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10,11 |
A sphere is constructed with the height of a cone as its diameter. The surface area of the part of the sphere lying inside the cone is equal to the surface area of the part of the cone lying inside the sphere. Find the angle in the axial section of the cone.
|
2 \arcsin\left( \frac{\sqrt{5} - 1}{2} \right)
|
0/8
|
13.260. Two material particles, being 295 m apart from each other, started moving towards each other simultaneously. The first particle moves uniformly at a speed of $15 \mathrm{~m} / \mathrm{c}$, while the second particle moved 1 m in the first second and 3 m more in each subsequent second than in the previous one. Through what angle will the second hand of a clock move during the time that has passed from the start of the particles' movement until their meeting?
|
60
|
4/8
|
5. The power in the kingdom of gnomes was seized by giants. The giants decided to get rid of the gnomes and told them the following: "Tomorrow we will line you up so that each of you will see those who stand after and not see those who stand before (i.e., the 1st sees everyone, the last sees no one). We will put either a black or a white hat on each of you (equally likely, each will have either a black or a white hat) and ask what color it is. Those who answer correctly will be released, and those who answer incorrectly will be executed." How many gnomes can be risked at a minimum with certain agreements before the execution, if there are p gnomes in the kingdom and p $<\infty$. Justify your answer. (12 points)
#
|
1
|
3/8
|
Regarding natural numbers \( n \) and \( m \), it is known that \(\sqrt{3} - \frac{m}{n} > 0\).
Prove that \(\sqrt{3} - \frac{m}{n} > \frac{1}{2 m n}\).
|
\sqrt{3} - \frac{m}{n} > \frac{1}{2mn}
|
3/8
|
## Task B-4.5.
In triangle $A B C$, $\varangle C A B=50^{\circ}$ and $\varangle A B C=60^{\circ}$. On side $\overline{A B}$ there is a point $D$, and on side $\overline{B C}$ there is a point $E$ such that $\varangle C A E=\varangle A C D=30^{\circ}$. Calculate the measure of angle $\varangle C D E$.
|
40^\circ
|
3/8
|
A circle $k$ has its center at $O$, and points $A, B, C, D$ are consecutive points on the circumference of $k$, such that $\angle AOB = \angle BOC = \angle COD = \alpha < 60^{\circ}$. The projection of $D$ onto the diameter $AO$ is $E$, and the point $F$ is the closer trisection point of segment $DE$ to $E$. Finally, the intersection of $AO$ and $BF$ is $G$. What does the size of angle $OGD$ approach as $\alpha \rightarrow 60^{\circ}$?
|
60^\circ
|
3/8
|
3. Two spheres $O_{1}$ and $O_{2}$, both with a radius of 1, are tangent to each other, and they are also tangent to the two half-planes of a dihedral angle $\alpha-l-\beta$ of $60^{\circ}$. There is another larger sphere $O$ that is tangent to both half-planes of the dihedral angle and is externally tangent to spheres $O_{1}$ and $O_{2}$. What is the radius $R$ of sphere $O$?
|
\dfrac{5 + \sqrt{13}}{3}
|
0/8
|
Through the vertex \( A \) of the rectangle \( ABCD \), a line \( \ell \) is drawn, as shown in the figure. From points \( B \) and \( D \), perpendiculars \( BX \) and \( DY \) are dropped onto the line \( \ell \). Find the length of segment \( XY \) if it is known that \( BX = 4 \), \( DY = 10 \), and \( BC = 2 AB \).
|
13
|
0/8
|
Let the set \( M = \{1, 2, \cdots, 2020\} \). The subset \( A \subseteq M \) is such that for any element \( x \) in \( A \), \( 4x \) is not in \( A \). What is the maximum number of elements in the set \( A \)?
|
1616
|
3/8
|
As shown in the figure, Rourou's garden is a large rectangle composed of 4 square plots of land and 1 small rectangular pool. If the area of each plot of land is 20 square meters and the length of the garden is 9 meters, what is the perimeter of the pool (the shaded area in the figure)? ___ meters.
|
18
|
5/8
|
One hundred mathematicians attending an international combinatorial conference are being accommodated in a hotel where the rooms are numbered from 1 to 100. The reception plans to assign the mathematicians to rooms according to their arrival order and their corresponding room numbers. However, the first guest forgets the instruction and randomly chooses a room. The receptionist then instructs the subsequent guests to take the room corresponding to their arrival number sequentially and, if that room is occupied, to choose any free room that they like. In how many different ways could the guests occupy the rooms?
|
2^{99}
|
2/8
|
In triangle ABC, the median BM is drawn. It is known that \(\angle \mathrm{BAC} = 30^\circ\) and \(\angle \mathrm{BMC} = 45^\circ\). Find angle BAC.
|
105
|
0/8
|
In the pentagon \( U V W X Y \), \(\angle U = \angle V = 90^\circ \), \( U Y = V W \), and \( Y X = X W \). Four equally spaced points are marked between \( U \) and \( V \), and perpendiculars are drawn through each point. The dark shaded region has an area of \( 13 \mathrm{~cm}^2 \) and the light shaded region has an area of \( 10 \mathrm{~cm}^2 \). What is the area, in \(\mathrm{cm}^2\), of the entire pentagon?
A) 45
B) 47
C) 49
D) 58
E) 60
|
45
|
0/8
|
Dinesh has several squares and regular pentagons, all with side length $ 1$. He wants to arrange the shapes alternately to form a closed loop (see diagram). How many pentagons would Dinesh need to do so?
[img]https://cdn.artofproblemsolving.com/attachments/8/9/6345d7150298fe26cfcfba554656804ed25a6d.jpg[/img]
|
10
|
1/8
|
Example: There are 3 bags with 10 balls each of red, white, and black. If 16 balls are drawn from them, and it is required that all three colors are included, how many different ways are there to do this?
|
75
|
5/8
|
5. Let $P$ be a point inside an equilateral $\triangle A B C$, with $A P=3$, $B P=4$, $C P=5$. Then the area of quadrilateral $A B C P$ is $\qquad$
|
4\sqrt{3} +6
|
0/8
|
## Task 5 - 261245
Determine all natural numbers $n \geq 3$ for which the following statement holds:
Every plane convex $n$-gon $A_{1} A_{2} \ldots A_{n}$ is completely covered by the areas of the $n$ circles that have the segments $A_{i} A_{i+1}$ as diameters $\left(i=1,2, \ldots, n\right.$; set $A_{n+1}=A_{1}$).
Here, each $n$-gon area and each circle area are understood to include their boundary points.
|
4
|
2/8
|
# Assignment 4. 20 points
## Variant 1
In country Alpha, only two goods, X and Y, are produced from a single production factor - factor Z, of which there are exactly 100 units in Alpha. The amount of good X produced from factor Z can be described by the function $X=\frac{\sqrt{Z_{X}}}{2}$, and one unit of good Y is produced from each unit of factor Z. Country Alpha can buy and sell both goods on the world market at prices $P_{X}=8$ and $P_{Y}=1$. The residents of the country always consume goods in sets: for every 3 units of good X, 184 units of good Y are consumed. The government of the country is concerned only with ensuring that the residents can consume as many such sets of goods as possible.
(a) Find the quantities of goods X and Y that will be produced and consumed by the residents of this country. Graphically represent the found values and the production possibilities frontier of the country on one diagram.
(b) On the world market, an increase in the price of good X by a factor of $\alpha$ is expected, while it is known that the price of good Y will not change. Do you think that country Alpha can benefit from the increase in the price of good X? If it can, find all such values of $\alpha$ for which the country will benefit, or explain why Alpha cannot benefit from the increase in the price of good X.
|
X = 1
|
1/8
|
In the right-angled triangle $\mathrm{ABC}$, the angle at vertex $B$ is $30^{\circ}$. The center of the square constructed outward on the hypotenuse $\mathrm{ABC}$ is $D$. What is the measure of the angle $A D B$?
|
60^\circ
|
1/8
|
## Task 3 - 050713
The driver of a car registered in the GDR fled the scene after a traffic accident. After questioning several witnesses, the following information was obtained about the police registration number of the car:
a) The two letters of the license plate were AB or AD.
b) The two front digits were the same and different from the last two digits.
c) The number formed by the last two digits was 69 or 96.
