## Task 1/69

For two non-intersecting circles of different sizes, the common tangents are drawn. The angle between the external tangents is $\alpha$, and the angle between the internal tangents is $\beta$.

The angle between the tangents from the center of the larger circle to the smaller circle is sought.

Answer: 2 \arcsin\left( \frac{\sin \frac{\beta}{2} - \sin \frac{\alpha}{2}}{2} \right)


Initial 26. Find all natural numbers of the form $\overline{30 x 070 y 03}$ that are divisible by 37.

Answer: 300070703


Let $P$ be a set of $n\ge 3$ points in the plane, no three of which are on a line. How many possibilities are there to choose a set $T$ of $\binom{n-1}{2}$ triangles, whose vertices are all in $P$, such that each triangle in $T$ has a side that is not a side of any other triangle in $T$?

Answer: n


I have 10 balls that look identical on the outside, but one of them is radioactive, and I don't know which one. One of my acquaintances would only buy non-radioactive balls from me, at 1 forint each. Another acquaintance of mine has a device that can determine if there are any radioactive balls among any number of balls. He charges 1 forint per measurement, but his device has the property that if there is a radioactive ball among the measured balls, all of them become radioactive during the measurement.

What is the maximum profit I can definitely achieve?

Answer: 5


Task 2 - 260712 In the material issuance of a company, the keys of twelve padlocks have been mixed up due to a mishap.

Since only one of the twelve keys fits each padlock and only one padlock fits each key, which cannot be distinguished from each other externally, it must be determined which key belongs to which padlock.

Apprentice Bernd, who was assigned this task, thought: "Now I have to try twelve keys on twelve padlocks, so if I'm unlucky, I have to perform $12 \cdot 12=144$ tests."

However, his friend Uwe said that much fewer tests would suffice.

Determine the smallest number of tests with which one can certainly (i.e., even in the worst case) find the matching key for each padlock!

Answer: 66


13. There is a sequence of numbers, the first 4 numbers are $2,0,1,8$, starting from the 5th number, each number is the unit digit of the sum of the previous 4 adjacent numbers, will the sequence $2,0,1, 7$ appear in this sequence of numbers?

Answer: No


1. In triangle ABC, the altitude to side BC, the perpendicular bisector of the arc $\mathrm{ABC}$, and the perpendicular bisector of side $\mathrm{AB}$ intersect at one point. Determine the measure of angle $\mathrm{ABC}$.

Answer: 60^\circ


12.390. A sphere is inscribed in a spherical sector of radius $R$ (Fig. 12.239). Find the radius of the circle of contact between the surfaces of the sphere and the sector, if the central angle in the axial section of the spherical sector is $\alpha$.

Answer: \dfrac{R \sin \alpha}{2 \left(1 + \sin \dfrac{\alpha}{2}\right)}


In the image, two rows of hexagonal fields are indicated, which continue to the right without limit. Fill in each field with one positive integer so that the product of the numbers in any three adjacent fields is 2018.

Determine the number that will be in the 2019th field in the upper row.

(L. Růžičková)

![](https://cdn.mathpix.com/cropped/2024_04_17_e836f4ee23919875e85ag-2.jpg?height=185&width=439&top_left_y=1278&top_left_x=817)

Hint. Which numbers can you fill in?

Answer: 1009


6. Unlocking the communicator is done by entering a 4-digit numerical code on the touch screen. The arrangement of digits on the keyboard changes after entering the code depending on a random prime number $k$ from 7 to 2017, and the digit $i$ is displayed as $a_{i}$, which is the last digit of the number $i k$. The user enters digits from the left column with the left hand, and the rest with the right hand. Restore the lock code if it is known that when entering the code, the user entered the digits as follows:

when $a_{3}=3$ - right, right, left, right;

when $a_{3}=9$ - left, left, left, left;

when $a_{3}=1$ - right, right, right, right;

when $a_{3}=7$ - left, right, right, right.

In your answer, specify the obtained code.

| 1 | 2 | 3 |  |
| :--- | :--- | :--- | :---: |
| 4 | 5 | 6 |  |
| 7 | 8 | 9 |  |
| 0 |  |  |  |
|  |  |  |  |

| $\mathrm{a}_{1}$ | $\mathrm{a}_{2}$ | $\mathrm{a}_{3}$ |
| :---: | :---: | :---: |
| $\mathrm{a}_{4}$ | $\mathrm{a}_{5}$ | $\mathrm{a}_{6}$ |
| $\mathrm{a}_{7}$ | $\mathrm{a}_{8}$ | $\mathrm{a}_{9}$ |
|  |  | $\mathrm{a}_{0}$ |
|  |  |  |
|  |  |  |

Answer: 3212


On the sides of triangle $ABC$, points $D, E, F, G$ are given, as shown in the figure. It is given that quadrilateral $DEFG$ is a rhombus and segments $AD, DE$, and $EB$ are congruent.

Determine the measure of angle $ACB$.

(I. Jančigová)

![](https://cdn.mathpix.com/cropped/2024_04_17_d278c4c03a37be47319bg-2.jpg?height=409&width=876&top_left_y=1323&top_left_x=590)

Hint. What is the relative position of lines $AC$ and $DF$?

Answer: 90^\circ


In the blackboard there are drawn $25$ points as shown in the figure.
Gastón must choose $4$ points that are vertices of a square.
In how many different ways can he make this choice?$$\begin{matrix}\bullet & \bullet & \bullet & \bullet & \bullet \\\bullet & \bullet & \bullet & \bullet & \bullet \\\bullet & \bullet & \bullet & \bullet & \bullet \\\bullet & \bullet & \bullet & \bullet & \bullet \\\bullet & \bullet & \bullet & \bullet & \bullet \end{matrix}$$

Answer: 50


33. As shown in the figure, square $A B C D$ shares a side with trapezoid $C D E F$, and $A F$ intersects $B C$ at point $G$. If $A D=D E=3$, and $A G: G F=1: 2$, then the area of trapezoid $C D E F$ is $\qquad$

Answer: 18


A scientist stores the design of their time machine in a computer, and the file is protected by a password that is a permutation of the set $\{1, 2, \ldots, 64\}$. They also design a program such that each time eight integers from 1 to 64 are inputted, the computer will indicate the order among these eight numbers in the password (from left to right). Design an operational plan that will determine this password in at most 45 inputs.

Answer: 45


Let \( \triangle ABC \) be an equilateral triangle with side length 1. Points \( A_1 \) and \( A_2 \) are chosen on side \( BC \), points \( B_1 \) and \( B_2 \) are chosen on side \( CA \), and points \( C_1 \) and \( C_2 \) are chosen on side \( AB \) such that \( BA_1 < BA_2 \), \( CB_1 < CB_2 \), and \( AC_1 < AC_2 \).

Suppose that the three line segments \( B_1C_2 \), \( C_1A_2 \), and \( A_1B_2 \) are concurrent, and the perimeters of triangles \( AB_2C_1 \), \( BC_2A_1 \), and \( CA_2B_1 \) are all equal. Find all possible values of this common perimeter.

Answer: 1


The set of five-digit numbers \( \{ N_1, \ldots, N_k \} \) is such that any five-digit number with all digits in increasing order coincides in at least one digit with at least one of the numbers \( N_1, \ldots, N_k \). Find the smallest possible value of \( k \).

Answer: 1


Given the ellipse \(\frac{x^{2}}{3}+\frac{y^{2}}{2}=1\) with right focus \(F\), two perpendicular chords \(AB\) and \(CD\) are drawn through \(F\). Let \(M\) and \(N\) be the midpoints of \(AB\) and \(CD\) respectively.
(1) Prove that the line \(MN\) passes through a fixed point, and find this fixed point.
(2) If the slopes of the chords \(AB\) and \(CD\) exist, find the maximum area \(S\) of the triangle \(FMN\).

Answer: \frac{4}{25}


The cells of a $50 \times 50$ table are colored in $n$ colors such that for any cell, the union of its row and column contains cells of all $n$ colors. Find the maximum possible number of blue cells if:

(a) $n=2$;

(b) $n=25$.

Answer: 1300


Let complex number \( z = \cos \frac{4\pi}{7} + i \sin \frac{4\pi}{7} \). Determine the value of \( \left| \frac{z}{1+z^2} + \frac{z^2}{1+z^4} + \frac{z^3}{1+z^6} \right| \).

Answer: 2


Let set \( A = \{1, 2, 3, \cdots, 1997\} \). For any 999-element subset \( X \) of \( A \), if there exist \( x, y \in X \) such that \( x < y \) and \( x \mid y \), then \( X \) is called a good subset. Find the largest natural number \( a \) (where \( a \in A \)) such that any 999-element subset containing \( a \) is a good subset.

Answer: 665


In trapezoid \(ABCD\), the side \(BC\) is equal to the diagonal \(BD\). On the smaller arc \(AB\) of the circumcircle of triangle \(ABC\), a point \(E\) is chosen such that \(BC = BE\). Find the angle \(\angle AED\).

Answer: 90


The NEMO (National Electronic Math Olympiad) is similar to the NIMO Summer Contest, in that there are fifteen problems, each worth a set number of points. However, the NEMO is weighted using Fibonacci numbers; that is, the  $n^{\text{th}}$  problem is worth  $F_n$  points, where  $F_1 = F_2 = 1$  and  $F_n = F_{n-1} + F_{n-2}$  for  $n \ge 3$ . The two problem writers are fair people, so they make sure that each of them is responsible for problems worth an equal number of total points. Compute the number of ways problem writing assignments can be distributed between the two writers.

*Proposed by Lewis Chen*

Answer: 32


In a qualification group with  $15$  volleyball teams, each team plays with all the other teams exactly once. Since there is no tie in volleyball, there is a winner in every match. After all matches played, a team would be qualified if its total number of losses is not exceeding  $N$ . If there are at least  $7$  teams qualified, find the possible least value of  $N$ .

