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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 HairColor is black? Please reason step by step, and put your final answer within \boxed{}
|
soup
|
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`, `Arnold`, `Alice`, `Eric`
- They all have a unique favorite flower: `roses`, `daffodils`, `carnations`, `lilies`
- Each person has a unique hobby: `photography`, `painting`, `cooking`, `gardening`
- Each person has a unique type of pet: `dog`, `fish`, `bird`, `cat`
- Each person has a favorite color: `red`, `yellow`, `green`, `white`
- Each person lives in a unique style of house: `craftsman`, `colonial`, `ranch`, `victorian`
## Clues:
1. The person in a Craftsman-style house is Arnold.
2. The person who loves the rose bouquet is somewhere to the right of Peter.
3. The photography enthusiast is the person who owns a dog.
4. The person who loves a bouquet of daffodils is not in the fourth house.
5. The person who loves the rose bouquet is the person whose favorite color is red.
6. The person in a Craftsman-style house is in the second house.
7. Eric is the person residing in a Victorian house.
8. The person with an aquarium of fish is the person who loves white.
9. The person who loves cooking is somewhere to the right of the person whose favorite color is red.
10. The person who loves white is the person who loves a carnations arrangement.
11. The person who loves white is somewhere to the right of the person who enjoys gardening.
12. The person who loves a bouquet of daffodils is the person who loves yellow.
13. The person living in a colonial-style house is the person whose favorite color is red.
14. The person who has a cat is Eric.
What is the value of attribute Color for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}
|
white
|
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`, `Arnold`, `Peter`, `Eric`, `Alice`
- Each person has a unique birthday month: `sept`, `mar`, `april`, `feb`, `jan`
- People have unique favorite sports: `baseball`, `basketball`, `soccer`, `tennis`, `swimming`
- Each person has a favorite color: `white`, `red`, `yellow`, `blue`, `green`
- Each person has an occupation: `doctor`, `teacher`, `lawyer`, `artist`, `engineer`
- The mothers' names in different houses are unique: `Kailyn`, `Holly`, `Aniya`, `Penny`, `Janelle`
## Clues:
1. There is one house between the person who is a doctor and the person whose birthday is in March.
2. The person whose mother's name is Penny is not in the fourth house.
3. The person who loves baseball is somewhere to the right of the person who is a doctor.
4. The person who loves soccer is Peter.
5. There is one house between Bob and The person whose mother's name is Kailyn.
6. The person who loves yellow is in the third house.
7. The person who loves yellow is The person whose mother's name is Kailyn.
8. The person who loves swimming is the person who loves white.
9. Alice is in the fourth house.
10. The person whose birthday is in February is The person whose mother's name is Holly.
11. The person who loves baseball is the person whose birthday is in January.
12. The person who loves white is the person whose birthday is in April.
13. The person whose mother's name is Aniya is the person who loves swimming.
14. Alice is the person who loves baseball.
15. The person who is a doctor and the person who is a lawyer are next to each other.
16. The person whose birthday is in April is somewhere to the left of the person whose favorite color is red.
17. The person who loves tennis is somewhere to the right of the person who is a teacher.
18. The person whose favorite color is green is in the second house.
19. Arnold is the person whose birthday is in February.
20. The person whose birthday is in February is the person who is an artist.
21. The person who loves blue is not in the fifth house.
22. The person who loves tennis is not in the fifth house.
23. The person whose mother's name is Holly is the person who loves basketball.
What is the value of attribute Birthday for the person whose attribute Occupation is lawyer? Please reason step by step, and put your final answer within \boxed{}
|
jan
|
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`, `Peter`, `Arnold`
- Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `desert`, `watermelon`
- People have unique favorite sports: `soccer`, `tennis`, `basketball`, `swimming`
- People own unique car models: `tesla model 3`, `toyota camry`, `honda civic`, `ford f150`
- They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `carnations`
## Clues:
1. The person who owns a Tesla Model 3 is the person who loves the rose bouquet.
2. Peter is the Dragonfruit smoothie lover.
3. The Desert smoothie lover is the person who owns a Toyota Camry.
4. The person who loves tennis is in the first house.
5. The person who owns a Toyota Camry and the person who loves basketball are next to each other.
6. Arnold is the person who loves basketball.
7. The person who owns a Honda Civic is the person who loves a bouquet of daffodils.
8. Eric is the person who loves the rose bouquet.
9. The Watermelon smoothie lover is not in the first house.
10. The person who owns a Honda Civic is somewhere to the right of the Desert smoothie lover.
11. The person who loves basketball is the person who loves the boquet of lilies.
12. The person who loves tennis and the person who loves soccer are next to each other.
What is the value of attribute Name for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}
|
Peter
|
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`, `Bob`, `Eric`, `Peter`
- People use unique phone models: `iphone 13`, `samsung galaxy s21`, `xiaomi mi 11`, `oneplus 9`, `google pixel 6`, `huawei p50`
- Each person has a unique birthday month: `april`, `mar`, `feb`, `may`, `jan`, `sept`
- Each person has an occupation: `nurse`, `doctor`, `engineer`, `teacher`, `artist`, `lawyer`
## Clues:
1. The person who uses a Google Pixel 6 is directly left of the person whose birthday is in March.
2. The person who is a nurse is Eric.
3. Arnold is directly left of the person whose birthday is in April.
4. Alice and the person whose birthday is in January are next to each other.
5. The person who is an artist is the person whose birthday is in May.
6. The person whose birthday is in September is not in the sixth house.
7. There is one house between the person whose birthday is in March and the person who is a nurse.
8. The person whose birthday is in March is the person who is a lawyer.
9. The person who uses a Xiaomi Mi 11 is directly left of the person who is a nurse.
10. The person who is a teacher is not in the sixth house.
11. Eric is the person who uses an iPhone 13.
12. The person who is an engineer and Peter are next to each other.
13. The person whose birthday is in January is in the third house.
14. The person who uses a Samsung Galaxy S21 is Bob.
15. The person who is a lawyer and the person whose birthday is in April are next to each other.
16. The person who uses a OnePlus 9 is somewhere to the right of the person who is a doctor.
What is the value of attribute House for the person whose attribute Name is Peter? 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: `Alice`, `Arnold`, `Peter`, `Eric`
- People have unique favorite sports: `tennis`, `swimming`, `basketball`, `soccer`
- Each person lives in a unique style of house: `victorian`, `colonial`, `craftsman`, `ranch`
- Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`, `dragonfruit`
- Each person has an occupation: `teacher`, `artist`, `engineer`, `doctor`
## Clues:
1. Alice and the person in a Craftsman-style house are next to each other.
2. The Desert smoothie lover is in the first house.
3. The Dragonfruit smoothie lover is Eric.
4. The person in a ranch-style home is somewhere to the right of the person living in a colonial-style house.
5. The person who is a doctor is not in the second house.
6. Peter is the person who likes Cherry smoothies.
7. The person who is an artist is the Dragonfruit smoothie lover.
8. Alice is in the third house.
9. The person who is an engineer is somewhere to the right of the person who loves swimming.
10. The person who loves basketball is the person who is an artist.
11. The Dragonfruit smoothie lover is not in the second house.
12. The person residing in a Victorian house is directly left of the person who loves soccer.
13. The person who loves tennis is somewhere to the left of the person who loves swimming.
What is the value of attribute Occupation for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}
|
teacher
|
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`, `Carol`, `Peter`, `Bob`, `Arnold`, `Alice`
- They all have a unique favorite flower: `tulips`, `lilies`, `iris`, `roses`, `carnations`, `daffodils`