What is the maximum possible number of cars that can meet these conditions?
|
32
|
0/8
|
$\mathbf{N 4 2}$ (37-4, Russia) Let positive integers $a, b$ be such that $15a + 16b$ and $16a - 15b$ are both squares of positive integers. Find the smallest value that the smaller of these two squares can take.
|
231361
|
3/8
|
1. Let $A B C D$ be a quadrilateral inscribed in a circle. Suppose $A B=$ $\sqrt{2+\sqrt{2}}$ and $A B$ subtends $135^{\circ}$ at the centre of the circle. Find the maximum possible area of $A B C D$.
|
\dfrac{5\sqrt{2} + 3\sqrt{6}}{8}
|
4/8
|
Let $S$ be a finite set of points in the plane, such that for each $2$ points $A$ and $B$ in $S$, the segment $AB$ is a side of a regular polygon all of whose vertices are contained in $S$. Find all possible values for the number of elements of $S$.
Proposed by [i]Viktor Simjanoski, Macedonia[/i]
|
3
|
2/8
|
Let $p$ be a prime number. How many monic polynomials are there in $\mathbb{Z} / p \mathbb{Z}$ of degree $p-2$ that have exactly $p-2$ distinct roots, and whose coefficients are all distinct and non-zero?
## Irreducibility
##
The translation is provided as requested, maintaining the original text's line breaks and format.
|
\phi(p-1)
|
2/8
|
Let $y(x)$ be the unique solution of the differential equation
$$
\frac{\mathrm{d} y}{\mathrm{~d} x}=\log _{e} \frac{y}{x}, \quad \text { where } x>0 \text { and } y>0,
$$
with the initial condition $y(1)=2018$.
How many positive real numbers $x$ satisfy the equation $y(x)=2000$ ?
|
1
|
4/8
|
Let \( a_n \) be the recurrence sequence defined by \( a_0 = 2 \) and \( a_{n+1} = 2a_n^2 - 1 \). Let \( N \geq 1 \) and \( p \) be a prime divisor of \( a_N \). Suppose there exists an integer \( x \) such that \( x^2 \equiv 3 \ (\bmod \ p) \). Show that \( 2^{N+2} \) divides \( p-1 \).
|
2^{N+2} \text{ divides } p-1
|
2/8
|
On an $n \times k$ chessboard, a bishop moves. The bishop starts from one of the light-colored corners and moves diagonally. When it reaches the edge of the board, it "bounces back". The movement ends when it reaches a corner again. For which pairs $(n, k)$ is it true that the bishop covers all light-colored squares?
|
\gcd(n-1, k-1) = 1
|
0/8
|
2. Usually, Dima leaves home at $8:10$ AM, gets into Uncle Vanya's car, who delivers him to school by a certain time. But on Thursday, Dima left home at 7:20 and ran in the opposite direction. Uncle Vanya waited for him and at $8:20$ drove after him, caught up with Dima, turned around, and delivered him to school 26 minutes late. How many times faster was Uncle Vanya's car speed compared to Dima's running speed?
|
\dfrac{17}{2}
|
0/8
|
10. Right triangle $X Y Z$ has right angle at $Y$ and $X Y=228, Y Z=$ 2004. Angle $Y$ is trisected, and the angle trisectors intersect $X Z$ at $P$ and $Q$ so that $X, P, Q, Z$ lie on $X Z$ in that order. Find the value of $(P Y+Y Z)(Q Y+X Y)$.
|
1370736
|
0/8
|
The 79 interns of the Animath internship each choose an activity for the free afternoon from 5 proposed activities. We know that:
- The swimming pool was at least as popular as football
- Students went shopping in groups of 5
- At most 4 students played cards
- At most one student stayed in their room
We write next to each activity the number of students who participated in it. How many different lists could we have written?
## Combinatorial identities
|
3240
|
4/8
|
4. Find the number of all 6-digit natural numbers such that the sum of their digits is 10 and each of the digits $0,1,2,3$ occurs at least once in them.
|
490
|
2/8
|
8. Find all integer values of the parameter \(a\) for which the system has at least one solution
\[
\left\{\begin{array}{l}
y-2=x(x+2) \\
x^{2}+a^{2}+2 x=y(2 a-y)
\end{array}\right.
\]
In the answer, specify the sum of the found values of the parameter \(a\).
|
3
|
5/8
|
It is a custom of five good friends that they wear a different tie each day, each one the one they wore the longest ago. Each of them has at least two ties, but none of them has a dozen. None of them has two ties of the same color, and there are no two of them who have the same number of ties. We have the following data from the last month of last year:
1. On December 1, Aladár wore a blue, Bandi and Feri wore red, Pista wore green, and Géza wore a yellow tie.
2. On December 19, Pista wore green, Géza wore yellow, Feri wore blue, and the other two wore red ties.
3. On December 23, Pista wore a white tie, and on December 26, he wore a yellow tie.
4. The colors of the ties worn on December 11 were: yellow, red, blue, green, and white.
5. On New Year's Eve, all five wore ties of the same color as on December 1.
Question: What tie did Bandi wear on January 1 of this year?
|
green
|
0/8
|
3.55. A truncated cone is described around a sphere, with the area of one base being 4 times larger than the area of the other. Find the angle between the slant height of the cone and the plane of its base.
## Group B
|
\arctan(2\sqrt{2})
|
3/8
|
## Task B-3.4.
While preparing for the competition, Matko discovered a bookstore with good mathematical literature. The bookstore offers 7 different books with problems only in geometry, 4 only in number theory, and 5 only in combinatorics. Furthermore, the store also offers books with problems from exactly two areas. Thus, there are 6 different books with problems in number theory and combinatorics, and 7 with problems in geometry and combinatorics. In how many ways can Matko choose literature from two of all the mentioned areas if he can buy at most two books?
|
270
|
0/8
|
7. The base $ABCD$ of the quadrilateral pyramid $P-ABCD$ is a rhombus with a top angle of $60^{\circ}$, and the angle between each side face and the base is $60^{\circ}$. There is a point $M$ inside the pyramid that is 1 unit away from the base and each side face. Then the volume of the pyramid is
|
8\sqrt{3}
|
5/8
|
2. Let $a_{1}, a_{2}, \ldots$ be a sequence of integers defined by $a_{1}=3, a_{2}=3$, and
$$
a_{n+2}=a_{n+1} a_{n}-a_{n+1}-a_{n}+2
$$
for all $n \geq 1$. Find the remainder when $a_{2020}$ is divided by 22 .
|
11
|
2/8
|
Let $K$ and $N > K$ be fixed positive integers. Let $n$ be a positive integer and let $a_1, a_2, ..., a_n$ be distinct integers. Suppose that whenever $m_1, m_2, ..., m_n$ are integers, not all equal to $0$, such that $\mid{m_i}\mid \le K$ for each $i$, then the sum
$$\sum_{i = 1}^{n} m_ia_i$$
is not divisible by $N$. What is the largest possible value of $n$?
[i]Proposed by Ilija Jovcevski, North Macedonia[/i]
|
\left\lfloor \log_{K+1} N \right\rfloor
|
1/8
|
10. Let the edge length of the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ be $1, \alpha$ be the plane passing through the line $B D_{1}$. Then the range of the area of the section cut by $\alpha$ on the cube is $\qquad$
|
\left[ \dfrac{\sqrt{6}}{2}, \sqrt{2} \right]
|
0/8
|
7. Given $S_{n}$ as the sum of the first $n$ terms of the sequence $\left\{a_{n}\right\}$, with the rule $S_{0}=0$. If for any $n \in \mathbf{Z}_{+}$, we have
$$
\begin{array}{l}
\frac{a_{n}}{2017}=-\frac{2017+S_{n-1}}{n}, \\
\text { then } \sum_{n=1}^{2017} 2^{n} a_{n}=
\end{array}
$$
|
-4034
|
1/8
|
In parallelogram $ABCD,$ let $O$ be the intersection of diagonals $\overline{AC}$ and $\overline{BD}$ . Angles $CAB$ and $DBC$ are each twice as large as angle $DBA,$ and angle $ACB$ is $r$ times as large as angle $AOB$ . Find the greatest integer that does not exceed $1000r$ .
