camping trips is the cat lover.
9. The person who likes going on cruises is in the sixth house.
10. The person whose birthday is in April is the dog owner.
11. Alice is The person whose mother's name is Aniya.
12. The person whose birthday is in May and The person whose mother's name is Sarah are next to each other.
13. The person whose mother's name is Holly is the cat lover.
14. There are two houses between the person whose birthday is in March and the rabbit owner.
15. The dog owner is directly left of the person who keeps horses.
16. The person whose birthday is in February is in the second house.
17. The rabbit owner is somewhere to the right of the person who goes on cultural tours.
18. Carol is in the second house.
19. The person whose birthday is in September is the person who prefers city breaks.
20. Eric is not in the first house.
What is the value of attribute House for the person whose attribute Birthday is sept? Please reason step by step, and put your final answer within \boxed{}
|
3
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Arnold`, `Carol`, `Peter`, `Bob`
- Each person lives in a unique style of house: `mediterranean`, `modern`, `craftsman`, `ranch`, `colonial`, `victorian`
- People have unique favorite music genres: `country`, `hip hop`, `pop`, `jazz`, `classical`, `rock`
- Each person has a unique hobby: `cooking`, `painting`, `photography`, `woodworking`, `gardening`, `knitting`
## Clues:
1. The person who loves rock music is in the fifth house.
2. The person who loves classical music and the woodworking hobbyist are next to each other.
3. The person in a Mediterranean-style villa is the person who loves hip-hop music.
4. There are two houses between Arnold and the person residing in a Victorian house.
5. The person who loves jazz music is directly left of Eric.
6. The person who loves hip-hop music is somewhere to the left of the person who enjoys knitting.
7. Carol is the person who loves hip-hop music.
8. The person in a Craftsman-style house is Arnold.
9. The person in a ranch-style home is Eric.
10. The woodworking hobbyist is the person residing in a Victorian house.
11. The person who loves country music is in the first house.
12. There is one house between the person who paints as a hobby and the person living in a colonial-style house.
13. Alice is the photography enthusiast.
14. The person who enjoys gardening is Eric.
15. Bob is in the third house.
What is the value of attribute MusicGenre for the person whose attribute HouseStyle is victorian? Please reason step by step, and put your final answer within \boxed{}
|
jazz
|
0/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Eric`
- Each mother is accompanied by their child: `Bella`, `Meredith`, `Fred`
- People use unique phone models: `samsung galaxy s21`, `iphone 13`, `google pixel 6`
- People have unique favorite book genres: `romance`, `science fiction`, `mystery`
- Everyone has a unique favorite cigar: `blue master`, `prince`, `pall mall`
- People have unique heights: `short`, `very short`, `average`
## Clues:
1. Eric is directly left of the Prince smoker.
2. The person who has an average height is somewhere to the right of Peter.
3. The person who uses a Samsung Galaxy S21 is in the second house.
4. The person who smokes Blue Master is in the third house.
5. The person who uses a Google Pixel 6 is Eric.
6. Arnold is somewhere to the right of the person who loves science fiction books.
7. The person who uses an iPhone 13 is the person's child is named Bella.
8. The person who is short is the Prince smoker.
9. The person who loves mystery books is the person who uses a Google Pixel 6.
10. The person's child is named Meredith and the person who is short are next to each other.
What is the value of attribute House for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}
|
3
|
3/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Alice`, `Peter`
- Everyone has a unique favorite cigar: `blue master`, `dunhill`, `pall mall`, `prince`
- Everyone has something unique for lunch: `stew`, `spaghetti`, `pizza`, `grilled cheese`
- People have unique favorite book genres: `fantasy`, `mystery`, `science fiction`, `romance`
## Clues:
1. Arnold is the person who loves eating grilled cheese.
2. The person who smokes Blue Master is Alice.
3. Arnold is in the second house.
4. The person who is a pizza lover and the person who loves the stew are next to each other.
5. Arnold is the person who loves science fiction books.
6. The person partial to Pall Mall is the person who loves eating grilled cheese.
7. Eric is somewhere to the left of Alice.
8. The person who is a pizza lover is somewhere to the left of the Dunhill smoker.
9. The person who loves fantasy books is the person who loves the stew.
10. The person who loves mystery books is not in the first house.
What is the value of attribute Food for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}
|
grilled cheese
|
2/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Alice`, `Peter`
- They all have a unique favorite flower: `lilies`, `carnations`, `roses`, `daffodils`
- Each person has an occupation: `teacher`, `engineer`, `artist`, `doctor`
- Everyone has a favorite smoothie: `desert`, `dragonfruit`, `watermelon`, `cherry`