Answer: 3


Let  $f(x) = ax^2+bx+c$  be a quadratic trinomial with  $a$ , $b$ , $c$  reals such that any quadratic trinomial obtained by a permutation of  $f$ 's coefficients has an integer root (including  $f$  itself).
Show that  $f(1)=0$ .

Answer: f(1) = 0


Round 9**p25.** Let  $S$  be the set of the first  $2017$  positive integers. Find the number of elements  $n \in S$  such that  $\sum^n_{i=1} \left\lfloor \frac{n}{i} \right\rfloor$  is even.**p26.** Let  $\{x_n\}_{n \ge 0}$  be a sequence with  $x_0 = 0$ , $x_1 = \frac{1}{20}$  , $x_2 = \frac{1}{17}$  , $x_3 = \frac{1}{10}$  , and  $x_n = \frac12 ((x_{n-2} +x_{n-4})$  for  $n\ge  4$ . Compute   $$  \left\lfloor \frac{1}{x_{2017!} -x_{2017!-1}} \right\rfloor. $$  **p27.** Let  $ABCDE$  be be a cyclic pentagon. Given that  $\angle CEB = 17^o$ , find  $\angle CDE  + \angle EAB$ , in degrees.

Round 10**p28.** Let  $S = \{1,2,4, ... ,2^{2016},2^{2017}\}$ . For each  $0 \le  i \le 2017$ , let  $x_i$  be chosen uniformly at random from the subset of  $S$  consisting of the divisors of  $2^i$  . What is the expected number of distinct values in the set  $\{x_0,x_1,x_2,... ,x_{2016},x_{2017}\}$ ?**p29.** For positive real numbers  $a$  and  $b$ , the points  $(a, 0)$ ,  $(20,17)$  and  $(0,b)$  are collinear. Find the minimum possible value of  $a+b$ .**p30.** Find the sum of the distinct prime factors of  $2^{36}-1$ .

Round 11**p31.** There exist two angle bisectors of the lines  $y = 20x$  and  $y = 17x$  with slopes  $m_1$  and  $m_2$ . Find the unordered pair  $(m_1,m_2)$ .**p32.** Triangle 4ABC has sidelengths  $AB = 13$ ,  $BC = 14$ ,  $C A =15$  and orthocenter  $H$ . Let  $\Omega_1$  be the circle through  $B$  and  $H$ , tangent to  $BC$ , and let  $\Omega_2$  be the circle through  $C$  and  $H$ , tangent to  $BC$ . Finally, let  $R \ne H$  denote the second intersection of  $\Omega_1$  and  $\Omega_2$ . Find the length  $AR$ .**p33.** For a positive integer  $n$ , let  $S_n = \{1,2,3, ...,n\}$  be the set of positive integers less than or equal to  $n$ . Additionally, let   $$ f (n) = |\{x \in S_n : x^{2017}\equiv x \,\, (mod \,\, n)\}|. $$   Find  $f (2016)- f (2015)+ f (2014)- f (2013)$ .

Round 12**p34.** Estimate the value of  $\sum^{2017}_{n=1} \phi (n)$ , where  $\phi (n)$  is the number of numbers less than or equal  $n$  that are relatively prime to n. If your estimate is  $E$  and the correct answer is  $A$ , your score for this problem will be max  $\max \left(0,\lfloor  15 - 75 \frac{|A-E|}{A} \rceil \right).$ **p35.** An up-down permutation of order  $n$  is a permutation  $\sigma$  of  $(1,2,3, ..., n)$  such that  $\sigma(i ) <\sigma (i +1)$  if and only if  $i$  is odd. Denote by  $P_n$  the number of up-down permutations of order  $n$ . Estimate the value of  $P_{20} +P_{17}$ . If your estimate is  $E$  and the correct answer is  $A$ , your score for this problem will be  $\max \left(0, 16 -\lceil  \max \left(\frac{E}{A}, 2- \frac{E}{A}\right) \rceil \right).$ **p36.** For positive integers  $n$ , superfactorial of  $n$ , denoted  $n\$   $, is defined as the product of the first $ n $ factorials. In other words, we have $ n\ $ = \prod^n_{i=1}(i !)$ . Estimate the number of digits in the product  $(20\$ )\cdot (17\ $)$ . If your estimate is  $E$  and the correct answer is  $A$ , your score for this problem will be   $\max \left(0, \lfloor 15 -\frac12 |A-E| \rfloor \right).$ PS. You should use hide for answers. Rounds 1-4 have been posted [here ](https://artofproblemsolving.com/community/c3h3158491p28715220) and 5-8 [here](https://artofproblemsolving.com/community/c3h3158514p28715373). Collected [here](https://artofproblemsolving.com/community/c5h2760506p24143309).

Answer: 163^\circ


Let  $N$  be a given positive integer. Consider a permutation of  $1,2,3,\cdots,N$ , denoted as  $p_1,p_2,\cdots,p_N$ . For a section  $p_l, p_{l+1},\cdots, p_r$ , we call it "extreme" if  $p_l$  and  $p_r$  are the maximum and minimum value of that section. We say a permutation  $p_1,p_2,\cdots,p_N$  is "super balanced" if there isn't an "extreme" section with a length at least  $3$ . For example,  $1,4,2,3$  is "super balanced", but  $3,1,2,4$  isn't. Please answer the following questions:
1. How many "super balanced" permutations are there?
2. For each integer  $M\leq N$ . How many "super balanced" permutations are there such that  $p_1=M$ ?

*Proposed by ltf0501*

Answer: \binom{N-1}{M-1}


Alice and Bob take turns alternatively on a  $2020\times2020$  board with Alice starting the game. In every move each person colours a cell that have not been coloured yet and will be rewarded with as many points as the coloured cells in the same row and column. When the table is coloured completely, the points determine the winner. Who has the wining strategy and what is the maximum difference he/she can grantees?

*Proposed by Seyed Reza Hosseini*

Answer: 2040200


Find all pairs of natural numbers  $(n, k)$  with the following property:
Given a  $k\times k$  array of cells, such that every cell contains one integer, there always exists a path from the left to the right edges such that the sum of the numbers on the path is a multiple of  $n$ .

Note: A path from the left to the right edge is a sequence of cells of the array  $a_1, a_2, ... , a_m$  so that  $a_1$  is a cell of the leftmost column,  $a_m$  is the cell of the rightmost column, and  $a_{i}$ ,  $a_{i+1}$  share an edge for all  $i = 1, 2, ... , m -1$ .

Answer: (n, k)


Let  $n, m$  be positive integers. A set  $S$  of positive integers is called  $(n, m)$ -good, if:

(1)  $m \in S$ ;
(2) for all  $a\in S$ , all divisors of  $a$  are also in  $S$ ;
(3) for all distinct  $a, b \in S$ ,  $a^n+b^n \in S$ .

For which  $(n, m)$ , the only  $(n, m)$ -good set is  $\mathbb{N}$ ?

Answer: (n, m)


A bus that moves along a 100 km route is equipped with a computer, which predicts how much more time is needed to arrive at its final destination. This prediction is made on the assumption that the average speed of the bus in the remaining part of the route is the same as that in the part already covered. Forty minutes after the departure of the bus, the computer predicts that the remaining travelling time will be 1 hour. And this predicted time remains the same for the next 5 hours. Could this possibly occur? If so, how many kilometers did the bus cover when these 5 hours passed? (Average speed is the number of kilometers covered divided by the time it took to cover them.)

Answer: 45 \text{ km}


There are  $ n$   students; each student knows exactly  $d $   girl students and  $d $  boy students ("knowing" is a symmetric relation). Find all pairs  $ (n,d) $   of integers .

Answer: (n, d)


Let  $n$  be a positive integer. Nancy is given a rectangular table in which each entry is a positive integer.  She is permitted to make either of the following two moves:

(1)  select a row and multiply each entry in this row by  $n$ ;

(2)  select a column and subtract  $n$  from each entry in this column.

Find all possible values of  $n$  for which the following statement is true:

Given any rectangular table, it is possible for Nancy to perform a finite sequence of moves to create a table in which each entry is  $0$ .

Answer: n = 2


The altitude from one vertex of a triangle, the bisector from the another one and the median from the remaining vertex were drawn, the common points of these three lines were marked, and after this everything was erased except three marked points. Restore the triangle. (For every two erased segments, it is known which of the three points was their intersection point.)

(A. Zaslavsky)

Answer: \triangle ABC


Richard has a four infinitely large piles of coins: a pile of pennies (worth 1 cent each), a pile of nickels (5 cents), a pile of dimes (10 cents), and a pile of quarters (25 cents). He chooses one pile at random and takes one coin from that pile. Richard then repeats this process until the sum of the values of the coins he has taken is an integer number of dollars.  (One dollar is 100 cents.) What is the expected value of this final sum of money, in cents?

*Proposed by Lewis Chen*

Answer: 1025


For an integer  $n$  let  $M (n) = \{n, n + 1, n + 2, n + 3, n + 4\}$ . Furthermore, be  $S (n)$  sum of squares and  $P (n)$  the product of the squares of the elements of  $M (n)$ . For which integers  $n$  is  $S (n)$  a divisor of  $P (n)$  ?

Answer: n = 3


Triangle  $ABC$  has circumcircle  $\Omega$ . Chord  $XY$  of  $\Omega$  intersects segment  $AC$  at point  $E$  and segment  $AB$  at point  $F$  such that  $E$  lies between  $X$  and  $F$ . Suppose that  $A$  bisects arc  $\widehat{XY}$ . Given that  $EC = 7, FB = 10, AF = 8$ , and  $YF - XE = 2$ , find the perimeter of triangle  $ABC$ .

Answer: 51


In a triangle  $ABC$  the area is  $18$ , the length  $AB$  is  $5$ , and the medians from  $A$  and  $B$  are orthogonal. Find the lengths of the sides  $BC,AC$ .