Please give the answer directly without any intermediate steps.
|
777
|
1/8
|
1. As shown in the figure, divide a line segment of length 1 into segments $x$ and $y$. Then, bend the segment of length $x$ into a semicircle $A C B$, and fold the segment of length $y$ into three sides $(B D, D E, E A)$ of a rectangle $A B D E$ to form a closed "curved polygon" $A C B D E A$. The maximum value of the area of this curved polygon is . $\qquad$
|
\dfrac{1}{2(\pi +4)}
|
4/8
|
Bethany is told to create an expression from $2 \square 0 \square 1 \square 7$ by putting a + in one box, a in another, and $a x$ in the remaining box. There are 6 ways in which she can do this. She calculates the value of each expression and obtains a maximum value of $M$ and a minimum value of $m$. What is $M-m$ ?
|
15
|
2/8
|
3. In quadrilateral $A B C D$, it is known that $B C=8, C D=12$, $A D=10, \angle A=\angle B=60^{\circ}$. Then $A B=$
|
9 + \sqrt{141}
|
4/8
|
A group of 6 students decided to make [i]study groups[/i] and [i]service activity groups[/i] according to the following principle:
Each group must have exactly 3 members. For any pair of students, there are same number of study groups and service activity groups that both of the students are members.
Supposing there are at least one group and no three students belong to the same study group and service activity group, find the minimum number of groups.
|
8
|
0/8
|
There are 2011 positive numbers with both their sum and the sum of their reciprocals equal to 2012. Let $x$ be one of these numbers. Find the maximum value of $x + \frac{1}{x}.$The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.
|
10057
|
4/8
|
15. Three rectangular pieces of paper (Jia, Bing, Ding) and one square piece (Yi) can be combined to form a large rectangle with an area of 480 square centimeters. It is known that the areas of Yi, Bing, and Ding are all three times that of Jia. The total perimeter of the four rectangles Jia, Yi, Bing, and Ding is $\qquad$ centimeters.
|
184
|
1/8
|
520. A circle of radius $r$ is inscribed in a triangle with perimeter $p$ and area $S$. How are these three quantities related?
|
S = \frac{r \cdot p}{2}
|
0/8
|
61st Putnam 2000 Problem A3 An octagon is incribed in a circle. One set of alternate vertices forms a square area 5. The other set forms a rectangle area 4. What is the maximum possible area for the octagon? Solution
|
3\sqrt{5}
|
1/8
|
4. For a truncated triangular pyramid, the sides of the smaller base are $7 \mathrm{~cm}$, $5 \mathrm{~cm}$, and $3 \mathrm{~cm}$, and the lateral edges form an angle of $45^{\circ}$ with the plane of the larger base. Calculate the volume of the truncated pyramid if its height is $\frac{2}{3}$ of the height of the corresponding pyramid.
|
\dfrac{455}{2}
|
1/8
|
4. Given 100 lines on a plane, let $T$ denote the set of right-angled triangles formed by some three of these lines. Find the maximum value of $|T|$. (Supplied by Zou Jin)
|
62500
|
1/8
|
12. Chris planned a $210 \mathrm{~km}$ bike ride. However, he rode $5 \mathrm{~km} / \mathrm{h}$ faster than he planned and finished his ride 1 hour earlier than he planned. His average speed for the ride was $x \mathrm{~km} / \mathrm{h}$. What is the value of $x$ ?
|
35
|
4/8
|
19. As shown in the figure, in the dihedral angle $\alpha-E F-\beta$, $A E \subset \alpha, B F \subset \beta$, and $A E \perp E F, B F \perp E F, E F=1, A E=2, A B=$ $\sqrt{2}$, find the maximum volume of the tetrahedron $A B E F$.
|
\dfrac{1}{3}
|
5/8
|
Exercise 4. We want to color the three-element subsets of $\{1,2,3,4,5,6,7\}$ such that if two of these subsets have no element in common, then they must be of different colors. What is the minimum number of colors needed to achieve this goal?
|
3
|
5/8
|
4. The base of the oblique prism is a kite, which has a shorter diagonal of length e. The internal angles of the kite at the endpoints of the longer diagonal measure $90^{\circ}$ and $60^{\circ}$. The height of the prism is equal to the longer diagonal of the kite. Express the volume of the prism in terms of e. The result should be exact.
|
\dfrac{(2 + \sqrt{3})e^3}{4}
|
1/8
|
11. As shown in Figure 5, in quadrilateral $A B C D$, $\angle A=$ $\angle B C D=90^{\circ}, B C=$ $C D, E$ is a point on the extension of $A D$. If $D E=A B$ $=3, C E=4 \sqrt{2}$, then the length of $A D$ is
|
5
|
5/8
|
2.2. Given a convex pentagon $A B C D E$, such that
$$
A B=A E=D C=B C+D E=1 \text { and } \angle A B C=D E A=90^{\circ} .
$$
What is the area of this pentagon?
|
1
|
3/8
|
II. Fill-in-the-blank Questions (Full marks 54 points, each question 9 points)
1. Given a positive integer $n$ does not exceed 2000, and can be expressed as the sum of at least 60 consecutive positive integers, then the number of such $n$ is $\qquad$.
|
6
|
4/8
|
$\begin{array}{l}\text { 15. Find the value of } x^{2}+y^{2}+z^{2}+w^{3} \text { . If } \\ \frac{x^{2}}{\varepsilon^{2}-1^{2}}+\frac{y^{2}}{2^{2}-3^{2}}+\frac{z^{2}}{2^{2}-5^{2}} \\ +\frac{w^{2}}{2^{2}-7^{2}}=1, \\ \frac{x^{2}}{4^{2}-1^{2}}+\frac{y^{2}}{4^{2}-3^{2}}+\frac{z^{2}}{4^{2}-5^{2}} \\ +\frac{w^{2}}{4^{2}-7^{2}}=1, \\ \frac{x^{2}}{6^{2}-1^{2}}+\frac{y^{2}}{6^{2}-3^{2}}+\frac{z^{2}}{6^{2}-5^{2}}+\frac{w^{2}}{6^{2}-7^{2}}=1, \\ \frac{x^{2}}{8^{2}-1^{2}}+\frac{y^{2}}{8^{2}-3^{2}}+\frac{z^{2}}{8^{2}-5^{2}} \\ +\frac{w^{2}}{8^{2}-7^{2}}=1 .\end{array}$
|
36
|
0/8
|
Say a real number $r$ is \emph{repetitive} if there exist two distinct complex numbers $z_1, z_2$ with $|z_1| = |z_2| = 1$ and $\{z_1, z_2\} \neq \{-i, i\}$ such that:
\[
z_1(z_1^3 + z_1^2 + rz_1 + 1) = z_2(z_2^3 + z_2^2 + rz_2 + 1).
\]
There exist real numbers $a, b$ such that a real number $r$ is \emph{repetitive} if and only if $a < r \le b$. If the value of $|a| + |b|$ can be expressed in the form $\frac{p}{q}$ for relatively prime positive integers $p$ and $q$, find $100p + q$.
|
2504
|
0/8
|
Suppose that a planet contains $(CCAMATHBONANZA_{71})^{100}$ people ($100$ in decimal), where in base $71$ the digits $A, B, C, \ldots, Z$ represent the decimal numbers $10, 11, 12, \ldots, 35$, respectively. Suppose that one person on this planet is snapping, and each time they snap, at least half of the current population disappears. Estimate the largest number of times that this person can snap without disappearing. An estimate of $E$ earns $2^{1-\frac{1}{200}\left|A-E\right|}$ points, where $A$ is the actual answer.
|
8355
|
0/8
|
In triangle $ABC$ with centroid $G$ and circumcircle $\omega$, line $\overline{AG}$ intersects $BC$ at $D$ and $\omega$ at $P$. Given that $GD = DP = 3$, and $GC = 4$, find $AB^2$.
|
168
|
2/8
|
Tanya wrote numbers in the form $n^7 - 1$ for $n = 2, 3, \ldots$ and noticed that for $n = 8$, she obtained a number divisible by $337$. For what minimal $n$ did she get a number divisible by $2022$?
|
79
|
5/8
|
You are trapped in a room with only one exit, a long hallway with a series of doors and land mines. To get out, you must open all the doors and disarm all the mines. In the room, there is a panel with $3$ buttons, which conveniently contains an instruction manual:
- The red button arms a mine.