## Clues:
1. The Dragonfruit smoothie lover is in the first house.
2. The person who is a doctor is somewhere to the right of Eric.
3. Eric is the person who likes Cherry smoothies.
4. Peter is directly left of the person who is an artist.
5. The Desert smoothie lover is the person who loves a carnations arrangement.
6. The person who is a teacher is directly left of the Desert smoothie lover.
7. The person who loves the boquet of lilies is directly left of the person who likes Cherry smoothies.
8. The person who is a teacher is the person who loves the rose bouquet.
9. The person who is an engineer is Alice.
What is the value of attribute House for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
2
|
1/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Bob`, `Peter`
- Each person prefers a unique type of vacation: `mountain`, `city`, `cruise`, `beach`, `camping`
- Each person has a unique level of education: `doctorate`, `high school`, `bachelor`, `associate`, `master`
- Each person has a favorite color: `blue`, `red`, `white`, `yellow`, `green`
- People use unique phone models: `google pixel 6`, `iphone 13`, `oneplus 9`, `huawei p50`, `samsung galaxy s21`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `stew`
## Clues:
1. The person who loves the stew is not in the first house.
2. There are two houses between the person who loves stir fry and the person with an associate's degree.
3. The person who enjoys mountain retreats is the person with a bachelor's degree.
4. The person with a doctorate is somewhere to the right of Bob.
5. The person who uses a Samsung Galaxy S21 is in the third house.
6. Eric is the person with a doctorate.
7. The person with a doctorate is in the third house.
8. The person who loves stir fry is the person with a bachelor's degree.
9. The person with a doctorate is the person who is a pizza lover.
10. The person whose favorite color is green is somewhere to the right of Peter.
11. The person who enjoys camping trips is the person who uses an iPhone 13.
12. The person who likes going on cruises is Alice.
13. There is one house between the person with a high school diploma and the person who uses a Samsung Galaxy S21.
14. The person who uses a Google Pixel 6 is Arnold.
15. The person who uses a OnePlus 9 is somewhere to the right of the person who uses a Huawei P50.
16. Arnold is the person who loves eating grilled cheese.
17. The person who loves eating grilled cheese is not in the fourth house.
18. There are two houses between the person with a bachelor's degree and the person whose favorite color is red.
19. The person who loves beach vacations is somewhere to the right of the person who prefers city breaks.
20. The person whose favorite color is green is not in the second house.
21. The person who loves blue is somewhere to the right of Peter.
22. There is one house between the person who enjoys camping trips and the person who loves yellow.
What is the value of attribute Food for the person whose attribute Vacation is camping? Please reason step by step, and put your final answer within \boxed{}
|
spaghetti
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Bob`, `Arnold`, `Carol`, `Eric`, `Alice`
- Everyone has something unique for lunch: `spaghetti`, `stir fry`, `stew`, `soup`, `grilled cheese`, `pizza`
- Everyone has a unique favorite cigar: `blends`, `pall mall`, `dunhill`, `yellow monster`, `prince`, `blue master`
- Each person has a unique favorite drink: `boba tea`, `water`, `coffee`, `root beer`, `milk`, `tea`
- Each person has a unique level of education: `associate`, `bachelor`, `trade school`, `doctorate`, `high school`, `master`