Answer: BC = 2\sqrt{13}


Let  $n$  be a positive integer. Every square in a  $n \times n$ -square grid is either white or black.
How many such colourings exist, if every  $2 \times 2$ -square consists of exactly two white and two black squares?
The squares in the grid are identified as e.g. in a chessboard, so in general colourings obtained from each other by rotation are different.

Answer: 2


A *short-sighted* rook is a rook that beats all squares in the same column and in the same row for which he can not go more than  $60$ -steps.
What is the maximal amount of short-sighted rooks that don't beat each other that can be put on a  $100\times 100$  chessboard.

Answer: 178


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Nationality, Pet.
The attributes have the following possible values:
- Job: electrician, firefighter, project-manager, scientist
- Food: banana, potato, pumpkin, radish
- Nationality: nigerian, pakistani, russian, spanish
- Pet: bird, cat, hamster, mouse

Given the following premises about the line of people:
- Job:project-manager is on the far left or far right
- Job:electrician is on the far right
- Food:radish is somewhere between Pet:mouse and Nationality:pakistani
- Pet:cat is somewhere to the right of Job:firefighter
- Job:electrician == Food:pumpkin
- Food:banana is somewhere to the right of Food:potato
- Nationality:russian is on the right of Nationality:nigerian
- Nationality:nigerian is somewhere to the left of Food:radish
- Nationality:pakistani == Pet:hamster
- Nationality:pakistani is on the far left

Answer the following question:

Question: Question: What is the Job of the person who has/is radish??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: scientist


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Nationality, Music-Genre, Hobby, Transport.
The attributes have the following possible values:
- Nationality: australian, brazilian, indian, italian, russian
- Music-Genre: ambient, hip-hop, house, rock, soul
- Hobby: baking, board-games, fishing, gardening, hiking
- Transport: bus, car, ship, skateboard, snowmobile

Given the following premises about the line of people:
- Transport:snowmobile is on the right of Nationality:italian
- Hobby:baking is on the left or right of Transport:snowmobile
- Hobby:gardening is somewhere to the right of Hobby:board-games
- Transport:ship is on the right of Nationality:australian
- Hobby:fishing == Transport:ship
- Music-Genre:soul is on the left or right of Music-Genre:house
- Nationality:brazilian is somewhere to the right of Nationality:indian
- Music-Genre:soul is somewhere to the left of Music-Genre:ambient
- Nationality:australian == Transport:car
- Transport:bus is on the right of Music-Genre:hip-hop
- Hobby:fishing is on the left or right of Nationality:indian
- Music-Genre:house == Hobby:hiking
- Nationality:italian == Transport:skateboard

Answer the following question:

Question: Question: What is the Nationality of the person who has/is house??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: indian


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Music-Genre, Pet.
The attributes have the following possible values:
- Job: accountant, chef, entrepreneur, security-guard
- Food: grapefruit, lime, mango, raspberry
- Music-Genre: ambient, electronic, gospel, trance
- Pet: cat, guinea-pig, lizard, mouse

Given the following premises about the line of people:
- Pet:lizard is somewhere to the right of Job:chef
- Pet:cat is not to the left of Food:raspberry
- Music-Genre:electronic is on the left of Food:grapefruit
- Music-Genre:gospel is between Pet:cat and Food:mango
- Job:accountant is not to the left of Music-Genre:gospel
- Pet:mouse is on the left of Music-Genre:ambient
- Music-Genre:ambient is on the left of Music-Genre:gospel
- Food:grapefruit is not to the right of Job:security-guard
- Job:chef is somewhere between Food:grapefruit and Food:mango

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is lime??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: gospel


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Beverage, Food, Hobby, Music-Genre.
The attributes have the following possible values:
- Beverage: 7up, cola, milk, water
- Food: cauliflower, cranberry, eggplant, pumpkin
- Hobby: board-games, filmmaking, rock-climbing, video-games
- Music-Genre: classical, indie, r&b, trance

Given the following premises about the line of people:
- Hobby:board-games is somewhere to the left of Music-Genre:indie
- Music-Genre:r&b is in an even position
- Beverage:milk is on the far left
- Music-Genre:trance is somewhere to the right of Food:cranberry
- Beverage:7up is on the left of Hobby:video-games
- Beverage:7up == Food:cauliflower
- Hobby:video-games is on the left or right of Beverage:cola
- Food:eggplant != Hobby:rock-climbing
- Music-Genre:trance is on the left or right of Hobby:filmmaking
- Music-Genre:r&b is on the far left or far right
- Food:eggplant is in an even position

Answer the following question:

Question: Question: What is the Food of the person who has/is video-games??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pumpkin


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Beverage, Nationality.
The attributes have the following possible values:
- Job: accountant, chef, dancer, freelancer
- Hobby: baking, hiking, rock-climbing, woodworking
- Beverage: iced-tea, lemonade, mirinda, soy-milk
- Nationality: dutch, nigerian, russian, spanish

Given the following premises about the line of people:
- Job:chef is somewhere to the right of Beverage:soy-milk
- Nationality:nigerian is somewhere between Job:accountant and Hobby:baking
- Nationality:russian is somewhere to the left of Nationality:dutch
- Hobby:woodworking is on the right of Hobby:baking
- Job:dancer is on the far left or far right
- Beverage:iced-tea is on the far left or far right
- Beverage:lemonade == Nationality:russian
- Hobby:hiking != Nationality:nigerian
- Beverage:iced-tea is in an odd position
- Beverage:soy-milk is on the right of Job:accountant

Answer the following question:

Question: Question: What is the Hobby of the person who is accountant??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: hiking


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Food, Pet.
The attributes have the following possible values:
- Job: designer, firefighter, manager, teacher
- Hobby: camping, cooking, drawing, video-games
- Food: garlic, kale, papaya, radish
- Pet: dog, ferret, hamster, horse

Given the following premises about the line of people:
- Food:garlic is somewhere to the left of Job:manager
- Job:teacher == Hobby:video-games
- Hobby:camping is somewhere to the right of Food:radish
- Pet:hamster is somewhere to the left of Pet:dog
- Pet:dog is somewhere to the left of Hobby:camping
- Job:manager is on the left of Hobby:camping
- Pet:ferret is between Job:firefighter and Job:manager
- Job:firefighter is somewhere to the left of Hobby:camping
- Hobby:drawing is on the right of Food:kale

Answer the following question:

Question: Question: What is the Job of the person who has/is video-games??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: teacher


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Nationality, Music-Genre, Food, Pet.
The attributes have the following possible values:
- Nationality: australian, egyptian, japanese, pakistani
- Music-Genre: country, metal, reggae, rock
- Food: grapefruit, kale, pomegranate, watermelon
- Pet: dog, horse, mouse, rabbit

Given the following premises about the line of people:
- Pet:horse is on the left or right of Nationality:egyptian
- Music-Genre:metal is on the left or right of Music-Genre:reggae
- Food:grapefruit is not to the right of Nationality:australian
- Pet:horse is on the right of Pet:dog
- Music-Genre:country and Pet:rabbit have the same parity positions
- Food:kale is on the right of Food:watermelon
- Music-Genre:metal is on the far right
- Nationality:pakistani is somewhere to the right of Nationality:australian
- Food:watermelon and Pet:mouse have the same parity positions
- Music-Genre:rock is somewhere to the right of Music-Genre:country
- Food:pomegranate is not to the right of Nationality:japanese
- Pet:dog is on the left or right of Pet:rabbit

Answer the following question:

Question: Question: What is the Food of the person who is pakistani??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: kale


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Beverage, Movie-Genre, Pet.
The attributes have the following possible values:
- Job: bartender, dancer, manager, security-guard
- Hobby: baking, video-games, woodworking, writing
- Beverage: cola, iced-tea, milk, soy-milk
- Movie-Genre: family, fantasy, spy, superhero
- Pet: chinchilla, ferret, goldfish, rat

Given the following premises about the line of people:
- Beverage:soy-milk is somewhere to the left of Beverage:milk
- Job:bartender is on the far right
- Movie-Genre:fantasy is on the right of Movie-Genre:spy
- Beverage:cola is on the right of Pet:ferret
- Pet:chinchilla is somewhere to the left of Hobby:writing
- Movie-Genre:spy is in an even position
- Job:manager is in an even position
- Hobby:writing is somewhere to the right of Beverage:cola
- Movie-Genre:spy is somewhere to the right of Job:security-guard
- Pet:rat is between Hobby:video-games and Beverage:soy-milk
- Hobby:woodworking is on the left of Movie-Genre:superhero

Answer the following question:

Question: Question: What is the Movie-Genre of the person who has/is video-games??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: family


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Nationality, Transport.
The attributes have the following possible values:
- Job: firefighter, journalist, project-manager, teacher
- Hobby: baking, camping, collecting, sudoku
- Nationality: american, british, malaysian, pakistani
- Transport: boat, helicopter, roller, van

Given the following premises about the line of people:
- Nationality:malaysian is on the far right
- Job:journalist is somewhere to the right of Job:teacher
- Job:teacher is on the left or right of Nationality:american
- Transport:helicopter is somewhere to the left of Nationality:british
- Job:teacher is not to the left of Transport:roller
- Hobby:baking and Transport:van have the same parity positions
- Job:project-manager is somewhere to the left of Transport:boat
- Nationality:pakistani is not to the left of Hobby:camping
- Job:teacher is somewhere to the right of Hobby:sudoku
- Nationality:british is somewhere to the right of Transport:boat

Answer the following question:

Question: Question: What is the Job of the person who has/is camping??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: project-manager


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Beverage, Movie-Genre, Nationality.
The attributes have the following possible values:
- Job: freelancer, musician, police-officer, scientist
- Beverage: fanta, hot-chocolate, mirinda, tea
- Movie-Genre: comedy, family, fantasy, superhero
- Nationality: australian, french, russian, spanish

Given the following premises about the line of people:
- Beverage:tea == Job:musician
- Job:police-officer == Movie-Genre:fantasy
- Beverage:mirinda is between Movie-Genre:family and Nationality:australian
- Beverage:mirinda is on the left or right of Nationality:russian
- Beverage:tea is somewhere to the left of Beverage:hot-chocolate
- Movie-Genre:superhero is on the left or right of Job:police-officer
- Nationality:french is on the left of Beverage:tea
- Job:police-officer is on the far right
- Job:scientist is on the right of Job:freelancer