- The yellow button disarms two mines and closes a door.
- The green button opens two doors.
Initially, $3$ doors are closed, and $3$ mines are armed. The manual warns that attempting to disarm two mines or open two doors when only one is armed/closed will reset the system to its initial state. What is the minimum number of buttons you must push to get out?
|
9
|
4/8
|
Given a $2018 \times 4$ grid, tint the cells with red and blue such that each row and each column has an equal number of red and blue cells. Determine the number of ways, $M$, to tint the grid with the mentioned requirement and find $M \pmod{2018}$.
|
6
|
0/8
|
For a natural number $n$, define the function $f(n)$ as the sum of the digits of the number $n$. For example, $f(16) = 7$, $f(f(78)) = 6$, and $f(f(f(5978))) = 2$.
Find the smallest natural number $n$ such that $f(f(f(n)))$ is not a one-digit number.
|
20000000000000000000000
|
3/8
|
A trifecta is an ordered triple of positive integers \((a, b, c)\) with \(a < b < c\) such that \(a\) divides \(b\), \(b\) divides \(c\), and \(c\) divides \(ab\). What is the largest possible sum \(a + b + c\) over all trifectas of three-digit integers?
|
1736
|
3/8
|
Let $S_0 = 0$ and let $S_k$ equal $a_1 + 2a_2 + \ldots + ka_k$ for $k \geq 1$. Define $a_i$ to be $1$ if $S_{i-1} < i$ and $-1$ if $S_{i-1} \geq i$. What is the largest $k \leq 2010$ such that $S_k = 0$?
|
1092
|
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: `Arnold`, `Peter`, `Alice`, `Eric`
- Each person has a favorite color: `yellow`, `red`, `white`, `green`
- Everyone has a unique favorite cigar: `dunhill`, `blue master`, `pall mall`, `prince`
- Each person has a unique level of education: `high school`, `associate`, `master`, `bachelor`
## Clues:
1. The person whose favorite color is green is somewhere to the left of the person with a high school diploma.
2. Eric is the person whose favorite color is red.
3. There are two houses between Alice and the person who loves white.
4. The person who smokes Blue Master and the person partial to Pall Mall are next to each other.
5. The person who loves white is the person with a master's degree.
6. Arnold is in the fourth house.
7. The person who loves yellow is the person who smokes Blue Master.
8. The Dunhill smoker is Alice.
9. The person partial to Pall Mall is the person with a master's degree.
10. The person who loves yellow is the person with a bachelor's degree.
What is the value of attribute Name for the person whose attribute Education is bachelor? Please reason step by step, and put your final answer within \boxed{}
|
Peter
|
3/8
|
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 Education is bachelor? Please reason step by step, and put your final answer within \boxed{}
|
Fred
|
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`, `Eric`, `Peter`, `Alice`, `Arnold`
- Everyone has something unique for lunch: `pizza`, `spaghetti`, `grilled cheese`, `stew`, `stir fry`
- The people keep unique animals: `bird`, `horse`, `cat`, `fish`, `dog`
- Each person has a unique level of education: `master`, `doctorate`, `high school`, `associate`, `bachelor`
## Clues:
1. Alice is not in the fifth house.
2. The person who is a pizza lover is somewhere to the right of Peter.
3. Peter is in the first house.
4. The person with a bachelor's degree is the person who is a pizza lover.
5. The cat lover is the person with a master's degree.
6. The person who loves stir fry is the person with a doctorate.
7. The person with a high school diploma is directly left of the person with a master's degree.
8. The dog owner is the person who loves stir fry.
9. There is one house between Arnold and the person with an associate's degree.
10. The person who loves eating grilled cheese is the fish enthusiast.
11. Arnold is in the second house.
12. The person who keeps horses is Arnold.
13. Eric is directly left of the person with an associate's degree.
14. The person who loves the spaghetti eater is the cat lover.
What is the value of attribute Food for the person whose attribute Animal is dog? 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: `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 Food for the person whose attribute Cigar is blue master? Please reason step by step, and put your final answer within \boxed{}
|
stew
|
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`, `Peter`, `Bob`, `Alice`
- Each person has an occupation: `engineer`, `doctor`, `artist`, `lawyer`, `teacher`
- Each person prefers a unique type of vacation: `cruise`, `beach`, `city`, `camping`, `mountain`
## Clues:
1. The person who prefers city breaks is somewhere to the left of the person who is an engineer.
2. There are two houses between the person who likes going on cruises and the person who enjoys camping trips.
3. Bob is in the fourth house.
4. The person who is a doctor is not in the fifth house.
5. The person who likes going on cruises is in the first house.
6. There are two houses between the person who is a doctor and the person who is a lawyer.
7. The person who is a lawyer and Arnold are next to each other.
8. There is one house between Peter and the person who is a teacher.
9. The person who enjoys mountain retreats is somewhere to the left of the person who loves beach vacations.
10. Alice is somewhere to the left of the person who is a teacher.
11. There is one house between the person who prefers city breaks and Arnold.
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{}
|
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: `Peter`, `Arnold`, `Eric`, `Bob`, `Carol`, `Alice`
- Each person prefers a unique type of vacation: `cruise`, `beach`, `cultural`, `mountain`, `city`, `camping`
- People have unique hair colors: `gray`, `black`, `brown`, `blonde`, `auburn`, `red`
- People use unique phone models: `oneplus 9`, `huawei p50`, `xiaomi mi 11`, `iphone 13`, `google pixel 6`, `samsung galaxy s21`
- Each person has a unique favorite drink: `root beer`, `boba tea`, `milk`, `coffee`, `tea`, `water`
## Clues:
1. There is one house between the boba tea drinker and Bob.
2. There are two houses between the person who uses a Google Pixel 6 and the person who enjoys camping trips.
3. The person who goes on cultural tours is Carol.
4. The person who enjoys camping trips is Eric.
5. The person who uses a Google Pixel 6 is not in the fifth house.
6. The person who uses a OnePlus 9 and the person who goes on cultural tours are next to each other.
7. The person who has gray hair and the person who goes on cultural tours are next to each other.
8. The person who uses a Samsung Galaxy S21 is somewhere to the right of the person who has red hair.
9. The person who enjoys mountain retreats is somewhere to the right of the person who uses a Xiaomi Mi 11.
10. The person who uses a OnePlus 9 is Peter.
11. The person who likes going on cruises is the person who has brown hair.
12. The coffee drinker is the person who goes on cultural tours.
13. The person who likes milk is directly left of the person who has black hair.
14. The person who uses a Xiaomi Mi 11 is directly left of the person who uses a Samsung Galaxy S21.
15. The person who prefers city breaks is not in the sixth house.
16. The person who has blonde hair is Arnold.
17. The person who goes on cultural tours is not in the sixth house.
18. The one who only drinks water and the person who goes on cultural tours are next to each other.
19. The tea drinker is somewhere to the left of the person who enjoys mountain retreats.
20. The person who likes milk is the person who uses a Huawei P50.
21. The person who has blonde hair is directly left of the person who has gray hair.
22. Bob is not in the third house.
23. Peter is the person who prefers city breaks.
What is the value of attribute HairColor for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{}
|
red
|
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`, `Arnold`, `Carol`, `Alice`, `Eric`, `Bob`
- People have unique favorite music genres: `pop`, `hip hop`, `rock`, `jazz`, `classical`, `country`
- The people keep unique animals: `fish`, `dog`, `cat`, `rabbit`, `horse`, `bird`
- Each person lives in a unique style of house: `modern`, `colonial`, `mediterranean`, `ranch`, `victorian`, `craftsman`
- Each person has a unique hobby: `gardening`, `woodworking`, `knitting`, `cooking`, `painting`, `photography`
- The people are of nationalities: `brit`, `german`, `norwegian`, `swede`, `dane`, `chinese`