## Clues:
1. Bob is not in the second house.
2. The person who smokes many unique blends is somewhere to the left of the person who is a pizza lover.
3. The person partial to Pall Mall is somewhere to the right of the Dunhill smoker.
4. The person who loves the soup is not in the first house.
5. The person who likes milk is directly left of the person who loves the stew.
6. The person who loves the soup is the person with a doctorate.
7. The coffee drinker is the person with a high school diploma.
8. There are two houses between the person who loves the spaghetti eater and the person with an associate's degree.
9. The Prince smoker is not in the third house.
10. The Dunhill smoker and Bob are next to each other.
11. There are two houses between Alice and the boba tea drinker.
12. The person with a high school diploma is Eric.
13. The person who attended trade school is the Prince smoker.
14. There is one house between the Dunhill smoker and the person who loves stir fry.
15. The Dunhill smoker is directly left of the person who is a pizza lover.
16. There is one house between the person partial to Pall Mall and the person who smokes Blue Master.
17. The person who smokes Blue Master is the coffee drinker.
18. The person with a bachelor's degree is the Dunhill smoker.
19. Alice is the tea drinker.
20. Arnold is directly left of the root beer lover.
21. The person with a master's degree is Peter.
22. Arnold is somewhere to the left of the person who likes milk.
What is the value of attribute Cigar for the person whose attribute House is 5? Please reason step by step, and put your final answer within \boxed{}
|
yellow monster
|
0/8
|
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`
- They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `carnations`
- Everyone has a favorite smoothie: `desert`, `watermelon`, `cherry`, `dragonfruit`
- Each person lives in a unique style of house: `craftsman`, `colonial`, `ranch`, `victorian`
- Each person has a unique hobby: `cooking`, `photography`, `gardening`, `painting`
- Each person has a unique favorite drink: `coffee`, `tea`, `milk`, `water`
## Clues:
1. The person in a Craftsman-style house is the Dragonfruit smoothie lover.
2. The tea drinker is the person who loves a bouquet of daffodils.
3. The Desert smoothie lover is the person living in a colonial-style house.
4. There is one house between the Watermelon smoothie lover and the person who loves a bouquet of daffodils.
5. The person who likes Cherry smoothies is directly left of the photography enthusiast.
6. The person who likes milk is the person who loves cooking.
7. The tea drinker is Arnold.
8. The person who loves the boquet of lilies is the person living in a colonial-style house.
9. The person who loves the boquet of lilies is not in the third house.
10. The person living in a colonial-style house is directly left of the person who paints as a hobby.
11. The person in a ranch-style home is the person who likes milk.
12. The person who loves the rose bouquet is the one who only drinks water.
13. Eric is somewhere to the left of the Dragonfruit smoothie lover.
14. The person who loves the rose bouquet is somewhere to the right of the person who loves a carnations arrangement.
15. Peter is the person who loves the boquet of lilies.
What is the value of attribute Hobby for the person whose attribute Smoothie is desert? Please reason step by step, and put your final answer within \boxed{}
|
gardening
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Alice`, `Arnold`, `Peter`, `Eric`
- The mothers' names in different houses are unique: `Penny`, `Aniya`, `Kailyn`, `Janelle`, `Holly`
- The people keep unique animals: `cat`, `bird`, `dog`, `fish`, `horse`
- Everyone has a favorite smoothie: `desert`, `dragonfruit`, `cherry`, `watermelon`, `lime`
- Each person has an occupation: `doctor`, `engineer`, `artist`, `teacher`, `lawyer`
## Clues:
1. Bob is the Desert smoothie lover.
2. The cat lover is the person who is an engineer.
3. The person whose mother's name is Penny is the bird keeper.
4. The person who is a lawyer is the fish enthusiast.
5. The person who likes Cherry smoothies is directly left of Alice.
6. The Watermelon smoothie lover and the person who is an engineer are next to each other.
7. The person whose mother's name is Holly is the dog owner.
8. The person who is a teacher is in the first house.
9. The person whose mother's name is Penny is in the second house.
10. The person who drinks Lime smoothies is the person who is a doctor.
11. The person whose mother's name is Janelle is the person who is a lawyer.
12. Arnold is not in the third house.
13. The Dragonfruit smoothie lover is directly left of Peter.
14. The person whose mother's name is Kailyn is the Dragonfruit smoothie lover.
15. Arnold is somewhere to the right of Peter.
16. The dog owner is not in the fifth house.
17. The Watermelon smoothie lover is somewhere to the left of the Desert smoothie lover.
What is the value of attribute Animal for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}
|
horse
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Alice`, `Eric`, `Arnold`, `Peter`
- Each mother is accompanied by their child: `Samantha`, `Meredith`, `Timothy`, `Bella`, `Fred`
- People have unique hair colors: `red`, `blonde`, `black`, `brown`, `gray`
- Each person has a unique hobby: `gardening`, `cooking`, `painting`, `knitting`, `photography`
- Each person has a unique type of pet: `hamster`, `bird`, `cat`, `fish`, `dog`
- They all have a unique favorite flower: `tulips`, `roses`, `carnations`, `lilies`, `daffodils`