Answer the following question:

Question: Question: What is the Beverage of the person who is musician??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: tea


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Beverage, Music-Genre, Pet, Sport.
The attributes have the following possible values:
- Beverage: 7up, juice, sprite, water
- Music-Genre: jazz, metal, pop, r&b
- Pet: cat, ferret, mouse, turtle
- Sport: ice-hockey, sailing, skiing, snowboarding

Given the following premises about the line of people:
- Beverage:sprite is somewhere to the right of Pet:mouse
- Pet:mouse is somewhere between Beverage:water and Music-Genre:jazz
- Pet:ferret is on the left or right of Music-Genre:r&b
- Pet:cat is on the left or right of Sport:sailing
- Sport:snowboarding is on the left of Music-Genre:jazz
- Sport:snowboarding is somewhere to the left of Beverage:juice
- Beverage:sprite is not to the right of Music-Genre:pop
- Beverage:7up and Sport:skiing have the same parity positions
- Beverage:sprite is on the left of Sport:sailing

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is water??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: metal


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`, `Alice`, `Peter`, `Eric`
 - Each person prefers a unique type of vacation: `camping`, `city`, `beach`, `cruise`, `mountain`
 - People have unique heights: `very tall`, `average`, `very short`, `short`, `tall`
 - They all have a unique favorite flower: `tulips`, `roses`, `carnations`, `lilies`, `daffodils`
 - Each person has a unique level of education: `bachelor`, `master`, `associate`, `high school`, `doctorate`
 - People own unique car models: `bmw 3 series`, `tesla model 3`, `toyota camry`, `ford f150`, `honda civic`

## Clues:
1. Eric is the person who prefers city breaks.
2. Arnold is the person who is tall.
3. The person who loves beach vacations is the person who loves the boquet of lilies.
4. The person who owns a BMW 3 Series is the person who is tall.
5. The person with an associate's degree is the person who loves the boquet of lilies.
6. The person who has an average height is Eric.
7. Peter is the person who owns a Toyota Camry.
8. The person who has an average height is somewhere to the right of the person who loves a bouquet of daffodils.
9. The person who owns a Honda Civic is somewhere to the left of the person who loves the boquet of lilies.
10. Eric is the person who owns a Ford F-150.
11. The person who loves the vase of tulips is in the fourth house.
12. The person who is very short is not in the fourth house.
13. Eric is the person with a high school diploma.
14. The person who enjoys mountain retreats is somewhere to the right of the person with a master's degree.
15. The person who likes going on cruises is not in the third house.
16. Bob is the person who is short.
17. The person with an associate's degree is directly left of Arnold.
18. The person with a bachelor's degree is the person who is very tall.
19. The person who loves a carnations arrangement is directly left of the person with a doctorate.
 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{}

Answer: 1


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Carol`, `Bob`, `Alice`, `Arnold`
 - People have unique favorite music genres: `country`, `classical`, `jazz`, `hip hop`, `rock`, `pop`
 - Each person has a unique birthday month: `jan`, `feb`, `april`, `mar`, `sept`, `may`

## Clues:
1. Peter is in the first house.
2. The person who loves rock music is the person whose birthday is in January.
3. Arnold is in the fourth house.
4. The person whose birthday is in January is somewhere to the right of the person who loves classical music.
5. Eric is not in the sixth house.
6. The person whose birthday is in February is somewhere to the left of Eric.
7. Bob is the person whose birthday is in March.
8. There is one house between Bob and the person who loves jazz music.
9. The person who loves rock music and Carol are next to each other.
10. The person who loves country music is not in the sixth house.
11. Alice is directly left of the person whose birthday is in February.
12. The person who loves pop music is somewhere to the left of the person who loves country music.
13. The person whose birthday is in April is not in the first house.
14. The person who loves rock music and the person whose birthday is in September are next to each other.
15. The person who loves classical music is the person whose birthday is in March.
 What is the value of attribute MusicGenre for the person whose attribute Birthday is may? Please reason step by step, and put your final answer within \boxed{}

Answer: pop


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`
 - Each person has a favorite color: `white`, `yellow`, `red`
 - Each person prefers a unique type of vacation: `city`, `mountain`, `beach`
 - Each person has a unique birthday month: `sept`, `april`, `jan`
 - Each mother is accompanied by their child: `Meredith`, `Fred`, `Bella`

## Clues:
1. The person whose birthday is in January is the person's child is named Bella.
2. The person who loves white is Arnold.
3. The person who loves beach vacations is Arnold.
4. The person whose birthday is in September is somewhere to the left of Arnold.
5. The person whose favorite color is red is directly left of the person who enjoys mountain retreats.
6. Peter is somewhere to the right of the person's child is named Fred.
7. The person who loves yellow is the person's child is named Bella.
 What is the value of attribute Birthday for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: sept


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`, `Carol`, `Alice`, `Eric`, `Arnold`, `Peter`
 - Everyone has something unique for lunch: `pizza`, `spaghetti`, `soup`, `grilled cheese`, `stew`, `stir fry`
 - Each person has a unique level of education: `associate`, `doctorate`, `trade school`, `high school`, `master`, `bachelor`
 - The people keep unique animals: `horse`, `fish`, `rabbit`, `cat`, `bird`, `dog`
 - Each person lives in a unique style of house: `ranch`, `victorian`, `modern`, `craftsman`, `mediterranean`, `colonial`

## Clues:
1. The person residing in a Victorian house is in the fourth house.
2. The fish enthusiast is in the first house.
3. The person in a ranch-style home is the bird keeper.
4. The person residing in a Victorian house is somewhere to the left of the person who loves the soup.
5. Carol is directly left of the person who keeps horses.
6. The person who loves stir fry is the person with a doctorate.
7. The person with a master's degree is somewhere to the left of the person with a doctorate.
8. There is one house between the person in a Mediterranean-style villa and the person with a bachelor's degree.
9. The person who attended trade school is the cat lover.
10. The person with a master's degree is the person who is a pizza lover.
11. The person who is a pizza lover is somewhere to the right of Alice.
12. The person living in a colonial-style house is the person who loves the stew.
13. Arnold is the person with a master's degree.
14. There is one house between Arnold and the person who loves eating grilled cheese.
15. The person in a modern-style house and the person who attended trade school are next to each other.
16. Eric is directly left of the person with a doctorate.
17. Alice and the person in a Mediterranean-style villa are next to each other.
18. The person with an associate's degree is directly left of Eric.
19. The dog owner is Bob.
 What is the value of attribute House for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


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 use unique phone models: `samsung galaxy s21`, `huawei p50`, `oneplus 9`, `iphone 13`, `google pixel 6`
 - Everyone has a favorite smoothie: `desert`, `dragonfruit`, `watermelon`, `cherry`, `lime`
 - The mothers' names in different houses are unique: `Janelle`, `Holly`, `Penny`, `Aniya`, `Kailyn`
 - Each person has an occupation: `doctor`, `lawyer`, `engineer`, `teacher`, `artist`

## Clues:
1. The person whose mother's name is Kailyn is Peter.
2. The Dragonfruit smoothie lover is not in the fourth house.
3. The person who uses an iPhone 13 is the person who is an artist.
4. The person whose mother's name is Aniya is Arnold.
5. The person whose mother's name is Aniya is the Desert smoothie lover.
6. The person whose mother's name is Aniya is in the second house.
7. The person who drinks Lime smoothies is in the first house.
8. The person who uses a Huawei P50 is the person who is a doctor.
9. Eric is the person who drinks Lime smoothies.
10. There is one house between the person who is a teacher and Bob.
11. The person whose mother's name is Aniya is the person who is a lawyer.
12. The person who uses an iPhone 13 is the person who likes Cherry smoothies.
13. Arnold is the person who uses a OnePlus 9.
14. The person who is a doctor is The person whose mother's name is Penny.
15. Peter is the person who uses a Samsung Galaxy S21.
16. Bob is not in the third house.
17. The person whose mother's name is Holly is directly left of Peter.
 What is the value of attribute Name for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Arnold`, `Peter`, `Alice`, `Eric`
 - Each person has a unique favorite drink: `boba tea`, `coffee`, `root beer`, `water`, `milk`, `tea`
 - Each person lives in a unique style of house: `ranch`, `victorian`, `craftsman`, `mediterranean`, `colonial`, `modern`
 - Everyone has a unique favorite cigar: `dunhill`, `prince`, `yellow monster`, `blue master`, `blends`, `pall mall`

## Clues:
1. Eric is the Dunhill smoker.
2. Peter and the root beer lover are next to each other.
3. The Prince smoker is Bob.
4. The person in a modern-style house is somewhere to the left of Arnold.
5. The one who only drinks water is somewhere to the right of Bob.
6. The person in a modern-style house is the person who smokes Blue Master.
7. The person in a ranch-style home is directly left of the person in a modern-style house.
8. The person who smokes Yellow Monster is somewhere to the right of the coffee drinker.
9. The root beer lover is in the sixth house.
10. The person who likes milk is somewhere to the left of the tea drinker.
11. Arnold is the person living in a colonial-style house.
12. The person in a Craftsman-style house is the coffee drinker.
13. The boba tea drinker is somewhere to the left of the person living in a colonial-style house.
14. The boba tea drinker is the person partial to Pall Mall.
15. The person residing in a Victorian house is not in the fifth house.
16. The person living in a colonial-style house is in the third house.
17. Alice is not in the first house.
 What is the value of attribute Name for the person whose attribute HouseStyle is mediterranean? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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`
 - People use unique phone models: `iphone 13`, `samsung galaxy s21`, `google pixel 6`, `oneplus 9`, `huawei p50`
 - Each person has a unique hobby: `knitting`, `photography`, `painting`, `cooking`, `gardening`
 - Everyone has a unique favorite cigar: `pall mall`, `blends`, `blue master`, `dunhill`, `prince`
 - People have unique favorite sports: `swimming`, `baseball`, `tennis`, `basketball`, `soccer`
 - Everyone has a favorite smoothie: `cherry`, `desert`, `lime`, `watermelon`, `dragonfruit`