## Clues:
1. The person who loves the vase of tulips is directly left of the person who loves a bouquet of daffodils.
2. Alice is somewhere to the right of Peter.
3. There are two houses between Carol and Peter.
4. The person who loves the boquet of lilies is Bob.
5. The person who loves the boquet of iris is not in the second house.
6. The person who loves the boquet of iris and the person who loves a carnations arrangement are next to each other.
7. Arnold is not in the second house.
8. The person who loves a bouquet of daffodils is Peter.
9. Bob is in the fifth house.
What is the value of attribute Flower for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}
|
tulips
|
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: `Eric`, `Arnold`, `Peter`
- Each mother is accompanied by their child: `Meredith`, `Fred`, `Bella`
- Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`
- Each person prefers a unique type of vacation: `mountain`, `city`, `beach`
- Each person has a favorite color: `white`, `red`, `yellow`
## Clues:
1. There is one house between the person's child is named Bella and the person's child is named Meredith.
2. The person who likes Cherry smoothies is the person who loves beach vacations.
3. The person who prefers city breaks is Arnold.
4. The person whose favorite color is red is the person's child is named Fred.
5. The person's child is named Fred is the Watermelon smoothie lover.
6. Eric is not in the first house.
7. The person's child is named Meredith is the person who loves white.
8. The person who loves white is the Desert smoothie lover.
9. The Desert smoothie lover is Eric.
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{}
|
1
|
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`
- Each person lives in a unique style of house: `victorian`, `ranch`, `colonial`, `craftsman`
- Each person has an occupation: `teacher`, `engineer`, `doctor`, `artist`
- Everyone has a unique favorite cigar: `prince`, `dunhill`, `pall mall`, `blue master`
- People have unique favorite music genres: `pop`, `rock`, `classical`, `jazz`
- People have unique heights: `very short`, `tall`, `average`, `short`
## Clues:
1. The person who loves classical music is the person living in a colonial-style house.
2. The person who smokes Blue Master is the person in a ranch-style home.
3. The person who loves rock music is the person who smokes Blue Master.
4. The Dunhill smoker is directly left of Peter.
5. Eric is in the first house.
6. The person residing in a Victorian house is in the third house.
7. The person who loves rock music and the person who loves classical music are next to each other.
8. The person who is a teacher is the person who is short.
9. The person who loves classical music is the Prince smoker.
10. The person who is a doctor is somewhere to the left of the person who is very short.
11. Arnold is the person who is an artist.
12. The person who smokes Blue Master is in the first house.
13. The person who is tall is directly left of the person who loves pop music.
14. The person residing in a Victorian house is the person who is a teacher.
What is the value of attribute Cigar for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}
|
prince
|
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: `Peter`, `Arnold`, `Carol`, `Eric`, `Bob`, `Alice`
- Everyone has something unique for lunch: `stir fry`, `stew`, `grilled cheese`, `soup`, `pizza`, `spaghetti`
## Clues:
1. The person who loves the soup is somewhere to the left of Carol.
2. The person who loves stir fry is in the fifth house.
3. Peter is not in the sixth house.
4. The person who loves the stew is somewhere to the left of Peter.
5. Bob is the person who loves the soup.
6. The person who loves eating grilled cheese is somewhere to the right of the person who loves the spaghetti eater.
7. The person who loves the spaghetti eater is directly left of the person who loves the soup.
8. Arnold is in the second house.
9. The person who loves the stew is directly left of Arnold.
10. Alice is directly left of the person who loves the soup.
What is the value of attribute Food for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}
|
spaghetti
|
5/8
|
## Task B-4.4.
How many passwords consisting of 4 characters from the set $\{a, b, c, 1,2,3,4,5,+,!\}$ are there such that all characters in the password are different or the password contains exactly two, not necessarily different letters and two, not necessarily different digits?
|
5670
|
4/8
|
On a blackboard, Kiara wrote 20 integers, all of them different from zero. Then, for each pair of numbers written by Kiara, Yndira wrote on the same blackboard the respective product between them (including, if the result of some product was already written, Yndira repeated it).
For example, if the numbers 2, 3, 4, and 6 were among those written by Kiara, then Yndira would have written the numbers $6, 8, 12, 12, 18$, and 24, because we have $6=2 \times 3$, $8=2 \times 4$, $12=2 \times 6=3 \times 4$, $18=3 \times 6$, and $24=4 \times 6$. Note that the number 6 would have been written again even though it was already written by Kiara, while the number 12 would have been written twice by Yndira.
a) In total, how many numbers were written by Kiara and Yndira on the blackboard?
b) Suppose that, of the total numbers written on the blackboard, exactly 120 are positive. If Kiara wrote more positive numbers than negative ones, how many of the numbers written by Kiara were positive?
|
210
|
0/8
|
7. (10 points) As shown in the figure, the length $AB$ of rectangle $ABCD$ is 20 cm, and the width $BC$ is 16 cm. Inside the rectangle, there are two overlapping squares $DEFG$ and $BHIJ$. It is known that the perimeters of the three shaded rectangles are equal. Therefore, the area of rectangle INFM is $\qquad$ square centimeters.
|
32
|
1/8
|
4. In a rectangular flower bed, install two identical sprinklers so that the entire flower bed can be watered. It is known that the watering area of each sprinkler is a circle with a radius of $10 \mathrm{~m}$. How should it be designed (find the distance between the two sprinklers and the length and width of the rectangle) to maximize the area of the rectangular flower bed?
|
10\sqrt{2}
|
1/8
|
Problem 4. Calculate: $\frac{2^{3} \cdot 4^{5} \cdot 6^{7}}{8^{9} \cdot 10^{11}}: 0.015^{7}$.
|
1000
|
4/8
|
A regular triangle's sides (in the same direction) were divided in the ratio $p: q$. By connecting the division points, a triangle is formed whose area is $\frac{19}{64}$ of the area of the original triangle. What is the ratio $p: q$? () Suggested by: Koncz Levente, Budapest
|
\dfrac{5}{3}
|
1/8
|
Let $ABC$ and $A_{1}B_{1}C_{1}$ be two triangles. Prove that
$\frac{a}{a_{1}}+\frac{b}{b_{1}}+\frac{c}{c_{1}}\leq\frac{3R}{2r_{1}}$ ,
where $a = BC$ , $b = CA$ , $c = AB$ are the sidelengths of triangle $ABC$ , where $a_{1}=B_{1}C_{1}$ , $b_{1}=C_{1}A_{1}$ , $c_{1}=A_{1}B_{1}$ are the sidelengths of triangle $A_{1}B_{1}C_{1}$ , where $R$ is the circumradius of triangle $ABC$ and $r_{1}$ is the inradius of triangle $A_{1}B_{1}C_{1}$ .
|
\frac{a}{a_{1}}+\frac{b}{b_{1}}+\frac{c}{c_{1}}\leq\frac{3R}{2r_{1}}
|
0/8
|
Problem 55. Find the best constant $k$ (smallest) for the inequality
$$a^{k}+b^{k}+c^{k} \geq a b+b c+c a$$
to hold for $a, b, c$ are three non-negative real numbers with $a+b+c=3$.
|
\log_{\frac{3}{2}} \frac{9}{8}
|
1/8
|
Given \( N \geq 3 \) points, numbered \( 1, 2, \ldots, N \). Each pair of points is connected by an arrow from the smaller number to the larger number. A coloring of all the arrows in red and blue is called monotone if there are no two points \( A \) and \( B \) such that one can travel from \( A \) to \( B \) using both red and blue arrows. Find the number of monotone colorings.
|
N!
|
0/8
|
8.8. (Austria - PDR, 79). For each value of $n \in \mathbf{N}$, find the greatest value of $k \in \mathbf{Z}^{+}$, for which the number $\left[(3+\sqrt{11})^{2 n-1}\right]$ is divisible by $2^{k}$.
|
n
|
3/8
|
9. Given that the increasing function $f(x)$ is defined on $(0,+\infty)$, and for any positive number $x$ it satisfies $f(x)$ $f\left[f(x)+\frac{1}{x}\right]=1$, find the value of $f(1)$.
|
\dfrac{1 - \sqrt{5}}{2}
|
2/8
|
Let $BCB'C'$ be a rectangle, let $M$ be the midpoint of $B'C'$, and let $A$ be a point on the circumcircle of the rectangle. Let triangle $ABC$ have orthocenter $H$, and let $T$ be the foot of the perpendicular from $H$ to line $AM$. Suppose that $AM=2$, $[ABC]=2020$, and $BC=10$. Then $AT=\frac{m}{n}$, where $m$ and $n$ are positive integers with $\gcd(m,n)=1$. Compute $100m+n$.