## Clues:
1. The person's child is named Samantha is somewhere to the right of the person's child is named Meredith.
2. The person who loves the boquet of lilies is the person who keeps a pet bird.
3. The person who has blonde hair is the person who loves the vase of tulips.
4. Bob is the person who has brown hair.
5. The person who paints as a hobby is the person with an aquarium of fish.
6. The person's child is named Fred is Peter.
7. The person with an aquarium of fish is somewhere to the left of the person who has a cat.
8. The person with a pet hamster is the person's child is named Samantha.
9. The person's child is named Bella is Arnold.
10. The person's child is named Bella is in the third house.
11. Peter is not in the first house.
12. Alice is the person who has blonde hair.
13. The person who loves the rose bouquet is not in the third house.
14. The person who owns a dog is the person's child is named Fred.
15. The person who has red hair is directly left of the person who has black hair.
16. The photography enthusiast is directly left of Eric.
17. The person who has black hair is the person who loves the rose bouquet.
18. The person who loves a carnations arrangement is not in the third house.
19. The person who enjoys knitting is somewhere to the right of the person's child is named Bella.
20. The person who loves the boquet of lilies is the person who enjoys gardening.
21. The person who keeps a pet bird is in the fifth house.
What is the value of attribute Flower for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}
|
tulips
|
0/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Arnold`, `Peter`
- The people keep unique animals: `horse`, `bird`, `cat`
- Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`
- The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`
- People have unique favorite music genres: `pop`, `classical`, `rock`
- Each person has a favorite color: `yellow`, `white`, `red`
## Clues:
1. The cat lover is in the third house.
2. There is one house between the person who loves yellow and the cat lover.
3. The person who loves classical music is directly left of Eric.
4. Arnold is the Desert smoothie lover.
5. The bird keeper is the Watermelon smoothie lover.
6. The person whose mother's name is Janelle is somewhere to the left of the person who loves white.
7. The person who loves yellow is the person who loves rock music.
8. The person whose mother's name is Holly is directly left of Peter.
What is the value of attribute Color for the person whose attribute Mother is Holly? Please reason step by step, and put your final answer within \boxed{}
|
yellow
|
2/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Eric`, `Arnold`, `Peter`, `Alice`
- Everyone has a unique favorite cigar: `blends`, `prince`, `pall mall`, `blue master`, `dunhill`
- Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `stew`, `pizza`, `stir fry`
- The people are of nationalities: `norwegian`, `swede`, `brit`, `dane`, `german`
- Each person has an occupation: `teacher`, `lawyer`, `doctor`, `artist`, `engineer`
- People have unique heights: `average`, `very tall`, `short`, `very short`, `tall`
## Clues:
1. The person who smokes Blue Master is the person who is a lawyer.
2. Alice is the person partial to Pall Mall.
3. The person partial to Pall Mall is somewhere to the left of the Dunhill smoker.
4. The German is the person who loves stir fry.
5. The person who is tall is the person who smokes many unique blends.
6. The person who is an artist is the person who loves the spaghetti eater.
7. Peter is the person who is short.
8. The Dunhill smoker is not in the fourth house.
9. The person who is very short is the person who smokes Blue Master.
10. There are two houses between the person who loves the spaghetti eater and the person who loves stir fry.
11. The person who has an average height is in the second house.
12. The Prince smoker is the person who is a doctor.
13. The Swedish person is the person who is an engineer.
14. Eric is the person who loves stir fry.
15. There is one house between the British person and the person who loves the stew.
16. The person who is very tall is the Norwegian.
17. The Dane is the person who is short.
18. The person who is very tall is Arnold.
19. There are two houses between the person who is a pizza lover and the person who is very tall.
20. The person who is a teacher is not in the third house.
What is the value of attribute Height for the person whose attribute Food is stew? Please reason step by step, and put your final answer within \boxed{}
|
short
|
0/8
|
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Eric`
- Each person has a unique birthday month: `april`, `jan`, `sept`
- People have unique favorite book genres: `mystery`, `romance`, `science fiction`
- Each person lives in a unique style of house: `ranch`, `victorian`, `colonial`
- They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`
## Clues:
1. The person who loves romance books is in the third house.
2. Arnold is the person who loves a carnations arrangement.
3. The person living in a colonial-style house is the person whose birthday is in September.
4. The person who loves a carnations arrangement is in the second house.
5. The person whose birthday is in April is the person in a ranch-style home.
6. The person who loves science fiction books is Arnold.
7. The person in a ranch-style home is the person who loves a carnations arrangement.
8. The person whose birthday is in January is somewhere to the left of Peter.
9. The person whose birthday is in April is somewhere to the left of the person who loves the boquet of lilies.
What is the value of attribute Birthday for the person whose attribute Flower is daffodils? Please reason step by step, and put your final answer within \boxed{}
|
jan
|
0/8
|
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Peter`, `Eric`, `Alice`, `Bob`
- Each person has a unique hobby: `painting`, `cooking`, `knitting`, `gardening`, `photography`
- People have unique heights: `very tall`, `tall`, `very short`, `average`, `short`
- Everyone has something unique for lunch: `stew`, `grilled cheese`, `stir fry`, `spaghetti`, `pizza`