## Clues:
1. Peter is in the first house.
2. The person who loves soccer is the person who paints as a hobby.
3. The person partial to Pall Mall is the person who enjoys knitting.
4. The person who uses a Google Pixel 6 is not in the fifth house.
5. The person who enjoys knitting is somewhere to the left of Alice.
6. Peter is directly left of the person who smokes Blue Master.
7. The Prince smoker is the person who uses a OnePlus 9.
8. The person who loves basketball is directly left of the photography enthusiast.
9. The Dunhill smoker is somewhere to the left of the photography enthusiast.
10. There is one house between the person who drinks Lime smoothies and the person who loves basketball.
11. The person who enjoys gardening is somewhere to the right of the person who enjoys knitting.
12. The Dragonfruit smoothie lover is in the third house.
13. The person who loves baseball is the person partial to Pall Mall.
14. Eric is the person who loves tennis.
15. The person who uses a OnePlus 9 is Peter.
16. The Dunhill smoker is the person who uses a Huawei P50.
17. The Desert smoothie lover is the person who loves soccer.
18. The person who uses a Samsung Galaxy S21 is directly left of Arnold.
19. The person who loves tennis is somewhere to the right of the Watermelon smoothie lover.
 What is the value of attribute Hobby for the person whose attribute Cigar is blends? Please reason step by step, and put your final answer within \boxed{}

Answer: photography


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Alice`, `Peter`, `Eric`, `Arnold`
 - Each person has a unique level of education: `master`, `doctorate`, `high school`, `bachelor`, `trade school`, `associate`
 - People have unique favorite book genres: `romance`, `fantasy`, `historical fiction`, `science fiction`, `mystery`, `biography`
 - Each mother is accompanied by their child: `Alice`, `Samantha`, `Timothy`, `Meredith`, `Bella`, `Fred`
 - Everyone has something unique for lunch: `stew`, `soup`, `stir fry`, `spaghetti`, `pizza`, `grilled cheese`
 - People have unique favorite sports: `volleyball`, `basketball`, `tennis`, `baseball`, `swimming`, `soccer`

## Clues:
1. Alice is the person who loves swimming.
2. The person's child is named Alice is directly left of the person who loves historical fiction books.
3. The person who loves the stew is the person who loves historical fiction books.
4. The person with a doctorate is the person who loves the soup.
5. The person who loves science fiction books is in the sixth house.
6. The person who attended trade school is directly left of the person who loves historical fiction books.
7. The person who loves baseball and the person's child is named Bella are next to each other.
8. The person with a master's degree is somewhere to the left of the person who loves mystery books.
9. The person who loves soccer is somewhere to the left of the person who loves fantasy books.
10. The person who loves stir fry is the person with an associate's degree.
11. The person who is a pizza lover is Peter.
12. Bob is not in the sixth house.
13. The person's child is named Meredith is directly left of the person who loves fantasy books.
14. The person's child is named Samantha is Eric.
15. There is one house between the person who loves eating grilled cheese and Bob.
16. The person who loves eating grilled cheese is the person's child is named Samantha.
17. The person who loves volleyball is the person's child is named Samantha.
18. The person's child is named Fred is somewhere to the left of the person's child is named Samantha.
19. Bob is the person who loves tennis.
20. The person who loves soccer is directly left of Carol.
21. The person who loves eating grilled cheese is somewhere to the left of the person who loves mystery books.
22. The person's child is named Meredith is the person who loves biography books.
23. The person's child is named Meredith is the person who loves the soup.
24. Carol is the person with a high school diploma.
 What is the value of attribute Food for the person whose attribute Children is Fred? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


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`
 - Everyone has a favorite smoothie: `cherry`, `blueberry`, `desert`, `lime`, `dragonfruit`, `watermelon`
 - People have unique favorite music genres: `rock`, `classical`, `jazz`, `pop`, `country`, `hip hop`
 - People have unique favorite book genres: `science fiction`, `romance`, `historical fiction`, `fantasy`, `mystery`, `biography`
 - Each person has a favorite color: `yellow`, `white`, `green`, `blue`, `red`, `purple`

## Clues:
1. The person who loves purple and the Dragonfruit smoothie lover are next to each other.
2. The person who loves classical music is in the fifth house.
3. Eric is somewhere to the left of the person who loves classical music.
4. The person who loves hip-hop music is directly left of the Desert smoothie lover.
5. The person who loves yellow is the person who loves science fiction books.
6. Arnold is the person who loves rock music.
7. Carol is the person who likes Cherry smoothies.
8. There are two houses between the person who loves jazz music and the Watermelon smoothie lover.
9. The person whose favorite color is green is somewhere to the right of the person who loves jazz music.
10. The person who drinks Blueberry smoothies is directly left of the Watermelon smoothie lover.
11. Arnold is somewhere to the left of the Watermelon smoothie lover.
12. Bob is somewhere to the left of the person who loves yellow.
13. Bob is the person who loves historical fiction books.
14. The person who loves biography books is the person who loves pop music.
15. The person who loves romance books is in the fifth house.
16. There are two houses between Bob and the person who loves mystery books.
17. The person who loves white is the person who loves historical fiction books.
18. Peter is somewhere to the left of the person who loves blue.
19. There is one house between the person who loves biography books and the person who loves yellow.
 What is the value of attribute MusicGenre for the person whose attribute Color is purple? Please reason step by step, and put your final answer within \boxed{}

Answer: pop


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`, `Carol`, `Alice`, `Bob`
 - People have unique favorite music genres: `country`, `classical`, `pop`, `hip hop`, `jazz`, `rock`
 - Each person lives in a unique style of house: `modern`, `mediterranean`, `victorian`, `craftsman`, `ranch`, `colonial`
 - People use unique phone models: `huawei p50`, `iphone 13`, `google pixel 6`, `oneplus 9`, `xiaomi mi 11`, `samsung galaxy s21`
 - Each person has a unique type of pet: `hamster`, `dog`, `cat`, `rabbit`, `fish`, `bird`

## Clues:
1. The person who has a cat is the person in a Mediterranean-style villa.
2. Peter is in the second house.
3. The person in a modern-style house is the person who uses a Samsung Galaxy S21.
4. The person who keeps a pet bird is the person who uses a Google Pixel 6.
5. The person who keeps a pet bird is directly left of the person who uses a Xiaomi Mi 11.
6. Arnold is the person residing in a Victorian house.
7. The person who loves rock music is the person living in a colonial-style house.
8. The person in a Craftsman-style house is Carol.
9. The person who owns a rabbit is in the sixth house.
10. The person who loves pop music is somewhere to the left of the person living in a colonial-style house.
11. The person who uses a Huawei P50 and the person who loves country music are next to each other.
12. The person who loves hip-hop music is the person who uses a Samsung Galaxy S21.
13. Carol and Peter are next to each other.
14. The person who uses a OnePlus 9 is Peter.
15. The person with a pet hamster is not in the first house.
16. The person in a ranch-style home is somewhere to the left of the person who loves classical music.
17. There are two houses between Carol and Alice.
18. The person who owns a dog is in the fifth house.
19. The person in a modern-style house is Eric.
20. Peter is the person living in a colonial-style house.
21. The person who has a cat is not in the fourth house.
 What is the value of attribute MusicGenre for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: pop


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`, `Eric`, `Bob`, `Peter`, `Carol`, `Alice`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Timothy`, `Meredith`, `Samantha`, `Alice`
 - Everyone has something unique for lunch: `pizza`, `stir fry`, `grilled cheese`, `spaghetti`, `soup`, `stew`
 - Each person has a unique type of pet: `rabbit`, `fish`, `cat`, `dog`, `bird`, `hamster`
 - Each person has a unique birthday month: `may`, `sept`, `mar`, `jan`, `april`, `feb`
 - Each person has a unique favorite drink: `water`, `milk`, `coffee`, `tea`, `boba tea`, `root beer`

## Clues:
1. The person whose birthday is in May is the person who loves the spaghetti eater.
2. The person's child is named Fred is the person who loves the stew.
3. The person who likes milk is the person with a pet hamster.
4. There is one house between the person who loves the spaghetti eater and the person who has a cat.
5. The person who is the mother of Timothy is Bob.
6. The person whose birthday is in January is directly left of the one who only drinks water.
7. Carol is the coffee drinker.
8. Peter is not in the fifth house.
9. The person whose birthday is in April is the person's child is named Alice.
10. The person who loves eating grilled cheese is somewhere to the right of the person whose birthday is in September.
11. The person's child is named Bella and Bob are next to each other.
12. The person who owns a rabbit is Peter.
13. The person who keeps a pet bird is the person who loves the soup.
14. The person who owns a rabbit is somewhere to the right of the person who loves stir fry.
15. The person who loves eating grilled cheese is somewhere to the left of the person who owns a rabbit.
16. The person whose birthday is in March is the tea drinker.
17. Peter is the person's child is named Bella.
18. The person who is the mother of Timothy is somewhere to the right of the person's child is named Bella.
19. The person with an aquarium of fish and the person's child is named Bella are next to each other.
20. The one who only drinks water is the person's child is named Fred.
21. The person whose birthday is in May is somewhere to the right of the person with an aquarium of fish.
22. The person with a pet hamster is the person's child is named Meredith.
23. The root beer lover is the person who loves the spaghetti eater.
24. Carol is directly left of Alice.
25. Eric is in the third house.
26. The person who is a pizza lover is Bob.
 What is the value of attribute House for the person whose attribute Pet is dog? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