## Clues:
1. The cat lover is the person in a Mediterranean-style villa.
2. The person who loves country music is somewhere to the right of the rabbit owner.
3. The person who loves pop music is not in the second house.
4. Alice is somewhere to the right of Arnold.
5. The person who loves jazz music and the photography enthusiast are next to each other.
6. The person who loves rock music is the German.
7. The woodworking hobbyist is somewhere to the right of the person in a modern-style house.
8. The person who loves hip-hop music is the Norwegian.
9. The cat lover is somewhere to the left of the woodworking hobbyist.
10. Alice is the person who paints as a hobby.
11. The person in a Craftsman-style house is Carol.
12. Peter is the fish enthusiast.
13. The person who loves hip-hop music is not in the fifth house.
14. The person who loves pop music is not in the sixth house.
15. The person who loves cooking is somewhere to the left of the Swedish person.
16. The Dane is directly left of the person who keeps horses.
17. The rabbit owner is somewhere to the left of the British person.
18. There is one house between Alice and the person who loves country music.
19. The person who paints as a hobby is the person living in a colonial-style house.
20. The German is somewhere to the left of the photography enthusiast.
21. Eric is the Norwegian.
22. The person residing in a Victorian house is directly left of the person who enjoys gardening.
23. There are two houses between the person who loves cooking and the person who loves classical music.
24. The bird keeper is the person who loves cooking.
25. The cat lover is directly left of Bob.
26. Eric is not in the first house.
27. Carol is somewhere to the right of the German.
28. The rabbit owner is directly left of the person in a modern-style house.
What is the value of attribute House for the person whose attribute HouseStyle is colonial? Please reason step by step, and put your final answer within \boxed{}
|
4
|
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: `Peter`, `Alice`, `Bob`, `Eric`, `Arnold`
- The people are of nationalities: `dane`, `swede`, `norwegian`, `brit`, `german`
- Everyone has a favorite smoothie: `desert`, `cherry`, `watermelon`, `dragonfruit`, `lime`
- They all have a unique favorite flower: `tulips`, `roses`, `daffodils`, `carnations`, `lilies`
- Each person lives in a unique style of house: `ranch`, `modern`, `victorian`, `colonial`, `craftsman`
- The people keep unique animals: `dog`, `horse`, `bird`, `fish`, `cat`
## Clues:
1. The person living in a colonial-style house is Peter.
2. The person who keeps horses is the person who drinks Lime smoothies.
3. Alice is the British person.
4. The Swedish person is in the first house.
5. The person who keeps horses and the dog owner are next to each other.
6. There is one house between the person in a Craftsman-style house and the Dane.
7. The person who loves the boquet of lilies is directly left of the fish enthusiast.
8. The person who loves the boquet of lilies is the person in a modern-style house.
9. The Desert smoothie lover is in the first house.
10. The person residing in a Victorian house is somewhere to the right of the Watermelon smoothie lover.
11. The person who loves a bouquet of daffodils is Alice.
12. The Dragonfruit smoothie lover is not in the third house.
13. The person who loves a carnations arrangement is the German.
14. The Dragonfruit smoothie lover is Eric.
15. Bob is somewhere to the right of the person who loves the rose bouquet.
16. The Watermelon smoothie lover is the Norwegian.
17. Bob is the person in a modern-style house.
18. The person residing in a Victorian house is not in the fifth house.
19. The person who loves a carnations arrangement is somewhere to the left of the person in a modern-style house.
20. The Desert smoothie lover is the bird keeper.
What is the value of attribute HouseStyle for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}
|
modern
|
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: `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 Name for the person whose attribute Nationality is norwegian? Please reason step by step, and put your final answer within \boxed{}
|
Peter
|
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`
- People have unique hair colors: `black`, `blonde`, `brown`, `red`
- People own unique car models: `tesla model 3`, `ford f150`, `honda civic`, `toyota camry`
## Clues:
1. Eric is somewhere to the right of Alice.
2. The person who has red hair is somewhere to the right of Eric.
3. Alice is not in the second house.
4. The person who owns a Honda Civic is somewhere to the left of the person who has brown hair.
5. The person who has red hair is in the fourth house.
6. The person who has blonde hair is the person who owns a Tesla Model 3.
7. Arnold is not in the second house.
8. Arnold is not in the fourth house.
9. The person who owns a Ford F-150 is in the second house.
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
|
5/8
|
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`
- Everyone has a unique favorite cigar: `prince`, `blue master`, `pall mall`
## Clues:
1. Arnold is not in the third house.
2. Arnold is somewhere to the right of the person partial to Pall Mall.
3. There is one house between Eric and the person who smokes Blue Master.
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
|
5/8
|
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`, `Bob`, `Alice`, `Eric`, `Peter`
- The people are of nationalities: `dane`, `swede`, `german`, `brit`, `norwegian`
- Each person has a unique hobby: `gardening`, `painting`, `knitting`, `photography`, `cooking`
- Everyone has a favorite smoothie: `dragonfruit`, `lime`, `watermelon`, `desert`, `cherry`
- People have unique hair colors: `brown`, `gray`, `black`, `blonde`, `red`
- People have unique favorite sports: `baseball`, `soccer`, `swimming`, `tennis`, `basketball`
## Clues:
1. The person who loves cooking is not in the second house.
2. The Watermelon smoothie lover is not in the fourth house.
3. The person who loves baseball is somewhere to the right of the Desert smoothie lover.
4. The person who drinks Lime smoothies is the person who has brown hair.
5. The person who has gray hair is somewhere to the right of the Swedish person.
6. The photography enthusiast is not in the fifth house.
7. The Swedish person is not in the first house.
8. The German is the person who has blonde hair.
9. There is one house between the Watermelon smoothie lover and the photography enthusiast.
10. Alice and the person who drinks Lime smoothies are next to each other.
11. The British person and the person who enjoys knitting are next to each other.
12. The person who has black hair is the Swedish person.
13. The British person is the person who enjoys gardening.
14. The person who loves swimming is the person who loves cooking.
15. The Dragonfruit smoothie lover is not in the third house.
16. The Watermelon smoothie lover is not in the second house.
17. Eric is somewhere to the left of the person who drinks Lime smoothies.
18. The person who loves soccer is Alice.
19. Peter is the photography enthusiast.
20. The person who enjoys gardening is directly left of the person who loves tennis.
21. The Norwegian and the photography enthusiast are next to each other.
22. The British person is Alice.
23. Bob is the person who has blonde hair.
What is the value of attribute FavoriteSport for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}
|
soccer
|
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`, `Bob`, `Alice`, `Eric`, `Carol`
- The mothers' names in different houses are unique: `Holly`, `Aniya`, `Kailyn`, `Janelle`, `Penny`, `Sarah`
- Everyone has something unique for lunch: `stir fry`, `stew`, `spaghetti`, `soup`, `pizza`, `grilled cheese`
- The people keep unique animals: `dog`, `horse`, `cat`, `fish`, `rabbit`, `bird`
- Everyone has a favorite smoothie: `watermelon`, `desert`, `lime`, `cherry`, `blueberry`, `dragonfruit`
- Each person lives in a unique style of house: `mediterranean`, `craftsman`, `victorian`, `colonial`, `modern`, `ranch`