## Clues:
1. Bob is the photography enthusiast.
2. The person who loves eating grilled cheese is the person who is tall.
3. Peter is not in the second house.
4. The person who is tall is directly left of the person who loves stir fry.
5. The person who loves cooking is the person who has an average height.
6. Alice is directly left of the person who is a pizza lover.
7. The person who loves the spaghetti eater is not in the second house.
8. Eric is not in the fifth house.
9. The person who is short is Peter.
10. The person who has an average height and the person who enjoys gardening are next to each other.
11. The person who paints as a hobby is directly left of the person who loves eating grilled cheese.
12. The person who is very short is in the fifth house.
13. The person who is tall is in the third house.
14. Alice is somewhere to the right of the photography enthusiast.
What is the value of attribute House for the person whose attribute Hobby is painting? Please reason step by step, and put your final answer within \boxed{}
|
2
|
1/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Bob`, `Peter`, `Eric`, `Alice`, `Carol`
- Each person has a unique birthday month: `april`, `feb`, `mar`, `jan`, `may`, `sept`
- Each person prefers a unique type of vacation: `city`, `beach`, `mountain`, `cruise`, `cultural`, `camping`
- Each person has a favorite color: `blue`, `white`, `green`, `purple`, `red`, `yellow`
## Clues:
1. The person whose birthday is in January is the person who loves blue.
2. The person whose birthday is in January is directly left of the person who loves white.
3. The person who enjoys camping trips is in the fourth house.
4. Eric is in the sixth house.
5. There are two houses between the person who likes going on cruises and the person whose birthday is in February.
6. The person whose birthday is in May is not in the sixth house.
7. Peter is directly left of the person who loves yellow.
8. The person who goes on cultural tours is Eric.
9. The person whose birthday is in September is directly left of the person whose favorite color is green.
10. Arnold and the person who loves purple are next to each other.
11. The person who loves beach vacations is the person whose birthday is in March.
12. The person whose favorite color is green is somewhere to the left of Carol.
13. The person whose birthday is in May is somewhere to the right of Peter.
14. The person who loves blue is Bob.
15. The person who enjoys mountain retreats is in the fifth house.
16. The person who loves purple is in the third house.
17. Carol is in the fourth house.
What is the value of attribute Color for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}
|
purple
|
0/8
|
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Bob`, `Alice`, `Eric`, `Peter`, `Carol`
- People have unique favorite sports: `volleyball`, `soccer`, `basketball`, `baseball`, `swimming`, `tennis`
- Each person has a unique hobby: `gardening`, `cooking`, `painting`, `woodworking`, `knitting`, `photography`
- Each mother is accompanied by their child: `Bella`, `Meredith`, `Alice`, `Samantha`, `Fred`, `Timothy`
- Each person has a unique birthday month: `feb`, `jan`, `mar`, `may`, `sept`, `april`
- Everyone has something unique for lunch: `stir fry`, `grilled cheese`, `pizza`, `spaghetti`, `stew`, `soup`
## Clues:
1. The person who loves soccer is somewhere to the right of Eric.
2. The person who paints as a hobby is somewhere to the left of the woodworking hobbyist.
3. The person whose birthday is in February is not in the third house.
4. The person who is the mother of Timothy is directly left of Arnold.
5. The person who loves cooking is somewhere to the left of the person's child is named Fred.
6. Alice is the person who paints as a hobby.
7. The person's child is named Alice is the person who loves cooking.
8. The person whose birthday is in March is the person's child is named Samantha.
9. The person who loves the soup is the person whose birthday is in May.
10. Carol is somewhere to the right of the person whose birthday is in May.
11. The person whose birthday is in March and the person who is a pizza lover are next to each other.
12. The person whose birthday is in February is not in the fourth house.
13. There are two houses between the person who loves baseball and the person who loves the stew.
14. The person whose birthday is in May is somewhere to the left of the person who loves volleyball.
15. The person whose birthday is in January is somewhere to the right of Arnold.
16. The person who loves cooking is not in the third house.
17. The person who enjoys knitting is the person whose birthday is in September.
18. The person who enjoys gardening is the person's child is named Meredith.
19. The person who is a pizza lover is the person who loves swimming.
20. There is one house between the person who loves basketball and the person whose birthday is in May.
21. The person who loves the soup is directly left of the person who loves the spaghetti eater.
22. The person who loves the stew is the person's child is named Bella.
23. The person who enjoys knitting is somewhere to the left of the person who loves the soup.
24. Bob is somewhere to the left of the person who loves the stew.
25. Arnold is the person who loves stir fry.
26. The woodworking hobbyist is directly left of the person who loves the soup.
What is the value of attribute House for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{}
|
6
|
0/8
|
Subsets and Splits
Filtered Answers A-D
Retrieves 100 rows where the answer is a single letter from A to D, providing basic filtering of the dataset.