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`, `Eric`, `Peter`, `Alice`
 - People use unique phone models: `iphone 13`, `huawei p50`, `oneplus 9`, `google pixel 6`, `xiaomi mi 11`, `samsung galaxy s21`
 - Everyone has a unique favorite cigar: `pall mall`, `yellow monster`, `prince`, `blends`, `dunhill`, `blue master`
 - Each person prefers a unique type of vacation: `cultural`, `beach`, `city`, `camping`, `cruise`, `mountain`
 - People have unique hair colors: `brown`, `red`, `gray`, `black`, `blonde`, `auburn`
 - Each person has a unique favorite drink: `coffee`, `boba tea`, `milk`, `water`, `root beer`, `tea`

## Clues:
1. The person who prefers city breaks is Bob.
2. The person who has brown hair is the one who only drinks water.
3. Eric is directly left of the person who uses a Samsung Galaxy S21.
4. There is one house between the person who loves beach vacations and the person who enjoys camping trips.
5. The one who only drinks water is somewhere to the left of the person who uses a Xiaomi Mi 11.
6. The person who has brown hair is the Dunhill smoker.
7. The person who has red hair is Arnold.
8. The person who has auburn hair is the person who uses an iPhone 13.
9. The person who has gray hair is not in the sixth house.
10. The person who likes milk is the person who has auburn hair.
11. The person who smokes Blue Master is Alice.
12. The person who uses a OnePlus 9 is the person who likes going on cruises.
13. The coffee drinker is the Prince smoker.
14. The coffee drinker is the person who uses a Huawei P50.
15. Eric is the tea drinker.
16. The Prince smoker is in the third house.
17. The person who smokes Yellow Monster is somewhere to the right of the coffee drinker.
18. The person who enjoys mountain retreats is Peter.
19. The person who uses a Huawei P50 is the person who has blonde hair.
20. There are two houses between the person who loves beach vacations and the person who uses a Google Pixel 6.
21. The one who only drinks water is in the fourth house.
22. Eric is the person partial to Pall Mall.
23. Bob is the boba tea drinker.
 What is the value of attribute House for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


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`, `Bob`, `Eric`, `Arnold`, `Peter`, `Carol`
 - People have unique heights: `short`, `tall`, `very short`, `average`, `very tall`, `super tall`
 - People have unique favorite music genres: `rock`, `jazz`, `classical`, `country`, `hip hop`, `pop`
 - Each mother is accompanied by their child: `Samantha`, `Alice`, `Fred`, `Bella`, `Meredith`, `Timothy`

## Clues:
1. The person who loves hip-hop music is not in the second house.
2. The person who is very tall is directly left of the person who is very short.
3. The person's child is named Samantha is in the first house.
4. The person who has an average height is directly left of the person who loves hip-hop music.
5. The person's child is named Alice is the person who loves jazz music.
6. The person who is the mother of Timothy is somewhere to the right of the person who loves jazz music.
7. Eric is directly left of the person who is tall.
8. The person who is short is the person who loves hip-hop music.
9. The person who is very short is the person who is the mother of Timothy.
10. Peter is the person who loves rock music.
11. The person's child is named Bella is Bob.
12. The person's child is named Fred is Alice.
13. The person who loves classical music is directly left of the person who loves pop music.
14. The person who loves rock music is somewhere to the right of the person who is very tall.
15. Carol is somewhere to the left of Alice.
16. Carol is somewhere to the right of Arnold.
17. The person who loves classical music is not in the first house.
18. The person who is super tall is Eric.
 What is the value of attribute Height for the person whose attribute Children is Samantha? Please reason step by step, and put your final answer within \boxed{}

Answer: super tall


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`, `Peter`, `Alice`, `Arnold`, `Bob`
 - People own unique car models: `toyota camry`, `honda civic`, `tesla model 3`, `bmw 3 series`, `ford f150`
 - Everyone has a unique favorite cigar: `dunhill`, `blends`, `prince`, `blue master`, `pall mall`

## Clues:
1. Alice is the person who owns a Honda Civic.
2. The person who owns a Ford F-150 is not in the third house.
3. Alice is the person who smokes many unique blends.
4. The person who smokes many unique blends is not in the third house.
5. Alice is not in the second house.
6. The person who owns a Tesla Model 3 is somewhere to the left of Eric.
7. Arnold is somewhere to the right of the person who smokes many unique blends.
8. Arnold is the Dunhill smoker.
9. Bob is the person who owns a BMW 3 Series.
10. The person partial to Pall Mall is directly left of the person who smokes many unique blends.
11. There is one house between the Prince smoker and the person partial to Pall Mall.
12. The person who owns a Toyota Camry is Arnold.
 What is the value of attribute CarModel for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: tesla model 3


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`, `Alice`, `Bob`, `Peter`, `Eric`, `Carol`
 - People have unique favorite sports: `baseball`, `soccer`, `swimming`, `basketball`, `volleyball`, `tennis`

## Clues:
1. Carol is in the first house.
2. Alice is not in the second house.
3. There are two houses between the person who loves baseball and Eric.
4. The person who loves tennis is not in the fourth house.
5. The person who loves baseball is not in the fifth house.
6. The person who loves swimming is not in the third house.
7. The person who loves volleyball is not in the sixth house.
8. Bob is in the sixth house.
9. Eric is the person who loves swimming.
10. Alice is not in the fourth house.
11. The person who loves tennis is Arnold.
12. Peter is somewhere to the right of the person who loves soccer.
 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{}

Answer: 1


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`, `Peter`, `Eric`, `Arnold`
 - Each person has an occupation: `doctor`, `teacher`, `engineer`, `artist`
 - Each mother is accompanied by their child: `Meredith`, `Fred`, `Bella`, `Samantha`
 - Everyone has something unique for lunch: `spaghetti`, `pizza`, `stew`, `grilled cheese`

## Clues:
1. The person who loves the spaghetti eater is directly left of the person who is a teacher.
2. Arnold is somewhere to the left of the person's child is named Samantha.
3. The person's child is named Bella is in the first house.
4. The person who loves the spaghetti eater is directly left of Peter.
5. The person who loves the stew is Arnold.
6. The person who is an artist is the person who is a pizza lover.
7. Arnold is the person who is an engineer.
8. Alice is the person's child is named Samantha.
9. The person who is a doctor is not in the first house.
10. The person's child is named Meredith is not in the fourth house.
11. Eric is the person's child is named Bella.
 What is the value of attribute House for the person whose attribute Children is Fred? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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`, `Bob`, `Alice`, `Peter`, `Arnold`
 - Each person has a favorite color: `yellow`, `green`, `red`, `white`, `blue`
 - Each mother is accompanied by their child: `Samantha`, `Fred`, `Meredith`, `Bella`, `Timothy`
 - People have unique favorite book genres: `biography`, `mystery`, `romance`, `science fiction`, `fantasy`
 - Each person has a unique birthday month: `april`, `feb`, `sept`, `jan`, `mar`
 - People have unique favorite sports: `soccer`, `basketball`, `swimming`, `baseball`, `tennis`

## Clues:
1. The person who loves swimming is the person who loves mystery books.
2. Eric is somewhere to the left of the person who is the mother of Timothy.
3. The person who loves basketball is somewhere to the left of the person who is the mother of Timothy.
4. The person who loves soccer is the person whose birthday is in September.
5. Eric is the person who loves biography books.
6. The person who loves baseball is the person who loves white.
7. The person who loves science fiction books is the person whose birthday is in March.
8. The person who loves swimming and the person whose favorite color is red are next to each other.
9. The person who loves biography books is not in the first house.
10. The person who loves baseball is somewhere to the left of the person whose favorite color is red.
11. The person who loves fantasy books is Bob.
12. The person's child is named Bella is the person whose birthday is in February.
13. The person who loves tennis and the person's child is named Samantha are next to each other.
14. The person's child is named Bella is not in the first house.
15. The person's child is named Meredith is the person whose birthday is in March.
16. The person who loves blue is directly left of the person who loves yellow.
17. There is one house between Alice and the person whose birthday is in March.
18. The person whose favorite color is red is directly left of the person whose birthday is in January.
19. The person's child is named Meredith is not in the first house.
20. Arnold is somewhere to the right of the person who loves swimming.
21. The person who loves fantasy books is the person who is the mother of Timothy.
 What is the value of attribute Children for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: Fred


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`, `Eric`, `Carol`, `Alice`, `Peter`
 - Each person has a unique level of education: `doctorate`, `trade school`, `associate`, `high school`, `bachelor`, `master`
 - People own unique car models: `chevrolet silverado`, `ford f150`, `honda civic`, `tesla model 3`, `bmw 3 series`, `toyota camry`
 - Each person has a unique favorite drink: `tea`, `water`, `boba tea`, `coffee`, `root beer`, `milk`
 - They all have a unique favorite flower: `carnations`, `iris`, `lilies`, `tulips`, `daffodils`, `roses`

## Clues:
1. Eric is the one who only drinks water.
2. The person with an associate's degree is the person who owns a Toyota Camry.
3. The boba tea drinker is in the fourth house.
4. The person who loves the vase of tulips is directly left of the person who owns a Tesla Model 3.
5. The person with a master's degree is somewhere to the left of the person who owns a BMW 3 Series.
6. The person who owns a Toyota Camry is directly left of the person who loves a bouquet of daffodils.
7. The person who loves the boquet of iris is somewhere to the left of the root beer lover.
8. The person who likes milk is somewhere to the right of the person who owns a Honda Civic.
9. Carol is the person who owns a Honda Civic.
10. The person with a high school diploma is in the second house.
11. The person with a master's degree is the boba tea drinker.
12. The person who owns a Tesla Model 3 is Arnold.
13. The person who loves the boquet of lilies is the person who owns a Tesla Model 3.
14. The person who loves a carnations arrangement is somewhere to the left of Alice.
15. The person with a bachelor's degree is somewhere to the right of the person who likes milk.
16. The one who only drinks water is the person who owns a Ford F-150.
17. Carol is somewhere to the left of the person with a doctorate.
18. There are two houses between the person who owns a Toyota Camry and the person who loves the vase of tulips.
19. The person who owns a Tesla Model 3 is somewhere to the left of the coffee drinker.
20. Bob is in the third house.
 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{}