[i]Proposed by Ankit Bisain[/i]
|
2102
|
1/8
|
In triangle $K L M$, the ratio of the radii of the circumscribed and inscribed circles is 3. The inscribed circle touches the sides of triangle $K L M$ at points $A, B$, and $C$. Find the ratio of the area of triangle $K L M$ to the area of triangle $A B C$.
#
|
6
|
4/8
|
$\textbf{Anna's Vintage Postcards}$
Anna organizes the postcards in her collection by country and by the decade in which they were issued. The prices she paid for them at a collectibles shop were: Italy and Germany, $7$ cents each; Japan $5$ cents each; and India $6$ cents each. (Italy and Germany are European countries, and Japan and India are Asian countries.) In that collection:
- 60s: Italy (5), Germany (7), Japan (6), India (8)
- 70s: Italy (9), Germany (6), Japan (10), India (12)
- 80s: Italy (10), Germany (12), Japan (15), India (11)
In dollars and cents, how much did her Asian postcards issued in the 80s cost her?
|
\$1.41
|
3/8
|
In triangle $PQR$, the angle bisectors are $PL$, $QM$, and $RN$, which intersect at the incenter $I$. If $\angle PRQ = 52^\circ$, then find the measure of $\angle PIM$, in degrees.
|
64^\circ
|
2/8
|
The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ is $C = \frac{5}{9}(F-32)$. An integer Fahrenheit temperature is converted to Celsius using truncation (floor function), converted back to Fahrenheit using truncation, and again converted to Celsius using truncation.
For how many integer Fahrenheit temperatures between 30 and 1200 inclusive does the original temperature equal the final Fahrenheit temperature after two conversions?
|
130
|
4/8
|
A rectangle with integer dimensions has an area that is numerically five times the number of units in its perimeter. What is the number of units in the perimeter of this rectangle if one of its sides is greater than 10 units?
|
90
|
0/8
|
Maria wants to save money for a down payment on a house and decides to invest in a savings account that compounds semiannually with an annual interest rate of \(8\%\). She needs a total of $\$100,\!000$ at the end of \(10\) years. To the nearest dollar, how much should she initially invest?
|
\$45,639
|
5/8
|
A rectangle and an isosceles triangle share a common side, which lies along the $x$-axis, with the right vertex of the rectangle and the left vertex of the triangle located at $(15, 0)$. The dimensions of the rectangle are $15$ units wide (along the $x$-axis) and $10$ units high, while the base and height of the triangle are both $10$ units. A segment is drawn from the top left vertex of the rectangle to the top vertex of the triangle. Calculate the area of the triangle formed by this segment and part of the $x$-axis.
|
75 \text{ sq. units}
|
0/8
|
In a similar race setup, all runners start at point $A$, must touch any part of a 1500-meter wall, and stop at point $B$. Given that the distances from $A$ to the closest point on the wall is 400 meters and from $B$ to the closest point on the wall is 600 meters, what is the minimum distance a participant must run? Round your answer to the nearest meter.
|
1803
|
1/8
|
A geometric sequence of positive integers is formed where the first term is 6 and the fourth term is 768. What is the second term of this sequence?
|
24
|
3/8
|
In the diagram, \( O \) is the center of a circle with radii \( OP=OQ=7 \). Determine the perimeter of the shaded region if \( \widehat{PQ} \) subtends an angle of \( 270^\circ \).
|
14 + \frac{21\pi}{2}
|
0/8
|
Margo walks to her friend's house in 15 minutes and takes 30 minutes using the same, but slippery, route to get back home. Her average walking rate for the outbound trip is 5 miles per hour and 3 miles per hour on the return trip. What are the total miles Margo walked, if her average speed for the entire trip was 3.6 miles per hour?
|
2.75 \text{ miles}
|
2/8
|
Determine the total number of pieces required to create a ten-row triangle using unit rods and connectors. Each n-row triangle uses rods in the pattern of the arithmetic sequence $3n$ and connectors forming an $(n+1)$-row triangle.
|
231
|
2/8
|
Cara is sitting with her seven friends in a line at a table. How many different combinations of friends can sit immediately next to her on the right?
|
7
|
3/8
|
There are 2 houses, numbered 1 to 2 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`
- The people keep unique animals: `cat`, `horse`
- People have unique heights: `short`, `very short`
- People have unique favorite book genres: `science fiction`, `mystery`
- Each person prefers a unique type of vacation: `mountain`, `beach`
## Clues:
1. The person who loves beach vacations is directly left of Eric.
2. The person who loves beach vacations and the person who is very short are next to each other.
3. The cat lover is the person who is short.
4. The person who is short is the person who loves mystery books.
What is the value of attribute Animal for the person whose attribute Vacation is mountain? Please reason step by step, and put your final answer within \boxed{}
|
horse
|
4/8
|
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`, `Peter`, `Eric`, `Arnold`, `Bob`
- Each person has a unique birthday month: `sept`, `mar`, `april`, `feb`, `jan`
- The people keep unique animals: `horse`, `bird`, `dog`, `fish`, `cat`
## Clues:
1. The person whose birthday is in September is Peter.
2. The dog owner is in the first house.
3. Bob is not in the second house.
4. The bird keeper is not in the second house.
5. The bird keeper is not in the fourth house.
6. The person whose birthday is in March is not in the second house.
7. Bob and the person whose birthday is in January are next to each other.
8. The person who keeps horses is the person whose birthday is in February.
9. Eric is in the first house.
10. The person whose birthday is in March and the person whose birthday is in April are next to each other.
11. The bird keeper is not in the third house.
12. The cat lover is not in the second house.
13. Arnold is in the fourth house.
What is the value of attribute House for the person whose attribute Birthday is mar? Please reason step by step, and put your final answer within \boxed{}
|
1
|
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: `Arnold`, `Peter`, `Eric`, `Alice`
- Each person lives in a unique style of house: `craftsman`, `colonial`, `victorian`, `ranch`
- People have unique hair colors: `red`, `blonde`, `black`, `brown`
- Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`, `Samantha`
- People have unique favorite book genres: `mystery`, `fantasy`, `romance`, `science fiction`
## Clues:
1. The person in a Craftsman-style house is in the third house.
2. Alice is the person who loves romance books.
3. The person who has brown hair is in the fourth house.
4. The person's child is named Samantha is in the fourth house.
5. The person in a ranch-style home is somewhere to the right of the person who has red hair.
6. Peter is the person's child is named Bella.
7. Arnold is the person who has red hair.
8. Alice is the person living in a colonial-style house.
9. The person who has black hair is in the second house.
10. The person who loves fantasy books is Peter.
11. Arnold is the person's child is named Meredith.
12. The person who has black hair is Eric.
13. The person who loves science fiction books is Arnold.
What is the value of attribute House for the person whose attribute BookGenre is mystery? 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: `Peter`, `Bob`, `Arnold`, `Alice`, `Eric`
- Each person has an occupation: `lawyer`, `teacher`, `artist`, `engineer`, `doctor`
- Each person lives in a unique style of house: `victorian`, `craftsman`, `modern`, `ranch`, `colonial`
- People have unique hair colors: `blonde`, `gray`, `red`, `brown`, `black`
- People have unique favorite book genres: `romance`, `biography`, `science fiction`, `mystery`, `fantasy`
## Clues:
1. Alice is not in the fifth house.
2. Peter is not in the second house.
3. Peter is directly left of Eric.
4. The person living in a colonial-style house is somewhere to the left of the person who loves fantasy books.
5. Arnold is the person who is a doctor.
6. The person who has gray hair is the person who loves fantasy books.
7. The person who loves science fiction books is not in the fifth house.
8. Peter is the person who has red hair.
9. The person who loves romance books is the person who has black hair.
10. Eric is the person who has black hair.
11. The person who is a doctor is somewhere to the right of Peter.
12. The person who has blonde hair is the person who is a teacher.
13. Peter is the person who loves mystery books.
14. The person who is a lawyer is Eric.
15. The person living in a colonial-style house is the person who is an engineer.
16. The person residing in a Victorian house is the person who loves mystery books.
17. The person who is a teacher is not in the fourth house.
18. The person who is an artist is somewhere to the left of the person in a modern-style house.
19. The person who is a teacher is not in the third house.
20. The person in a ranch-style home is directly left of the person in a Craftsman-style house.
What is the value of attribute BookGenre for the person whose attribute HouseStyle is ranch? Please reason step by step, and put your final answer within \boxed{}
|
fantasy
|
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`
- People have unique favorite sports: `swimming`, `tennis`, `basketball`, `soccer`
- Each person prefers a unique type of vacation: `cruise`, `beach`, `mountain`, `city`
- Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `stew`, `pizza`
## Clues:
1. The person who loves the spaghetti eater is somewhere to the left of the person who likes going on cruises.
2. The person who loves the stew is directly left of the person who loves eating grilled cheese.
3. The person who is a pizza lover is in the fourth house.
4. Peter is somewhere to the left of the person who enjoys mountain retreats.
5. The person who likes going on cruises is in the third house.
6. Arnold is the person who loves soccer.
7. The person who loves basketball is not in the first house.
8. There are two houses between the person who prefers city breaks and Eric.
9. The person who loves tennis is the person who likes going on cruises.
10. Alice is in the first house.
What is the value of attribute Name for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}
|
Peter
|
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: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
- The mothers' names in different houses are unique: `Penny`, `Kailyn`, `Aniya`, `Janelle`, `Holly`
- Everyone has a unique favorite cigar: `blue master`, `pall mall`, `prince`, `dunhill`, `blends`
- The people keep unique animals: `bird`, `cat`, `horse`, `fish`, `dog`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `stew`
## Clues:
1. The person who loves the stew is somewhere to the left of the fish enthusiast.
2. The person who is a pizza lover is somewhere to the right of the Dunhill smoker.
3. Peter is the cat lover.
4. The dog owner is directly left of the person who loves the spaghetti eater.
5. The person who loves stir fry is The person whose mother's name is Aniya.
6. There are two houses between the fish enthusiast and Eric.
7. The person who smokes many unique blends is The person whose mother's name is Kailyn.
8. The fish enthusiast is the person who loves the spaghetti eater.
9. The fish enthusiast is in the second house.
10. The person whose mother's name is Kailyn is the person who loves the stew.
11. The person whose mother's name is Janelle is not in the fifth house.
12. The person whose mother's name is Holly is the person who smokes Blue Master.
13. Arnold is The person whose mother's name is Aniya.
14. The person who loves the spaghetti eater and the person partial to Pall Mall are next to each other.
15. Peter is not in the third house.
16. Arnold is the person who keeps horses.
17. The person whose mother's name is Holly is Bob.
What is the value of attribute Food for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}
|
stir fry
|
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`, `Eric`, `Alice`, `Peter`, `Arnold`
- People have unique heights: `super tall`, `tall`, `very short`, `average`, `very tall`, `short`
- People use unique phone models: `google pixel 6`, `iphone 13`, `samsung galaxy s21`, `xiaomi mi 11`, `oneplus 9`, `huawei p50`
- Each mother is accompanied by their child: `Fred`, `Timothy`, `Alice`, `Bella`, `Meredith`, `Samantha`
## Clues:
1. The person who uses a Xiaomi Mi 11 is the person who is short.
2. Alice is somewhere to the right of Bob.
3. The person who uses a OnePlus 9 is Carol.
4. The person who uses a Xiaomi Mi 11 is the person's child is named Alice.
5. The person who has an average height is not in the fourth house.
6. The person who uses a Samsung Galaxy S21 is in the second house.
7. Alice is directly left of the person's child is named Fred.
8. The person's child is named Meredith and Arnold are next to each other.
9. The person's child is named Samantha is the person who is super tall.
10. The person who is short is somewhere to the right of the person who uses a Samsung Galaxy S21.
11. The person who is very tall is the person who is the mother of Timothy.
12. Bob is not in the fourth house.
13. The person who is very short is the person who uses a Huawei P50.
14. The person who uses a Samsung Galaxy S21 is directly left of the person who is super tall.
15. Peter is somewhere to the right of the person who is tall.
16. Arnold is somewhere to the left of the person's child is named Bella.
17. The person who uses a Google Pixel 6 is directly left of the person who uses an iPhone 13.
18. Eric is in the first house.
What is the value of attribute Height for the person whose attribute PhoneModel is google pixel 6? Please reason step by step, and put your final answer within \boxed{}
|
super tall
|
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`, `Alice`, `Arnold`, `Peter`, `Bob`
- People have unique heights: `average`, `tall`, `short`, `very short`, `very tall`
- Each person has a unique hobby: `cooking`, `knitting`, `photography`, `gardening`, `painting`
- Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`, `camping`
- People own unique car models: `ford f150`, `toyota camry`, `tesla model 3`, `honda civic`, `bmw 3 series`
- Each person has a unique level of education: `bachelor`, `doctorate`, `master`, `high school`, `associate`
## Clues:
1. The person who is short is directly left of the person with a high school diploma.
2. The person who enjoys mountain retreats is the person who paints as a hobby.
3. The person who loves cooking is the person with a doctorate.
4. The person who owns a Honda Civic is in the third house.
5. The person who owns a Honda Civic is the person who has an average height.
6. Bob is the person who paints as a hobby.
7. The person with a master's degree is Eric.
8. The person who enjoys knitting is directly left of the person with a high school diploma.
9. The person who owns a Toyota Camry and the person who enjoys camping trips are next to each other.
10. Peter is not in the fifth house.
11. The person who prefers city breaks is the person who owns a BMW 3 Series.
12. The person who owns a Honda Civic is Eric.
13. The person who paints as a hobby is the person with a bachelor's degree.
14. Arnold is not in the second house.
15. The person who owns a Ford F-150 is not in the second house.
16. The person who enjoys gardening is the person who likes going on cruises.
17. The person who loves beach vacations is the person who is very short.
18. The person who owns a BMW 3 Series is not in the first house.
19. The person who owns a Toyota Camry is directly left of the person who is tall.
20. Arnold is not in the fifth house.
What is the value of attribute CarModel for the person whose attribute Hobby is photography? Please reason step by step, and put your final answer within \boxed{}
|
ford f150
|
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`, `Peter`, `Eric`, `Arnold`, `Carol`, `Bob`
- People have unique heights: `very short`, `very tall`, `short`, `super tall`, `tall`, `average`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `soup`, `stew`
- The mothers' names in different houses are unique: `Holly`, `Janelle`, `Penny`, `Aniya`, `Kailyn`, `Sarah`
- Each person has a unique favorite drink: `tea`, `water`, `milk`, `coffee`, `boba tea`, `root beer`
- Each person has a unique type of pet: `rabbit`, `fish`, `bird`, `hamster`, `cat`, `dog`
## Clues:
1. Arnold is the person who loves the stew.
2. The person who owns a dog is directly left of the person who has a cat.
3. The person whose mother's name is Holly is in the sixth house.
4. The tea drinker is somewhere to the left of the boba tea drinker.
5. The tea drinker is in the second house.
6. The person who is very tall is Bob.
7. The person who has a cat is The person whose mother's name is Penny.
8. The person who is very short is directly left of Alice.
9. Carol is the person who is a pizza lover.
10. The person who has an average height is not in the sixth house.
11. The person who loves stir fry is Bob.
12. The person with a pet hamster is not in the third house.
13. The person whose mother's name is Janelle is somewhere to the left of the person with a pet hamster.
14. Eric is the person who loves the soup.
15. The person whose mother's name is Kailyn is directly left of the person who keeps a pet bird.
16. The one who only drinks water is somewhere to the right of the person who likes milk.
17. The person who owns a rabbit is the person who loves the stew.
18. The person who is tall is The person whose mother's name is Aniya.
19. The person who is very short is somewhere to the left of the person who likes milk.
20. The person who is tall is not in the fifth house.
21. The person who is very short is in the second house.
22. The person who loves the stew is the root beer lover.
23. The person whose mother's name is Kailyn is the boba tea drinker.
24. The person who is tall is not in the fourth house.
25. The person who is super tall is directly left of the person who loves eating grilled cheese.
26. Carol is directly left of the root beer lover.
What is the value of attribute Drink for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}
|
milk
|
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`, `Peter`, `Alice`, `Arnold`
- Each person has a unique birthday month: `sept`, `feb`, `april`, `jan`
- People have unique favorite book genres: `romance`, `fantasy`, `mystery`, `science fiction`
- They all have a unique favorite flower: `roses`, `daffodils`, `lilies`, `carnations`
- Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`
## Clues:
1. There are two houses between the person who loves fantasy books and the person whose birthday is in April.
2. The person whose birthday is in February is directly left of the person who loves a bouquet of daffodils.
3. The person who likes going on cruises is the person who loves a carnations arrangement.
4. The person whose birthday is in September is directly left of the person who loves science fiction books.
5. The person who loves a bouquet of daffodils is the person who prefers city breaks.
6. The person whose birthday is in April is Arnold.
7. The person whose birthday is in February is the person who loves a carnations arrangement.
8. Alice is the person who likes going on cruises.
9. The person who loves the boquet of lilies is the person who enjoys mountain retreats.
10. Eric is not in the third house.
11. The person who loves science fiction books is the person who loves the boquet of lilies.
12. The person who loves mystery books is Eric.
13. Eric and the person whose birthday is in January are next to each other.
What is the value of attribute BookGenre for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
mystery
|
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: `Peter`, `Bob`, `Arnold`, `Eric`, `Alice`
- Each person has a favorite color: `red`, `white`, `green`, `blue`, `yellow`
- Each person has a unique hobby: `gardening`, `cooking`, `painting`, `photography`, `knitting`
- People have unique heights: `very tall`, `tall`, `average`, `short`, `very short`
- People have unique hair colors: `black`, `blonde`, `brown`, `gray`, `red`
## Clues:
1. The person whose favorite color is green is somewhere to the right of the person who has black hair.
2. The person who has an average height is somewhere to the right of the person who loves blue.
3. The person who has red hair is Alice.
4. The person who loves cooking is not in the first house.
5. The person who loves yellow is the person who has gray hair.
6. The person who is short is somewhere to the left of the person who loves yellow.
7. The person who enjoys gardening is the person who loves white.
8. Arnold is somewhere to the left of the person who has black hair.
9. The person who is short is somewhere to the right of the person who has blonde hair.
10. Eric and the person who loves cooking are next to each other.
11. The person who has black hair is directly left of the person who loves blue.
12. The person who is very short is the person who has black hair.
13. Bob is the person who loves blue.
14. The person who is tall is directly left of the photography enthusiast.
15. The person who loves white is not in the first house.
16. The person who loves yellow is the person who enjoys knitting.
17. The person who loves blue is the person who has blonde hair.
What is the value of attribute Hobby for the person whose attribute Color is white? 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`, `Eric`, `Arnold`, `Peter`
- The mothers' names in different houses are unique: `Aniya`, `Janelle`, `Penny`, `Kailyn`, `Holly`
- People have unique favorite music genres: `pop`, `jazz`, `rock`, `classical`, `hip hop`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `stew`, `spaghetti`, `pizza`
## Clues:
1. Eric is somewhere to the left of the person who loves classical music.
2. The person who loves eating grilled cheese is directly left of The person whose mother's name is Janelle.
3. The person whose mother's name is Penny is directly left of Alice.
4. The person who loves stir fry is Peter.
5. The person who loves the spaghetti eater is Alice.
6. Eric is somewhere to the left of the person who loves rock music.
7. The person whose mother's name is Kailyn is directly left of The person whose mother's name is Aniya.
8. The person who loves rock music is not in the third house.
9. The person who loves eating grilled cheese is directly left of the person who loves the stew.
10. The person who loves pop music is The person whose mother's name is Kailyn.
11. The person who loves the spaghetti eater is the person who loves jazz music.
12. The person who loves pop music is Arnold.
What is the value of attribute MusicGenre for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}
|
hip hop
|
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`, `Eric`, `Arnold`
- The people keep unique animals: `cat`, `horse`, `bird`
- Each person has a favorite color: `yellow`, `white`, `red`
- The people are of nationalities: `brit`, `swede`, `dane`
- They all have a unique favorite flower: `daffodils`, `lilies`, `carnations`
## Clues:
1. The bird keeper and Eric are next to each other.
2. The person whose favorite color is red is the Dane.
3. The Dane is the person who loves a carnations arrangement.
4. The person who loves the boquet of lilies is the bird keeper.
5. The Dane is somewhere to the left of the person who loves a bouquet of daffodils.
6. The British person is somewhere to the left of the person who loves yellow.
7. Arnold is the person who keeps horses.
8. Eric is the Swedish person.
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{}
|
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: `Arnold`, `Carol`, `Bob`, `Alice`, `Eric`, `Peter`
- People have unique favorite sports: `swimming`, `basketball`, `volleyball`, `soccer`, `tennis`, `baseball`
- People have unique favorite music genres: `rock`, `pop`, `jazz`, `country`, `hip hop`, `classical`
- Each person has a unique level of education: `doctorate`, `trade school`, `bachelor`, `high school`, `associate`, `master`
## Clues:
1. Alice is in the fourth house.
2. Alice is somewhere to the right of the person with a doctorate.
3. The person with a high school diploma is somewhere to the right of the person who loves basketball.
4. The person who loves volleyball is the person with a bachelor's degree.
5. Alice is directly left of the person who loves jazz music.
6. The person with a master's degree is the person who loves swimming.
7. There is one house between the person who loves rock music and the person with a bachelor's degree.
8. Carol is in the second house.
9. The person who loves rock music is somewhere to the left of the person who loves pop music.
10. The person who loves swimming is somewhere to the left of Carol.
11. Eric is directly left of the person who loves hip-hop music.
12. Alice is the person with an associate's degree.
13. Alice is the person who loves classical music.
14. Arnold is the person who loves soccer.
15. The person who loves basketball and the person who loves volleyball are next to each other.
16. Peter is the person who loves tennis.
17. The person with a doctorate is Peter.
What is the value of attribute Education for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
master
|
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`, `Eric`, `Peter`, `Arnold`, `Alice`, `Bob`
- Everyone has a favorite smoothie: `watermelon`, `lime`, `dragonfruit`, `desert`, `blueberry`, `cherry`
## Clues:
1. Peter is somewhere to the right of the person who drinks Lime smoothies.
2. The person who likes Cherry smoothies is not in the fourth house.
3. Eric is not in the sixth house.
4. The Watermelon smoothie lover is somewhere to the left of Eric.
5. The Desert smoothie lover is somewhere to the right of Peter.
6. The person who drinks Blueberry smoothies is directly left of the person who drinks Lime smoothies.
7. The Desert smoothie lover is somewhere to the right of Alice.
8. Eric is not in the fifth house.
9. The person who drinks Lime smoothies is Arnold.
10. Bob is directly left of Peter.
What is the value of attribute Smoothie for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}
|
lime
|
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: `Alice`, `Eric`, `Arnold`, `Bob`, `Peter`
- They all have a unique favorite flower: `tulips`, `roses`, `lilies`, `daffodils`, `carnations`
- The people keep unique animals: `dog`, `horse`, `cat`, `bird`, `fish`
## Clues:
1. Alice is in the second house.
2. The person who loves the boquet of lilies is the bird keeper.
3. Peter is somewhere to the right of the person who loves the vase of tulips.
4. The fish enthusiast is the person who loves a bouquet of daffodils.
5. The person who keeps horses is Eric.
6. There are two houses between the dog owner and Bob.
7. The fish enthusiast is directly left of Bob.
8. Alice is directly left of the person who keeps horses.
9. The person who loves a carnations arrangement is directly left of the person who loves the vase of tulips.
10. The cat lover is not in the first house.
What is the value of attribute Animal for the person whose attribute Flower is tulips? Please reason step by step, and put your final answer within \boxed{}
|
horse
|
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`
- People own unique car models: `ford f150`, `tesla model 3`, `toyota camry`
- Each person prefers a unique type of vacation: `beach`, `mountain`, `city`
- The people are of nationalities: `dane`, `swede`, `brit`
- People have unique hair colors: `blonde`, `black`, `brown`
- Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`
## Clues:
1. The Swedish person is the person who owns a Ford F-150.
2. The person who has blonde hair is not in the second house.
3. The person who owns a Toyota Camry and Arnold are next to each other.
4. The person who has black hair is somewhere to the right of the person in a ranch-style home.
5. The person who has black hair is the Dane.
6. The person residing in a Victorian house is not in the second house.
7. Peter is directly left of the person who loves beach vacations.
8. The person living in a colonial-style house is the person who has blonde hair.
9. The person who has black hair is Arnold.
10. The Dane is the person who loves beach vacations.
11. Peter is the person who prefers city breaks.
What is the value of attribute House for the person whose attribute CarModel is ford f150? Please reason step by step, and put your final answer within \boxed{}
|
1
|
4/8
|
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`, `Arnold`, `Alice`
- The mothers' names in different houses are unique: `Kailyn`, `Aniya`, `Holly`, `Janelle`
- Each person has a unique birthday month: `feb`, `sept`, `jan`, `april`
- Each person has a unique hobby: `cooking`, `gardening`, `photography`, `painting`
## Clues:
1. Peter is the person whose birthday is in February.
2. Arnold is not in the third house.
3. The person whose mother's name is Aniya is somewhere to the left of the person who enjoys gardening.
4. The person whose birthday is in January is in the second house.
5. The person whose birthday is in February is not in the third house.
6. The person whose birthday is in February is the photography enthusiast.
7. Alice is somewhere to the right of the person whose birthday is in April.
8. The person whose mother's name is Kailyn is somewhere to the left of the person whose birthday is in September.
9. The person who enjoys gardening is not in the fourth house.
10. The person who loves cooking is The person whose mother's name is Janelle.
11. Peter is The person whose mother's name is Kailyn.
What is the value of attribute Birthday for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}
|
feb
|
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`, `Peter`, `Arnold`, `Eric`, `Alice`, `Carol`
- People have unique hair colors: `red`, `gray`, `auburn`, `blonde`, `brown`, `black`
- People have unique favorite book genres: `historical fiction`, `biography`, `romance`, `fantasy`, `mystery`, `science fiction`
- People have unique heights: `very short`, `very tall`, `tall`, `short`, `super tall`, `average`
- Each person has a unique level of education: `associate`, `doctorate`, `high school`, `trade school`, `bachelor`, `master`
- Each person has a unique favorite drink: `boba tea`, `milk`, `water`, `root beer`, `coffee`, `tea`
## Clues:
1. The person with a doctorate and Bob are next to each other.
2. There is one house between Carol and the person who has black hair.
3. Peter is the person with a doctorate.
4. The person who loves science fiction books is Eric.
5. The one who only drinks water is the person who has an average height.
6. Alice is the person who loves mystery books.
7. The person who loves romance books is Bob.
8. The person who has brown hair is in the second house.
9. The person who has an average height is in the fourth house.
10. The boba tea drinker is the person who is very tall.
11. The person with a high school diploma is Bob.
12. The person who is short is somewhere to the left of the person who is super tall.
13. The person who loves historical fiction books and the person with a bachelor's degree are next to each other.
14. The person who attended trade school is the person who has red hair.
15. Carol is the person who has auburn hair.
16. The person who is very short is somewhere to the right of the person who has gray hair.
17. There are two houses between Eric and the person who loves fantasy books.
18. There are two houses between the tea drinker and the person who is very short.
19. Eric is somewhere to the left of the person with a bachelor's degree.
20. The root beer lover is Alice.
21. The person with an associate's degree is Arnold.
22. The person who is tall is not in the second house.
23. The person who loves science fiction books is the boba tea drinker.
24. The person who has black hair is not in the fourth house.
25. The person who is short is the coffee drinker.
26. The coffee drinker and the person with a high school diploma are next to each other.
27. The coffee drinker is not in the second house.
What is the value of attribute HairColor for the person whose attribute BookGenre is science fiction? Please reason step by step, and put your final answer within \boxed{}
|
red
|
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`, `Alice`, `Eric`, `Bob`, `Peter`
- People have unique hair colors: `gray`, `blonde`, `red`, `brown`, `black`
- Each person has an occupation: `engineer`, `artist`, `lawyer`, `teacher`, `doctor`
## Clues:
1. The person who has black hair is the person who is a teacher.
2. The person who is a doctor is somewhere to the right of the person who is an artist.
3. There is one house between Eric and Alice.
4. Eric is somewhere to the left of Alice.
5. The person who has brown hair and Alice are next to each other.
6. Alice is the person who has red hair.
7. There are two houses between the person who has brown hair and the person who has blonde hair.
8. Alice is the person who is an engineer.
9. Arnold is the person who has blonde hair.
10. The person who is a doctor is Peter.
11. The person who has brown hair is somewhere to the left of the person who is a teacher.
What is the value of attribute House for the person whose attribute Occupation is doctor? 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: `Peter`, `Arnold`, `Eric`, `Alice`, `Bob`
- Each person has a unique level of education: `associate`, `doctorate`, `high school`, `bachelor`, `master`
- Each mother is accompanied by their child: `Fred`, `Meredith`, `Bella`, `Timothy`, `Samantha`
- Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`, `dunhill`, `blends`
- The people are of nationalities: `swede`, `brit`, `dane`, `german`, `norwegian`
- People have unique favorite book genres: `romance`, `mystery`, `biography`, `science fiction`, `fantasy`
## Clues:
1. The person with a master's degree is the person partial to Pall Mall.
2. The person with a high school diploma is in the fourth house.
3. The person's child is named Samantha is in the first house.
4. The Norwegian and the person with a master's degree are next to each other.
5. The German is the Dunhill smoker.
6. The person who is the mother of Timothy is directly left of the person with a master's degree.
7. Arnold and the Dane are next to each other.
8. The Swedish person is the person who loves mystery books.
9. The Swedish person is Alice.
10. Arnold is the person with an associate's degree.
11. The person with a doctorate is in the second house.
12. Peter is somewhere to the right of the person who loves biography books.
13. The person who smokes many unique blends is Alice.
14. The person who loves fantasy books is in the first house.
15. Peter is the Norwegian.
16. The person with a doctorate is the person's child is named Meredith.
17. The Prince smoker is somewhere to the left of the person who smokes many unique blends.
18. The person partial to Pall Mall is the person's child is named Bella.
19. The person who loves romance books is Bob.
What is the value of attribute House for the person whose attribute Education is bachelor? Please reason step by step, and put your final answer within \boxed{}
|
3
|
0/8
|
On the inside of a square with side length 60, construct four congruent isosceles triangles each with base
60 and height 50, and each having one side coinciding with a different side of the square. Find the area of
the octagonal region common to the interiors of all four triangles.
|
360
|
0/8
|
There are digits a and b so that the 15-digit number 7a7ba7ab7ba7b77 is divisible by 99.
Find 10a + b.
|
53
|
4/8
|
Ten spherical balls are stacked in a pyramid. The bottom level of the stack has six balls each with radius 6 arranged
in a triangular formation with adjacent balls tangent to each other. The middle level of the stack has three
balls each with radius 5 arranged in a triangular formation each tangent to three balls in the bottom level.
The top level of the stack has one ball with radius 6 tangent to the three balls in the middle level. The
diagram shows the stack of ten balls with the balls in the middle shaded. The height of this stack of balls is m +$\sqrt{n}$, where m and n are positive integers. Find $m + n.$
|
304
|
3/8
|
You have a collection of small wooden blocks that are rectangular solids measuring $3$×$4$×$6$. Each of the six faces of each block is to be painted a solid color, and you have three colors of paint to use. Find the
number of distinguishable ways you could paint the blocks. (Two blocks are distinguishable if you cannot
rotate one block so that it looks identical to the other block.)
|
243
|
0/8
|
Consider an alphabetized list of all the arrangements of the letters in the word BETWEEN. Then BEEENTW would be in position $1$ in the list, BEEENWT would be in position $2$ in the list, and so forth. Find the position that BETWEEN would be in the list.
|
46
|
2/8
|
Leaving his house at noon, Jim walks at a constant rate of $4$ miles per hour along a $4$ mile square route returning to his house at $1$ PM. At a randomly chosen time between noon and $1$ PM, Sally chooses a random location along Jim's route and begins running at a constant rate of $7$ miles per hour along Jim's route in the same direction that Jim is walking until she completes one $4$ mile circuit of the square route.
The probability that Sally runs past Jim while he is walking is given by $\frac{m}{n}$ , where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
|
64
|
0/8
|
Let $a$ be a solution to the equation $\sqrt{x^2 + 2} = \sqrt[3]{x^3 + 45}$. Evaluate the ratio of $\frac{2017}{a^2}$ to $a^2 - 15a + 2$.
|
6
|
3/8
|
There are integers $a_1, a_2, a_3,...,a_{240}$ such that $x(x + 1)(x + 2)(x + 3) ... (x + 239) =\sum_{n=1}^{240}a_nx^n$. Find the number of integers $k$ with $1\le k \le 240$ such that ak is a multiple of $3$.
|
159
|
4/8
|
Let $a, b$, and $c$ be real numbers. Let $u = a^2 + b^2 + c^2$ and $v = 2ab + 2bc + 2ca$. Suppose $2018u = 1001v + 1024$. Find the maximum possible value of $35a - 28b - 3c$.
|
32
|
1/8
|
99. There are 6 identical-looking coins, but 4 are genuine, of the same weight, while 2 are counterfeit, lighter, and also weigh the same. What is the minimum number of weighings on a balance scale without weights that are needed to find both counterfeit coins?
|
3
|
5/8
|
3. At a banquet of a university, there are 2017 mathematicians, each with two different main courses on their order menu, and no two people have the same pair of main courses on their menu. The price of each main course is equal to the number of mathematicians who ordered that main course. The university pays for the cheaper of the two main courses for each mathematician (if the prices are the same, either can be chosen). For all possible sets of order menus, find the maximum total payment of the university.
|
127009
|
1/8
|
In the rectangular coordinate system, \( O \) is the origin, \( A \) and \( B \) are points in the first quadrant, and \( A \) lies on the line \( y = \tan \theta x \), where \( \theta \in \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \) and \(|OA| = \frac{1}{\sqrt{2} - \cos \theta} \). Point \( B \) lies on the hyperbola \( x^2 - y^2 = 1 \) such that the area of \( \triangle OAB \) is minimized. Determine the value of \( \theta \) within \( \left(\frac{\pi}{4}, \frac{\pi}{2}\right) \) that maximizes the area of \( \triangle OAB \), and find the maximum value of the area.
|
\arccos \frac{\sqrt{2}}{4}
|
0/8
|
4. On a machine that operates with tokens of 1, 10, and 25 kuna, you can play this game: if you insert a 1 kuna token, you get one 10 kuna token; if you insert a 10 kuna token, you get one 1 kuna token and one 25 kuna token; if you insert a 25 kuna token, you get two 10 kuna tokens. At the beginning, you had one 10 kuna token. After some time, you found that you had exactly 100 1 kuna tokens and some other tokens. What is the smallest value of tokens you could have won by then?
|
1110
|
0/8
|
A sequence $a_1, a_2, a_3, \ldots$ of positive integers satisfies $a_1 > 5$ and $a_{n+1} = 5 + 6 + \cdots + a_n$ for all positive integers $n$. Determine all prime numbers $p$ such that, regardless of the value of $a_1$, this sequence must contain a multiple of $p$.
|
2
|
3/8
|
7. Let $D$ be a point inside acute $\triangle A B C$ such that $\angle A D B=\angle A C B+90^{\circ}$, and $A C \cdot B D=A D \cdot B C$. Calculate the ratio: $\frac{A B \cdot C D}{A C \cdot B D}$.
|
\sqrt{2}
|
3/8
|
Task 1. The administration divided the region into several districts based on the principle: the population of a large district exceeds $8 \%$ of the region's population and for any large district, there are two non-large districts with a combined population that is larger. Into what minimum number of districts was the region divided?
|
8
|
0/8
|
6. Given that $P$ is a point on a sphere $O$ with radius $r$, and through $P$ three mutually perpendicular moving chords $P A$, $P B$, and $P C$ are drawn. If the maximum distance from point $P$ to the plane $A B C$ is 1, then $r=$ $\qquad$
|
\dfrac{3}{2}
|
2/8
|
10. (12th IMO Problem) Let real numbers $x_{1}, x_{2}, \cdots, x_{1997}$ satisfy the following conditions:
(1) $-\frac{1}{\sqrt{3}} \leqslant x_{i} \leqslant \sqrt{3}$, where $i=1,2, \cdots, 1997$.
(2) $x_{1}+x_{2}+\cdots+x_{1997}=-318 \sqrt{3}$.
Find: $x_{1}^{12}+x_{2}^{12}+\cdots+x_{1997}^{12}$'s maximum value.
|
189548
|
4/8
|
## Task A-2.5.
In a coordinate system, all integer points $(x, y)$ are marked where $1 \leqslant x \leqslant$ 200 and $1 \leqslant y \leqslant 100$, a total of 20000 points. How many line segments of length $\sqrt{5}$ have their endpoints at the marked points?
|
78208
|
5/8
|
4.4. Through the vertex $A$ of the parallelogram $A B C D$, a line is drawn intersecting the diagonal $B D$, the side $C D$, and the line $B C$ at points $E, F$, and $G$ respectively. Find $B E$, if $F G$ : $F E=9, E D=1$. Round your answer to the nearest hundredth if necessary.
|
3.16
|
5/8
|
Yasinsky V.
On the plane, there are $n(n>2)$ points, no three of which lie on the same line. In how many different ways can this set of points be divided into two non-empty subsets such that the convex hulls of these subsets do not intersect?
|
\frac{n(n-1)}{2}
|
1/8
|
Example 1.2. Find $\int \frac{x d x}{1+x^{2}}$.
|
\dfrac{1}{2} \ln\left(1 + x^2\right)
|
0/8
|
Let \( x_{i} \in \mathbb{R} \) for \( i = 1, \cdots, n \) with \( \sum_{i=1}^{n} x_{i} = 1 \), and \( k, m \in \mathbb{N}^{+} \). Prove that \(\sum_{i=1}^{n}\left(x_{i}^{k}+\frac{1}{x_{i}^{k}}\right)^{m} \geq n\left(n^{k}+\frac{1}{n^{k}}\right)^{m}\).
|
\sum_{i=1}^{n}\left(x_{i}^{k}+\frac{1}{x_{i}^{k}}\right)^{m} \geq n\left(n^{k}+\frac{1}{n^{k}}\right)^{m}
|
4/8
|
5. (3 points) In a regular triangular pyramid (not a regular tetrahedron), the area of the base is three times smaller than the area of a lateral face. The height of the pyramid is 10 cm.
Let's construct the following (infinite) sequence of spheres. Let \( S_{1} \) be the inscribed sphere of this pyramid. Then \( S_{2} \) is the sphere that touches the lateral faces of the pyramid and the sphere \( S_{1} \); \( S_{3} \) is the sphere that touches the lateral faces of the pyramid and the sphere \( S_{2} \), not equal to \( S_{1} \), and so on; \( S_{n+1} \) is the sphere that touches the lateral faces of the pyramid and the sphere \( S_{n} \), not equal to \( S_{n-1} \).
Find the total volume of all these spheres.
|
\dfrac{500}{183} \pi
|
3/8
|
5.52 One day, three boys, Jia, Yi, and Bing, met at the library. Jia said, “From now on, I will come to the library every other day.” Yi said he would come every two days, and Bing said he would come every three days. After hearing their conversation, the librarian pointed out that the library is closed every Wednesday. The children replied that if any of them was supposed to come on a day when the library was closed, they would come the next day instead, and their subsequent visits to the library would be based on this new day. The children all followed this rule. One day, they met again at the library, and it was a Monday. On which day of the week did the above conversation take place?
|
Saturday
|
0/8
|
4. As shown in Figure 3, in $\triangle ABC$, it is given that $D$ is a point on side $BC$ such that $AD = AC$, and $E$ is the midpoint of side $AD$ such that $\angle BAD = \angle ACE$. If $S_{\triangle BDE} = 1$, then $S_{\triangle ABC}$ is $\qquad$.
|
4
|
3/8
|
Let N be a positive integer greater than 2. We number the vertices
of a regular 2n-gon clockwise with the numbers 1, 2, . . . ,N,−N,−N +
1, . . . ,−2,−1. Then we proceed to mark the vertices in the following way.
In the first step we mark the vertex 1. If ni is the vertex marked in the
i-th step, in the i+1-th step we mark the vertex that is |ni| vertices away
from vertex ni, counting clockwise if ni is positive and counter-clockwise
if ni is negative. This procedure is repeated till we reach a vertex that has
already been marked. Let $f(N)$ be the number of non-marked vertices.
(a) If $f(N) = 0$ , prove that 2N + 1 is a prime number.
(b) Compute $f(1997)$ .
|
3810
|
5/8
|
The incircle of a triangle $ABC$ touches the side $AB$ and $AC$ at respectively at $X$ and $Y$ . Let $K$ be the midpoint of the arc $\widehat{AB}$ on the circumcircle of $ABC$ . Assume that $XY$ bisects the segment $AK$ . What are the possible measures of angle $BAC$ ?
|
120
|
2/8
|
For each integer $n \ge 2$ , let $A(n)$ be the area of the region in the coordinate plane defined by the inequalities $1\le x \le n$ and $0\le y \le x \left\lfloor \sqrt x \right\rfloor$ , where $\left\lfloor \sqrt x \right\rfloor$ is the greatest integer not exceeding $\sqrt x$ . Find the number of values of $n$ with $2\le n \le 1000$ for which $A(n)$ is an integer.
|
483
|
0/8
|
Let $ABC$ be a triangle. An interior point $P$ of $ABC$ is said to be *good*if we can find exactly $27$ rays emanating from $P$ intersecting the sides of the triangle $ABC$ such that the triangle is divided by these rays into $27$ *smaller triangles of equal area.* Determine the number of good points for a given triangle $ABC$ .
|
1
|
3/8
|
Let $P(x)=x^{2020}+x+2$ , which has $2020$ distinct roots. Let $Q(x)$ be the monic polynomial of degree $\binom{2020}{2}$ whose roots are the pairwise products of the roots of $P(x)$ . Let $\alpha$ satisfy $P(\alpha)=4$ . Compute the sum of all possible values of $Q(\alpha^2)^2$ .
*Proposed by Milan Haiman.*
|
2020\times2^{2019}
|
0/8
|
There are $2022$ distinct integer points on the plane. Let $I$ be the number of pairs among these points with exactly $1$ unit apart. Find the maximum possible value of $I$ .
(*Note. An integer point is a point with integer coordinates.*)
*Proposed by CSJL.*
|
3954
|
2/8
|
Jenny and Kenny are walking in the same direction, Kenny at 3 feet per second and Jenny at 1 foot per second, on parallel paths that are 200 feet apart. A tall circular building 100 feet in diameter is centered midway between the paths. At the instant when the building first blocks the line of sight between Jenny and Kenny, they are 200 feet apart. Let $t$ be the amount of time, in seconds, before Jenny and Kenny can see each other again. If $t$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?
|
163
|
1/8
|
There are 13 cities in a certain kingdom. Between some pairs of cities two-way direct bus, train or plane connections are established. What is the least possible number of connections to be established in order that choosing any two means of transportation one can go from any city to any other without using the third kind of vehicle?
|
18
|
4/8
|
4. A train $110 \mathrm{~m}$ long is moving at a speed of $\frac{25}{3} \mathrm{~m} / \mathrm{s}$. On its way to the track at $09.10 \mathrm{~h}$, it encountered a pedestrian walking in the same direction and passed him in $15 \mathrm{sec}$. At $09.16 \mathrm{~h}$, it met a pedestrian walking towards it and passed him in $12 \mathrm{sec}$. At what time did the pedestrians meet?
|
09:40
|
2/8
|
8. A classroom has desks arranged in 6 rows and 7 columns, with 40 students. Two positions in the last row are left empty, and the rest of the students are seated based on their height and vision. There are 24 students who are tall, 18 students who have good vision, and 6 students who have both conditions. It is known that if a student is short and has poor vision, they must sit in the first three rows; if a student is tall and has good vision, they must sit in the last three rows. Let the method of seating arrangement be $A$, then the number of times 2 appears in the prime factorization of $A$ is $\qquad$
|
35
|
2/8
|
Let $ABC$ be an isosceles obtuse-angled triangle, and $D$ be a point on its base $AB$ such that $AD$ equals to the circumradius of triangle $BCD$. Find the value of $\angle ACD$.
|
30^\circ
|
4/8
|
Agakhanov N.K.
Find all angles $\alpha$ for which the set of numbers $\sin \alpha, \sin 2 \alpha, \sin 3 \alpha$ coincides with the set $\cos \alpha, \cos 2 \alpha, \cos 3 \alpha$.
|
\alpha = \dfrac{\pi}{8} + \dfrac{k\pi}{2}
|
0/8
|
11. (IND $\left.3^{\prime}\right)^{\mathrm{IMO}}$ Given a circle with two chords $A B, C D$ that meet at $E$, let $M$ be a point of chord $A B$ other than $E$. Draw the circle through $D, E$, and $M$. The tangent line to the circle $D E M$ at $E$ meets the lines $B C, A C$ at $F, G$, respectively. Given $\frac{A M}{A B}=\lambda$, find $\frac{G E}{E F}$.
|
\dfrac{\lambda}{1 - \lambda}
|
2/8
|
Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
f(x f(y)+1)=y+f(f(x) f(y))
$$
for all $x, y \in \mathbb{R}$.
Answer. The only such function is $f(x)=x-1, x \in \mathbb{R}$.
|
f(x) = x - 1
|
2/8
|
If $n$ quantities form a geometric sequence, $P$ is their product, $S$ is their sum, and $S'$ is the sum of their reciprocals. Express $P$ in terms of $S$, $S'$, and $n$.
|
P = \left( \dfrac{S}{S'} \right)^{\frac{n}{2}}
|
0/8
|
If we increase the sides of an isosceles right triangle by $4 \mathrm{~cm}$, then the area of the triangle increases by $112 \mathrm{~cm}^{2}$. What are the sides of the original triangle?
|
26
|
1/8
|
PROBLEM 3. Let the function $f:[0,+\infty) \rightarrow \mathbb{R}$, defined by $f(x)=\left\{\begin{array}{cl}x, & \text { if } 0 \leq x \leq 1 \\ x-1, & \text { if } x>1\end{array}\right.$. Calculate $\int_{0}^{1} \frac{f\left(e^{t}\right)}{f\left(e^{-t}\right)} \mathrm{d} t$.
|
\dfrac{(e-1)^2}{2}
|
0/8
|
2. In the positive term sequence $\left\{a_{n}\right\}$, $a_{1}=10, a_{n+1}=10 \sqrt{a_{n}}$, find the general formula for this sequence.
|
10^{2 - \left(\frac{1}{2}\right)^{n-1}}
|
5/8
|
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.