## Clues:
1. The person whose mother's name is Penny is the person residing in a Victorian house.
2. The person in a modern-style house is The person whose mother's name is Kailyn.
3. The person in a modern-style house is somewhere to the right of the person residing in a Victorian house.
4. The person who drinks Blueberry smoothies is not in the sixth house.
5. The person whose mother's name is Sarah is the person who drinks Blueberry smoothies.
6. The person who likes Cherry smoothies is not in the third house.
7. The person who likes Cherry smoothies is Eric.
8. The person whose mother's name is Janelle is not in the third house.
9. The person who loves the spaghetti eater is in the third house.
10. The fish enthusiast is The person whose mother's name is Holly.
11. The person who keeps horses is in the first house.
12. The person in a Mediterranean-style villa is the person who loves the stew.
13. The bird keeper is in the third house.
14. The person living in a colonial-style house is the person who drinks Blueberry smoothies.
15. Carol is the person who keeps horses.
16. There are two houses between the Desert smoothie lover and Peter.
17. The person who loves eating grilled cheese is the Dragonfruit smoothie lover.
18. The person who is a pizza lover is somewhere to the right of the Dragonfruit smoothie lover.
19. The person whose mother's name is Janelle is somewhere to the left of Arnold.
20. Carol is directly left of The person whose mother's name is Aniya.
21. The person in a ranch-style home is The person whose mother's name is Aniya.
22. Arnold is somewhere to the right of the person in a Craftsman-style house.
23. The cat lover is Bob.
24. There is one house between the Watermelon smoothie lover and the person who is a pizza lover.
25. There are two houses between the cat lover and the person who loves stir fry.
26. Arnold is the rabbit owner.
27. Peter is The person whose mother's name is Janelle.
What is the value of attribute House for the person whose attribute Smoothie is dragonfruit? 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: `Bob`, `Arnold`, `Peter`, `Alice`, `Eric`
- Each person has a unique favorite drink: `milk`, `root beer`, `coffee`, `tea`, `water`
- Each person has a favorite color: `blue`, `green`, `white`, `yellow`, `red`
- They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `tulips`, `carnations`
- Each person has a unique hobby: `painting`, `cooking`, `photography`, `gardening`, `knitting`
## Clues:
1. Alice is not in the fourth house.
2. The root beer lover is the person who enjoys gardening.
3. The person whose favorite color is green is the coffee drinker.
4. The person whose favorite color is green is the person who loves the boquet of lilies.
5. The person who loves blue is somewhere to the right of the person who loves a bouquet of daffodils.
6. The person who loves cooking is the person who loves blue.
7. Eric is directly left of the tea drinker.
8. The one who only drinks water is Peter.
9. Arnold is the photography enthusiast.
10. The person who loves white is the person who loves the rose bouquet.
11. There is one house between the person who loves a carnations arrangement and the person whose favorite color is red.
12. The person who loves cooking is somewhere to the left of the person who paints as a hobby.
13. The one who only drinks water is in the third house.
14. The person who loves a carnations arrangement is the root beer lover.
15. The person who loves white is in the second house.
What is the value of attribute Color for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}
|
yellow
|
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`, `Bob`, `Peter`, `Eric`, `Arnold`
- They all have a unique favorite flower: `lilies`, `tulips`, `roses`, `daffodils`, `iris`, `carnations`
- The people are of nationalities: `norwegian`, `dane`, `swede`, `german`, `brit`, `chinese`
- Everyone has a favorite smoothie: `cherry`, `watermelon`, `desert`, `dragonfruit`, `blueberry`, `lime`
- Each person has a unique hobby: `photography`, `cooking`, `knitting`, `woodworking`, `painting`, `gardening`
- Each person has a unique type of pet: `rabbit`, `hamster`, `fish`, `cat`, `bird`, `dog`
## Clues:
1. The Swedish person is the person who loves cooking.
2. The person who drinks Blueberry smoothies is Alice.
3. The person who loves the rose bouquet is not in the sixth house.
4. The photography enthusiast is somewhere to the right of the Dragonfruit smoothie lover.
5. The person who loves cooking is the person who loves a bouquet of daffodils.
6. The person who loves the boquet of lilies and the person who loves the boquet of iris are next to each other.
7. The person who paints as a hobby is Alice.
8. Arnold is somewhere to the right of the Watermelon smoothie lover.
9. The woodworking hobbyist is somewhere to the right of the German.
10. The woodworking hobbyist is somewhere to the left of the person who loves a bouquet of daffodils.
11. The Dane is the Watermelon smoothie lover.
12. The Dragonfruit smoothie lover is Peter.
13. The person who drinks Lime smoothies is the woodworking hobbyist.
14. There is one house between the Watermelon smoothie lover and the person who likes Cherry smoothies.
15. The person who keeps a pet bird is the person who drinks Blueberry smoothies.
16. The Desert smoothie lover is the person who enjoys gardening.
17. The person with a pet hamster is in the fifth house.
18. The person who owns a dog is the Norwegian.
19. The person who has a cat is somewhere to the right of Bob.
20. The British person is directly left of Carol.
21. The person who loves the boquet of iris is Arnold.
22. The German is somewhere to the right of the person who loves a carnations arrangement.
23. Bob is the photography enthusiast.
24. The person with an aquarium of fish is Arnold.
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{}
|
6
|
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`, `Eric`, `Peter`
- People use unique phone models: `xiaomi mi 11`, `iphone 13`, `huawei p50`, `google pixel 6`, `oneplus 9`, `samsung galaxy s21`
- People have unique favorite book genres: `science fiction`, `fantasy`, `mystery`, `historical fiction`, `romance`, `biography`
## Clues:
1. Bob is somewhere to the left of the person who uses a Samsung Galaxy S21.
2. The person who uses a OnePlus 9 is Alice.
3. The person who loves romance books is Alice.
4. The person who loves biography books is Bob.
5. The person who loves science fiction books is Arnold.
6. Eric is somewhere to the left of the person who uses a Google Pixel 6.
7. There is one house between Eric and Peter.
8. The person who loves fantasy books is Carol.
9. The person who loves science fiction books and the person who uses a Huawei P50 are next to each other.
10. The person who uses a Huawei P50 and the person who loves fantasy books are next to each other.
11. The person who loves romance books is directly left of the person who loves science fiction books.
12. The person who uses a Xiaomi Mi 11 is in the sixth house.
13. The person who loves historical fiction books is not in the fourth house.
What is the value of attribute House for the person whose attribute PhoneModel is samsung galaxy s21? 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: `Carol`, `Peter`, `Arnold`, `Bob`, `Eric`, `Alice`
- People use unique phone models: `iphone 13`, `google pixel 6`, `oneplus 9`, `huawei p50`, `samsung galaxy s21`, `xiaomi mi 11`
- People have unique hair colors: `gray`, `auburn`, `red`, `brown`, `black`, `blonde`
- Each person has a unique favorite drink: `coffee`, `water`, `root beer`, `tea`, `milk`, `boba tea`
- People have unique favorite music genres: `classical`, `jazz`, `rock`, `country`, `hip hop`, `pop`
## Clues:
1. Alice is the person who uses a Huawei P50.
2. The person who uses a Xiaomi Mi 11 is somewhere to the left of the one who only drinks water.
3. The one who only drinks water is somewhere to the left of Bob.
4. Carol is the person who has gray hair.
5. Eric is the tea drinker.
6. The person who has black hair is not in the sixth house.
7. The person who uses a Samsung Galaxy S21 is directly left of the person who loves classical music.
8. The person who uses a OnePlus 9 is not in the third house.
9. Alice is somewhere to the right of Carol.
10. The person who loves jazz music is Alice.
11. The person who loves jazz music is the boba tea drinker.
12. There is one house between the person who uses a OnePlus 9 and Eric.
13. The person who has brown hair is the person who loves hip-hop music.
14. The person who loves pop music is not in the first house.
15. The root beer lover is in the second house.
16. Eric is the person who uses an iPhone 13.
17. The person who has red hair is the person who uses an iPhone 13.
18. The person who has red hair and the coffee drinker are next to each other.
19. Peter is in the first house.
20. Arnold is somewhere to the right of the person who has auburn hair.
21. The person who has gray hair is not in the second house.
22. The person who loves country music is in the fifth house.
What is the value of attribute House for the person whose attribute Drink is root beer? Please reason step by step, and put your final answer within \boxed{}
|
2
|
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`, `Arnold`, `Alice`
- People have unique favorite music genres: `pop`, `classical`, `jazz`, `rock`
- Each person has a unique hobby: `cooking`, `gardening`, `painting`, `photography`
- Each person has a unique level of education: `master`, `associate`, `high school`, `bachelor`
- Each person has a unique type of pet: `fish`, `bird`, `dog`, `cat`
## Clues:
1. The person who loves classical music is not in the fourth house.
2. Arnold is the person with a master's degree.
3. Alice is the person who owns a dog.
4. The person who enjoys gardening is not in the third house.
5. The person with a bachelor's degree is Alice.
6. Alice is the photography enthusiast.
7. Arnold is directly left of the person who loves pop music.
8. The person with an associate's degree is directly left of the photography enthusiast.
9. The person who loves rock music is the person who loves cooking.
10. The person with an associate's degree is Eric.
11. The person who has a cat is the person who loves jazz music.
12. Arnold is somewhere to the right of the person with an aquarium of fish.
What is the value of attribute House for the person whose attribute MusicGenre is classical? Please reason step by step, and put your final answer within \boxed{}
|
2
|
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`, `Eric`, `Peter`, `Bob`, `Carol`
- People use unique phone models: `huawei p50`, `iphone 13`, `xiaomi mi 11`, `samsung galaxy s21`, `google pixel 6`, `oneplus 9`
## Clues:
1. The person who uses an iPhone 13 is not in the third house.
2. There are two houses between Eric and Peter.
3. Bob is somewhere to the left of the person who uses a Samsung Galaxy S21.
4. There is one house between Eric and Alice.
5. The person who uses a OnePlus 9 is in the second house.
6. The person who uses a Samsung Galaxy S21 is not in the third house.
7. The person who uses a Xiaomi Mi 11 is in the sixth house.
8. The person who uses a Huawei P50 is not in the fifth house.
9. The person who uses an iPhone 13 and Bob are next to each other.
10. The person who uses a Samsung Galaxy S21 is not in the fifth house.
11. The person who uses a Google Pixel 6 is Carol.
12. Arnold is somewhere to the right of Eric.
13. Arnold is not in the fourth house.
What is the value of attribute House for the person whose attribute PhoneModel is iphone 13? 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: `Bob`, `Alice`, `Peter`, `Eric`, `Arnold`, `Carol`
- Each mother is accompanied by their child: `Fred`, `Timothy`, `Samantha`, `Alice`, `Meredith`, `Bella`
- People have unique favorite music genres: `pop`, `hip hop`, `classical`, `jazz`, `rock`, `country`
- People have unique heights: `average`, `very tall`, `tall`, `super tall`, `very short`, `short`
## Clues:
1. There is one house between the person's child is named Samantha and the person who is short.
2. The person's child is named Alice is Bob.
3. The person who loves country music is directly left of Arnold.
4. Alice is the person who is tall.
5. The person who loves pop music is Eric.
6. Bob is somewhere to the right of the person who is super tall.
7. The person's child is named Fred is Peter.
8. The person's child is named Bella is the person who loves hip-hop music.
9. The person who is the mother of Timothy is not in the sixth house.
10. The person who is super tall is somewhere to the right of the person who has an average height.
11. The person's child is named Alice is somewhere to the right of Arnold.
12. There is one house between the person who is short and the person who is very short.
13. The person who is very short is in the fifth house.
14. The person who loves jazz music is not in the fifth house.
15. Carol is somewhere to the left of the person who is the mother of Timothy.
16. The person who is very tall is not in the sixth house.
17. The person who loves classical music is in the sixth house.
18. The person who loves rock music is in the first house.
What is the value of attribute MusicGenre for the person whose attribute Children is Bella? Please reason step by step, and put your final answer within \boxed{}
|
hip hop
|
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`, `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 Occupation for the person whose attribute Height is short? Please reason step by step, and put your final answer within \boxed{}
|
teacher
|
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: `Alice`, `Arnold`, `Peter`, `Eric`, `Bob`, `Carol`
- People have unique favorite sports: `baseball`, `tennis`, `swimming`, `basketball`, `soccer`, `volleyball`
## Clues:
1. The person who loves tennis is Eric.
2. The person who loves volleyball is in the fifth house.
3. Arnold is somewhere to the right of Carol.
4. Carol is not in the first house.
5. The person who loves baseball is Bob.
6. There is one house between the person who loves swimming and the person who loves basketball.
7. Alice is in the fourth house.
8. The person who loves swimming is Peter.
9. Alice and Arnold are next to each other.
10. Peter is somewhere to the right of Eric.
11. The person who loves swimming is not in the sixth house.
What is the value of attribute House for the person whose attribute FavoriteSport is baseball? Please reason step by step, and put your final answer within \boxed{}
|
6
|
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: `Alice`, `Arnold`, `Eric`, `Peter`
- Each person has a unique level of education: `master`, `bachelor`, `associate`, `high school`
- People have unique favorite sports: `tennis`, `soccer`, `swimming`, `basketball`
- Each person has an occupation: `teacher`, `engineer`, `doctor`, `artist`
- They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`, `roses`
- People have unique heights: `very short`, `average`, `tall`, `short`
## Clues:
1. Eric is the person who loves a carnations arrangement.
2. The person who loves swimming is somewhere to the left of the person who is an artist.
3. Arnold is directly left of the person who is tall.
4. The person who loves swimming and the person who is a teacher are next to each other.
5. The person who loves basketball is the person with a bachelor's degree.
6. The person who is a doctor is the person who loves the rose bouquet.
7. The person who loves the boquet of lilies is the person who loves tennis.
8. The person who loves a carnations arrangement is the person with a master's degree.
9. The person who is a teacher is directly left of Alice.
10. The person who is an artist is the person with an associate's degree.
11. The person who loves a bouquet of daffodils is the person who is an artist.
12. The person who loves soccer is not in the fourth house.
13. The person who loves a bouquet of daffodils is somewhere to the right of the person who is short.
14. The person with a master's degree is the person who is very short.
What is the value of attribute Education for the person whose attribute FavoriteSport is swimming? 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: `Eric`, `Bob`, `Carol`, `Arnold`, `Peter`, `Alice`
- Everyone has a unique favorite cigar: `blends`, `prince`, `dunhill`, `yellow monster`, `blue master`, `pall mall`
- People have unique hair colors: `auburn`, `gray`, `blonde`, `black`, `red`, `brown`
- Each person has a unique favorite drink: `boba tea`, `root beer`, `water`, `tea`, `coffee`, `milk`
- Each person has an occupation: `artist`, `nurse`, `teacher`, `doctor`, `engineer`, `lawyer`
## Clues:
1. Bob is the tea drinker.
2. The Dunhill smoker is not in the second house.
3. There is one house between Carol and Arnold.
4. The Prince smoker is the person who has black hair.
5. The person who has auburn hair is not in the third house.
6. Arnold is in the fourth house.
7. The Prince smoker is not in the fourth house.
8. The person who is an artist is the person partial to Pall Mall.
9. The person who is an engineer is directly left of the root beer lover.
10. The boba tea drinker is the person who has brown hair.
11. The person who is a lawyer is in the fifth house.
12. The person who is an engineer is the person who smokes Blue Master.
13. The person who likes milk is the person who has auburn hair.
14. Alice is somewhere to the left of the person who is a teacher.
15. The person who has blonde hair is the person who smokes Yellow Monster.
16. The person who has black hair is the person who is a doctor.
17. Arnold is somewhere to the right of the person who has gray hair.
18. The person who has auburn hair is not in the first house.
19. The one who only drinks water is the person who smokes many unique blends.
20. The person who smokes many unique blends is somewhere to the right of the person who has brown hair.
21. Arnold is the root beer lover.
22. The person who has brown hair is not in the third house.
23. The person who smokes many unique blends is somewhere to the left of Peter.
24. The person who likes milk is somewhere to the left of the person who has blonde hair.
What is the value of attribute Drink for the person whose attribute Cigar is blends? Please reason step by step, and put your final answer within \boxed{}
|
water
|
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`, `Alice`, `Peter`, `Eric`
- People own unique car models: `ford f150`, `tesla model 3`, `toyota camry`, `honda civic`
- Each person has a unique birthday month: `april`, `sept`, `feb`, `jan`
- Each person has an occupation: `teacher`, `artist`, `engineer`, `doctor`
- Everyone has something unique for lunch: `pizza`, `stew`, `spaghetti`, `grilled cheese`
## Clues:
1. The person who owns a Toyota Camry is in the first house.
2. Eric and the person who loves the spaghetti eater are next to each other.
3. The person who is an engineer is the person who loves eating grilled cheese.
4. Peter is the person who owns a Toyota Camry.
5. The person whose birthday is in April is directly left of the person whose birthday is in February.
6. The person who is a doctor is somewhere to the right of the person who is an artist.
7. The person who owns a Ford F-150 is the person who is a doctor.
8. The person whose birthday is in September is somewhere to the left of Alice.
9. Arnold is the person who is an artist.
10. The person who loves the spaghetti eater is the person who owns a Ford F-150.
11. The person who is an engineer is the person whose birthday is in April.
12. The person whose birthday is in February and the person who is a pizza lover are next to each other.
13. The person who owns a Honda Civic is Eric.
What is the value of attribute Food for the person whose attribute Birthday is april? Please reason step by step, and put your final answer within \boxed{}
|
grilled cheese
|
1/8
|
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`
- People have unique favorite sports: `basketball`, `swimming`, `soccer`, `tennis`
- People have unique hair colors: `black`, `brown`, `blonde`, `red`
- Each person has a favorite color: `yellow`, `red`, `white`, `green`
- The people are of nationalities: `dane`, `norwegian`, `brit`, `swede`
- Each person has a unique birthday month: `april`, `feb`, `jan`, `sept`
## Clues:
1. The person who has brown hair is in the first house.
2. The person who loves soccer is directly left of the person who loves tennis.
3. The person who has brown hair is directly left of Eric.
4. The person who has blonde hair is somewhere to the left of the British person.
5. The person who loves white is directly left of the Norwegian.
6. The person who has blonde hair and Arnold are next to each other.
7. The person whose birthday is in January is the Swedish person.
8. The person whose birthday is in April is the British person.
9. The person who loves basketball is somewhere to the right of the person who has black hair.
10. The person who has brown hair and the person who loves yellow are next to each other.
11. The person who loves swimming is Peter.
12. The person whose favorite color is red is Peter.
13. The person who has blonde hair is the Swedish person.
14. Eric is the person whose birthday is in February.
What is the value of attribute Color for the person whose attribute Nationality is dane? Please reason step by step, and put your final answer within \boxed{}
|
white
|
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`, `Bob`, `Arnold`, `Carol`
- Everyone has a unique favorite cigar: `pall mall`, `yellow monster`, `dunhill`, `blue master`, `prince`, `blends`
- People have unique favorite music genres: `hip hop`, `jazz`, `country`, `pop`, `classical`, `rock`
- Each person has a unique favorite drink: `water`, `milk`, `boba tea`, `tea`, `root beer`, `coffee`
- The mothers' names in different houses are unique: `Kailyn`, `Penny`, `Janelle`, `Holly`, `Sarah`, `Aniya`
- Everyone has something unique for lunch: `soup`, `pizza`, `spaghetti`, `stir fry`, `stew`, `grilled cheese`
## Clues:
1. Carol is directly left of the person who loves eating grilled cheese.
2. Eric is not in the second house.
3. The person whose mother's name is Holly is somewhere to the right of Carol.
4. The person who loves eating grilled cheese is somewhere to the right of the person who loves rock music.
5. Eric is directly left of Carol.
6. The person who loves pop music is not in the third house.
7. Eric is the person who loves country music.
8. The person who loves classical music is in the sixth house.
9. The coffee drinker is Bob.
10. The person who smokes many unique blends is Peter.
11. The person who loves the stew is not in the fifth house.
12. The root beer lover is directly left of The person whose mother's name is Janelle.
13. There are two houses between The person whose mother's name is Sarah and the person who smokes Yellow Monster.
14. Eric is the tea drinker.
15. The person partial to Pall Mall is somewhere to the right of the person who loves stir fry.
16. The person who loves the soup is Bob.
17. The person who loves hip-hop music is directly left of The person whose mother's name is Kailyn.
18. Arnold is somewhere to the right of The person whose mother's name is Kailyn.
19. The one who only drinks water is directly left of the person who smokes Blue Master.
20. The person who loves the spaghetti eater is somewhere to the left of the person who smokes many unique blends.
21. The person whose mother's name is Sarah is directly left of the person who loves jazz music.
22. The person who loves hip-hop music is directly left of the root beer lover.
23. The one who only drinks water is the person who loves the stew.
24. The Dunhill smoker is not in the second house.
25. The person who likes milk is The person whose mother's name is Janelle.
26. Eric is The person whose mother's name is Aniya.
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
|
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 Children for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}
|
Timothy
|
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 Vacation for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}
|
mountain
|
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`, `Bob`, `Arnold`, `Carol`
- People have unique favorite book genres: `mystery`, `fantasy`, `romance`, `historical fiction`, `science fiction`, `biography`
- Everyone has a favorite smoothie: `cherry`, `desert`, `lime`, `watermelon`, `blueberry`, `dragonfruit`
- The people keep unique animals: `fish`, `rabbit`, `bird`, `cat`, `horse`, `dog`
- People have unique favorite music genres: `classical`, `hip hop`, `country`, `jazz`, `rock`, `pop`
- Everyone has a unique favorite cigar: `prince`, `dunhill`, `blends`, `pall mall`, `blue master`, `yellow monster`
## Clues:
1. The person who smokes many unique blends is the person who loves fantasy books.
2. The person who loves biography books is the Desert smoothie lover.
3. There are two houses between the person who loves pop music and the person who loves country music.
4. The rabbit owner is in the third house.
5. Arnold is the bird keeper.
6. The person who loves country music is in the fifth house.
7. The person who loves mystery books is not in the first house.
8. The person who drinks Lime smoothies is not in the third house.
9. The fish enthusiast is somewhere to the right of the person who loves rock music.
10. The Prince smoker is somewhere to the left of the person who likes Cherry smoothies.
11. Bob is the cat lover.
12. Eric is the person who likes Cherry smoothies.
13. The person who smokes Yellow Monster is in the sixth house.
14. The Prince smoker is the Dragonfruit smoothie lover.
15. Carol is directly left of Arnold.
16. The person who smokes Blue Master is directly left of the person who loves classical music.
17. The person who loves classical music is the person who loves historical fiction books.
18. The Dunhill smoker and the person who loves science fiction books are next to each other.
19. The person who keeps horses is directly left of Peter.
20. The Watermelon smoothie lover is the cat lover.
21. The person who smokes many unique blends is directly left of the person who loves jazz music.
22. The cat lover is in the first house.
23. The Desert smoothie lover is the person who loves jazz music.
24. The person who drinks Lime smoothies is directly left of the fish enthusiast.
25. The person who smokes Blue Master is not in the fifth house.
What is the value of attribute House for the person whose attribute Smoothie is cherry? Please reason step by step, and put your final answer within \boxed{}
|
6
|
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`, `Bob`, `Peter`, `Arnold`, `Alice`
- Each person prefers a unique type of vacation: `cultural`, `beach`, `mountain`, `cruise`, `camping`, `city`
- The people are of nationalities: `chinese`, `brit`, `norwegian`, `swede`, `dane`, `german`
- Everyone has a favorite smoothie: `lime`, `desert`, `watermelon`, `blueberry`, `dragonfruit`, `cherry`
## Clues:
1. The person who likes Cherry smoothies is the person who enjoys mountain retreats.
2. Eric is the Dane.
3. The German is Peter.
4. The Desert smoothie lover is in the sixth house.
5. The Swedish person is the Dragonfruit smoothie lover.
6. Arnold is the Dragonfruit smoothie lover.
7. The Watermelon smoothie lover is the British person.
8. The Norwegian is the person who enjoys camping trips.
9. The person who likes going on cruises is the British person.
10. There are two houses between Bob and the person who enjoys camping trips.
11. The person who drinks Blueberry smoothies is directly left of the person who goes on cultural tours.
12. Bob is directly left of the Dragonfruit smoothie lover.
13. The person who likes going on cruises is directly left of Peter.
14. The person who prefers city breaks is not in the sixth house.
15. Carol is in the fifth house.
What is the value of attribute Smoothie for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}
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lime
|
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 HouseStyle for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}
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ranch
|
0/8
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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.