Answer: high school


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`, `Alice`, `Eric`, `Arnold`
 - The people keep unique animals: `horse`, `cat`, `fish`, `bird`
 - People use unique phone models: `oneplus 9`, `google pixel 6`, `iphone 13`, `samsung galaxy s21`
 - Each person has a favorite color: `red`, `white`, `yellow`, `green`
 - Each person lives in a unique style of house: `colonial`, `victorian`, `ranch`, `craftsman`

## Clues:
1. The fish enthusiast is the person who uses an iPhone 13.
2. Alice is in the fourth house.
3. Peter is in the first house.
4. The person residing in a Victorian house is the person whose favorite color is red.
5. The person who loves white is the person in a Craftsman-style house.
6. The person whose favorite color is green is in the fourth house.
7. The person living in a colonial-style house is Eric.
8. The bird keeper is Peter.
9. The person who uses a Google Pixel 6 is in the fourth house.
10. The person who loves white is the person who uses a Samsung Galaxy S21.
11. The person living in a colonial-style house is the cat lover.
12. Eric is not in the third house.
 What is the value of attribute Color for the person whose attribute HouseStyle is ranch? Please reason step by step, and put your final answer within \boxed{}

Answer: green


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`, `Arnold`, `Bob`, `Eric`
 - Each person has a unique hobby: `photography`, `cooking`, `knitting`, `gardening`, `painting`
 - Each person has a unique favorite drink: `root beer`, `milk`, `water`, `coffee`, `tea`

## Clues:
1. Eric is the coffee drinker.
2. The tea drinker is the person who paints as a hobby.
3. The person who enjoys knitting is not in the fourth house.
4. Peter is not in the fourth house.
5. Eric is somewhere to the right of the root beer lover.
6. Arnold is the person who loves cooking.
7. The one who only drinks water is somewhere to the right of the person who enjoys gardening.
8. There is one house between Bob and the person who paints as a hobby.
9. The person who enjoys gardening is directly left of the root beer lover.
10. The photography enthusiast is the one who only drinks water.
 What is the value of attribute Hobby for the person whose attribute House is 5? Please reason step by step, and put your final answer within \boxed{}

Answer: knitting


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`, `Bob`, `Arnold`, `Peter`, `Alice`
 - People have unique favorite book genres: `romance`, `science fiction`, `biography`, `fantasy`, `mystery`
 - Each person prefers a unique type of vacation: `camping`, `cruise`, `beach`, `mountain`, `city`

## Clues:
1. The person who loves biography books is Eric.
2. The person who loves biography books is directly left of the person who loves mystery books.
3. The person who loves science fiction books is directly left of the person who loves fantasy books.
4. There are two houses between Bob and the person who likes going on cruises.
5. The person who enjoys mountain retreats is in the first house.
6. The person who loves mystery books is somewhere to the right of the person who prefers city breaks.
7. The person who enjoys camping trips is Arnold.
8. Alice is not in the third house.
9. The person who loves mystery books is not in the fifth house.
10. The person who loves beach vacations is the person who loves mystery books.
 What is the value of attribute House for the person whose attribute Vacation is camping? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


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`
 - People own unique car models: `toyota camry`, `ford f150`, `tesla model 3`
 - Each person lives in a unique style of house: `ranch`, `colonial`, `victorian`
 - Each person has a unique type of pet: `cat`, `dog`, `fish`
 - Each person has an occupation: `engineer`, `doctor`, `teacher`
 - Each person prefers a unique type of vacation: `city`, `mountain`, `beach`

## Clues:
1. The person with an aquarium of fish is in the first house.
2. The person who owns a Toyota Camry is in the second house.
3. The person who enjoys mountain retreats is not in the second house.
4. The person who prefers city breaks is not in the second house.
5. The person in a ranch-style home is somewhere to the left of Peter.
6. The person who owns a Toyota Camry is directly left of the person living in a colonial-style house.
7. Arnold is the person who has a cat.
8. Eric is somewhere to the left of the person who enjoys mountain retreats.
9. The person who is an engineer is not in the third house.
10. The person who owns a Tesla Model 3 is somewhere to the left of the person who is a teacher.
11. The person who owns a dog is the person who is an engineer.
 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{}

Answer: 2


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 use unique phone models: `iphone 13`, `samsung galaxy s21`, `google pixel 6`
 - People have unique heights: `very short`, `average`, `short`
 - Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`
 - People own unique car models: `tesla model 3`, `toyota camry`, `ford f150`

## Clues:
1. Peter is somewhere to the right of Eric.
2. The person living in a colonial-style house is in the second house.
3. The person who owns a Tesla Model 3 is the person who is very short.
4. The person who is short is directly left of the person who uses a Samsung Galaxy S21.
5. The person who uses an iPhone 13 is directly left of the person who uses a Google Pixel 6.
6. The person living in a colonial-style house is somewhere to the right of the person in a ranch-style home.
7. Arnold is in the second house.
8. The person who owns a Ford F-150 is somewhere to the right of the person who owns a Toyota Camry.
9. The person who has an average height is in the first house.
 What is the value of attribute PhoneModel for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: google pixel 6


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`, `Arnold`, `Eric`, `Bob`
 - Each person lives in a unique style of house: `ranch`, `modern`, `victorian`, `colonial`, `craftsman`
 - The people keep unique animals: `dog`, `horse`, `cat`, `bird`, `fish`

## Clues:
1. The dog owner is Arnold.
2. Arnold is not in the second house.
3. The person in a ranch-style home is somewhere to the left of Alice.
4. Peter is the person in a modern-style house.
5. The person in a modern-style house is somewhere to the right of the person living in a colonial-style house.
6. The person who keeps horses is somewhere to the left of Bob.
7. There is one house between the bird keeper and Peter.
8. The bird keeper is somewhere to the left of the cat lover.
9. The bird keeper is the person living in a colonial-style house.
10. The person residing in a Victorian house is Arnold.
11. The person who keeps horses is Peter.
 What is the value of attribute HouseStyle for the person whose attribute Animal is fish? Please reason step by step, and put your final answer within \boxed{}

Answer: ranch


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`, `Eric`, `Alice`, `Peter`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`, `dunhill`
 - Each person has a unique favorite drink: `milk`, `coffee`, `water`, `tea`
 - People have unique hair colors: `blonde`, `black`, `red`, `brown`

## Clues:
1. The person who has brown hair is not in the fourth house.
2. The person who likes milk is the person who has brown hair.
3. The person partial to Pall Mall is somewhere to the right of the person who has black hair.
4. Peter is somewhere to the left of the Dunhill smoker.
5. The person who smokes Blue Master is directly left of Alice.
6. The tea drinker is Peter.
7. Eric is the person who has brown hair.
8. Eric is not in the third house.
9. Alice is the Dunhill smoker.
10. The person who has blonde hair is the Prince smoker.
11. The one who only drinks water is not in the fourth house.
 What is the value of attribute Drink for the person whose attribute Cigar is blue master? Please reason step by step, and put your final answer within \boxed{}

Answer: milk


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`
 - Each person has a unique level of education: `bachelor`, `high school`, `associate`, `master`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`, `Kailyn`
 - The people keep unique animals: `fish`, `horse`, `cat`, `bird`
 - Each person has a unique birthday month: `jan`, `feb`, `sept`, `april`
 - People have unique favorite music genres: `rock`, `pop`, `jazz`, `classical`

## Clues:
1. The person with an associate's degree is The person whose mother's name is Aniya.
2. Peter is the person whose birthday is in September.
3. The person with a bachelor's degree is directly left of the person who loves pop music.
4. Arnold is The person whose mother's name is Janelle.
5. The person with a master's degree is Arnold.
6. The person whose mother's name is Janelle is the person who loves classical music.
7. The person whose birthday is in April is somewhere to the right of the person who loves rock music.
8. The cat lover is in the second house.
9. The fish enthusiast is in the third house.
10. Eric is the person whose birthday is in April.
11. The person who loves pop music is the person whose birthday is in January.
12. The person whose mother's name is Holly is the person with a bachelor's degree.
13. The person who keeps horses is the person with a master's degree.
14. The person whose mother's name is Aniya is the fish enthusiast.
15. Arnold is somewhere to the left of the fish enthusiast.
 What is the value of attribute House for the person whose attribute Education is associate? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


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`, `Alice`, `Eric`, `Carol`
 - The people keep unique animals: `rabbit`, `bird`, `dog`, `horse`, `cat`, `fish`
 - Each person has an occupation: `doctor`, `teacher`, `lawyer`, `artist`, `engineer`, `nurse`

## Clues:
1. Arnold is not in the sixth house.
2. The person who is an engineer is directly left of Eric.
3. Carol and the rabbit owner are next to each other.
4. The person who is an artist is Peter.
5. The person who keeps horses is in the second house.
6. Eric is directly left of the person who is a lawyer.
7. The person who is an artist is somewhere to the left of the person who is a doctor.
8. The cat lover is not in the sixth house.
9. Peter is in the fifth house.
10. The dog owner is the person who is an artist.
11. The person who keeps horses is directly left of the rabbit owner.
12. The bird keeper is Alice.
13. The person who is a teacher and Alice are next to each other.
14. Alice is not in the first house.
 What is the value of attribute House for the person whose attribute Occupation is lawyer? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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`
 - Each person has a unique birthday month: `sept`, `feb`, `april`, `jan`
 - The mothers' names in different houses are unique: `Aniya`, `Kailyn`, `Holly`, `Janelle`
 - The people keep unique animals: `horse`, `bird`, `cat`, `fish`
 - Each person has a favorite color: `green`, `white`, `yellow`, `red`
 - People have unique favorite sports: `swimming`, `basketball`, `tennis`, `soccer`

## Clues:
1. The bird keeper is The person whose mother's name is Kailyn.
2. The fish enthusiast is not in the fourth house.
3. The person who loves white is Arnold.
4. The person who keeps horses is Peter.
5. The person who keeps horses is not in the first house.
6. The person whose mother's name is Kailyn is Arnold.
7. The person whose birthday is in January is in the first house.
8. The person whose birthday is in April is somewhere to the left of the person whose birthday is in September.
9. Alice is the person whose birthday is in September.
10. The person whose mother's name is Aniya and the person whose birthday is in September are next to each other.
11. Peter is directly left of the person whose favorite color is red.
12. There is one house between the person whose birthday is in April and the person who loves soccer.
13. The fish enthusiast is the person whose birthday is in September.
14. The person who loves swimming is The person whose mother's name is Holly.
15. The person whose favorite color is green is the person who loves swimming.
16. The person who loves yellow is the person who loves basketball.
 What is the value of attribute Mother for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: Holly


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`, `Carol`, `Eric`, `Arnold`, `Bob`
 - People have unique heights: `very tall`, `very short`, `average`, `tall`, `short`, `super tall`

## Clues:
1. Eric is in the second house.
2. Arnold is the person who is short.
3. Alice is somewhere to the left of the person who has an average height.
4. The person who is tall is somewhere to the right of Peter.
5. Arnold is not in the fourth house.
6. The person who is short is somewhere to the right of Eric.
7. There is one house between Peter and Bob.
8. Arnold is somewhere to the left of the person who is very tall.
9. The person who has an average height is Carol.
10. The person who is very short is Eric.
 What is the value of attribute House for the person whose attribute Height is very short? Please reason step by step, and put your final answer within \boxed{}

Answer: 2


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`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`
 - Each person has a unique hobby: `gardening`, `cooking`, `photography`
 - People have unique favorite sports: `tennis`, `soccer`, `basketball`
 - They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`
 - Everyone has a favorite smoothie: `desert`, `cherry`, `watermelon`

## Clues:
1. The person who loves soccer is the person who loves a bouquet of daffodils.
2. Arnold is the person who loves the boquet of lilies.
3. The person who loves beach vacations is directly left of Eric.
4. The Desert smoothie lover is the person who loves basketball.
5. The person who loves the boquet of lilies is directly left of the person who loves a carnations arrangement.
6. Eric is directly left of Peter.
7. The person who loves basketball and the person who loves a bouquet of daffodils are next to each other.
8. The person who loves a bouquet of daffodils is the person who likes Cherry smoothies.
9. The person who enjoys mountain retreats is the person who loves cooking.
10. The photography enthusiast is the person who loves basketball.
 What is the value of attribute Vacation for the person whose attribute Hobby is cooking? Please reason step by step, and put your final answer within \boxed{}

Answer: mountain


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: `Arnold`, `Eric`
 - Each person has an occupation: `engineer`, `doctor`
 - Each person has a unique birthday month: `april`, `sept`
 - Each person lives in a unique style of house: `victorian`, `colonial`
 - People have unique heights: `very short`, `short`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`

## Clues:
1. The person who is an engineer is in the first house.
2. The person whose birthday is in April and the person who is a doctor are next to each other.
3. The person living in a colonial-style house is the person who is an engineer.
4. The person who is very short is the person who is an engineer.
5. The person who is short is the person partial to Pall Mall.
6. The person who is an engineer is Eric.
 What is the value of attribute Cigar for the person whose attribute Occupation is engineer? Please reason step by step, and put your final answer within \boxed{}

Answer: prince


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`, `Eric`, `Bob`, `Alice`, `Peter`
 - Each person has a unique birthday month: `feb`, `mar`, `sept`, `jan`, `may`, `april`
 - Everyone has something unique for lunch: `stew`, `soup`, `grilled cheese`, `stir fry`, `spaghetti`, `pizza`
 - People have unique heights: `very short`, `average`, `super tall`, `short`, `very tall`, `tall`
 - People own unique car models: `chevrolet silverado`, `ford f150`, `bmw 3 series`, `tesla model 3`, `toyota camry`, `honda civic`

## Clues:
1. The person who owns a Honda Civic is the person who is short.
2. The person who owns a Ford F-150 is in the fifth house.
3. The person who loves stir fry is somewhere to the left of Eric.
4. The person whose birthday is in May is somewhere to the left of Carol.
5. The person who is very short is somewhere to the left of the person whose birthday is in April.
6. The person who owns a BMW 3 Series is not in the third house.
7. There are two houses between the person who loves stir fry and the person who is a pizza lover.
8. The person who loves the soup is directly left of Eric.
9. The person who loves the spaghetti eater and the person whose birthday is in May are next to each other.
10. Alice is directly left of the person who owns a BMW 3 Series.
11. The person who owns a Tesla Model 3 is somewhere to the left of the person who is tall.
12. The person who is very tall is the person who owns a Toyota Camry.
13. Peter is directly left of the person who is a pizza lover.
14. The person who loves the stew is not in the third house.
15. There is one house between the person whose birthday is in September and the person who is very short.
16. There is one house between the person whose birthday is in March and the person who is super tall.
17. The person who is tall is Bob.
18. The person whose birthday is in May is somewhere to the right of Alice.
19. The person who is very short is in the fourth house.
20. The person whose birthday is in March is the person who is short.
21. Carol is the person who owns a Tesla Model 3.
22. Eric is the person whose birthday is in January.
 What is the value of attribute Food for the person whose attribute CarModel is bmw 3 series? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


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`
 - People own unique car models: `ford f150`, `toyota camry`, `honda civic`, `tesla model 3`
 - Everyone has a unique favorite cigar: `prince`, `dunhill`, `blue master`, `pall mall`
 - People have unique favorite sports: `soccer`, `swimming`, `tennis`, `basketball`

## Clues:
1. The person who owns a Tesla Model 3 is not in the third house.
2. The person partial to Pall Mall is not in the third house.
3. The person who owns a Honda Civic is the Prince smoker.
4. Peter is the person who loves soccer.
5. The person who smokes Blue Master is the person who loves swimming.
6. The person who owns a Ford F-150 is not in the fourth house.
7. The person who smokes Blue Master is not in the first house.
8. The person who owns a Ford F-150 is not in the third house.
9. The person who loves soccer is in the second house.
10. The person who loves tennis is directly left of Arnold.
11. Alice is directly left of the person who owns a Honda Civic.
 What is the value of attribute CarModel for the person whose attribute FavoriteSport is basketball? Please reason step by step, and put your final answer within \boxed{}

Answer: ford f150


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`
 - The people are of nationalities: `brit`, `swede`, `norwegian`, `dane`
 - They all have a unique favorite flower: `carnations`, `lilies`, `roses`, `daffodils`
 - Each person has a unique level of education: `high school`, `bachelor`, `master`, `associate`

## Clues:
1. The Norwegian is directly left of the person who loves the rose bouquet.
2. The person with a high school diploma is Eric.
3. Arnold is not in the first house.
4. The person with an associate's degree is the person who loves a carnations arrangement.
5. The Dane is not in the third house.
6. Peter is the person who loves the rose bouquet.
7. The Swedish person and the Norwegian are next to each other.
8. Eric is in the second house.
9. The person who loves the boquet of lilies is the person with a master's degree.
10. The person who loves the boquet of lilies is the Swedish person.
 What is the value of attribute Nationality for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: swede


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`, `Eric`, `Peter`, `Alice`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Kailyn`, `Aniya`
 - The people are of nationalities: `dane`, `norwegian`, `brit`, `swede`
 - People have unique favorite book genres: `science fiction`, `romance`, `fantasy`, `mystery`
 - The people keep unique animals: `fish`, `cat`, `bird`, `horse`
 - People have unique hair colors: `black`, `blonde`, `red`, `brown`

## Clues:
1. The Swedish person is the person who has black hair.
2. The bird keeper is in the first house.
3. Arnold is the person who loves fantasy books.
4. The person who loves science fiction books is not in the second house.
5. The British person and Arnold are next to each other.
6. The bird keeper is the person who has red hair.
7. The person who keeps horses is Peter.
8. The person who has black hair is the person who loves romance books.
9. The person whose mother's name is Kailyn is Arnold.
10. The Swedish person is The person whose mother's name is Janelle.
11. The person who has blonde hair is in the third house.
12. Alice is The person whose mother's name is Aniya.
13. The Swedish person is the fish enthusiast.
14. Arnold is directly left of the person who has black hair.
15. The Norwegian is not in the first house.
 What is the value of attribute House for the person whose attribute HairColor is brown? Please reason step by step, and put your final answer within \boxed{}

Answer: 2


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`, `Alice`, `Arnold`, `Eric`
 - The people keep unique animals: `horse`, `bird`, `fish`, `cat`
 - Each person has a unique level of education: `high school`, `bachelor`, `associate`, `master`
 - Each person has a unique favorite drink: `tea`, `water`, `coffee`, `milk`
 - People have unique favorite book genres: `fantasy`, `science fiction`, `romance`, `mystery`
 - Each person has a unique birthday month: `april`, `feb`, `sept`, `jan`

## Clues:
1. Peter is the person whose birthday is in February.
2. The person with a master's degree is the bird keeper.
3. The person who keeps horses is not in the second house.
4. The person whose birthday is in January is the person who loves science fiction books.
5. The person who loves mystery books is Alice.
6. There is one house between the person who likes milk and Alice.
7. The person whose birthday is in April is the person who loves fantasy books.
8. The person with a high school diploma is not in the second house.
9. Eric is directly left of the person who likes milk.
10. The fish enthusiast is the person whose birthday is in February.
11. The tea drinker is somewhere to the left of Peter.
12. The one who only drinks water is the person with a master's degree.
13. The person with a bachelor's degree is somewhere to the right of the person whose birthday is in January.
14. Peter is in the third house.
15. The person who loves science fiction books is Arnold.
 What is the value of attribute Drink for the person whose attribute BookGenre is science fiction? Please reason step by step, and put your final answer within \boxed{}

Answer: milk


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 Name for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter