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`, `Eric`, `Arnold`, `Peter`
 - Each person has a unique hobby: `painting`, `gardening`, `photography`, `cooking`
 - People have unique favorite book genres: `romance`, `science fiction`, `mystery`, `fantasy`
 - Each person prefers a unique type of vacation: `city`, `beach`, `mountain`, `cruise`
 - People have unique favorite music genres: `rock`, `pop`, `classical`, `jazz`
 - Each person has a unique level of education: `high school`, `associate`, `bachelor`, `master`

## Clues:
1. The person who loves science fiction books is somewhere to the right of the person who loves fantasy books.
2. The person who paints as a hobby is the person who loves fantasy books.
3. Arnold is the person who loves fantasy books.
4. The person with a high school diploma is the person who loves pop music.
5. The person who loves cooking is somewhere to the right of Eric.
6. There are two houses between the photography enthusiast and the person who loves beach vacations.
7. The person who loves romance books is Peter.
8. The person who enjoys mountain retreats is not in the second house.
9. The person with a bachelor's degree is somewhere to the right of the person with a high school diploma.
10. The person who loves classical music is not in the third house.
11. The person who prefers city breaks is the person who loves science fiction books.
12. The person who loves rock music is Peter.
13. The person with a bachelor's degree is not in the fourth house.
14. The person with a master's degree is the person who loves jazz music.
15. The person who enjoys gardening is the person who loves romance books.
 What is the value of attribute Hobby for the person whose attribute BookGenre is romance? Please reason step by step, and put your final answer within \boxed{}

Answer: gardening


## Task 3.

In triangle $A B C$, the angle at vertex $B$ is $120^{\circ}$. Let $A_{1}, B_{1}, C_{1}$ be points on the sides $\overline{B C}$, $\overline{C A}$, $\overline{A B}$, respectively, such that $A A_{1}$, $B B_{1}$, $C C_{1}$ are the angle bisectors of triangle $A B C$. Determine the angle $\varangle A_{1} B_{1} C_{1}$.

Answer: 90^{\circ}


22. Let $O$ be an interior point of $\triangle A B C$. Extend $A O$ to meet the side $B C$ at $D$. Similarly, extend $B O$ and $C O$ to meet $C A$ and $A B$ respectively at $E$ and $F$. If $A O=30, F O=20, B O=60, D O=10$ and $C O=20$, find $E O$.

Answer: 20


In a qualification football round there are six teams and each two play one versus another exactly once. No two matches are played at the same time. At every moment the difference between the number of already played matches for any two teams is $0$ or $1$. A win is worth $3$ points, a draw is worth $1$ point and a loss is worth $0$ points. Determine the smallest positive integer $n$ for which it is possible that after the $n$-th match all teams have a different number of points and each team has a non-zero number of points.

Answer: 9


Given a complex number \( z \) such that \( |z| = 1 \), let \( u = z^4 - z^3 - 3i z^2 - z + 1 \). Find \(\max |u|\) and \(\min |u|\).

Answer: 5


## Problem B2

If $\mathrm{P}$ and $\mathrm{Q}$ are two points in the plane, let $\mathrm{m}(\mathrm{PQ})$ be the perpendicular bisector of $\mathrm{PQ} . \mathrm{S}$ is a finite set of $n>1$ points such that: (1) if $P$ and $Q$ belong to $S$, then some point of $m(P Q)$ belongs to S, (2) if PQ, $\mathrm{P}^{\prime} \mathrm{Q}^{\prime}, \mathrm{P}^{\prime \prime} \mathrm{Q}^{\prime \prime}$ are three distinct segments, whose endpoints are all in S, then if there is a point in all of $\mathrm{m}(\mathrm{PQ}), \mathrm{m}\left(\mathrm{P}^{\prime} \mathrm{Q}^{\prime}\right), \mathrm{m}\left(\mathrm{P}^{\prime \prime} \mathrm{Q}^{\prime \prime}\right)$ it does not belong to $\mathrm{S}$. What are the possible values of $n$ ?

## Answer

$\mathrm{n}=3$ (equilateral triangle), 5 (regular pentagon).

Answer: 3


8. On the sides $B C, C A, A B$ of an equilateral triangle $A B C$ with side length 7, points $A_{1}, B_{1}, C_{1}$ are taken respectively. It is known that $A C_{1}=B A_{1}=C B_{1}=3$. Find the ratio of the area of triangle $A B C$ to the area of the triangle formed by the lines $A A_{1}, B B_{1}, C C_{1}$.

Answer: 37


Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an $11$ on the next quiz, her mean will increase by $1$ . If she scores an $11$ on each of the next three quizzes, her mean will increase by $2$ . What is the mean of her quiz scores currently? $\textbf{(A) }4\qquad\textbf{(B) }5\qquad\textbf{(C) }6\qquad\textbf{(D) }7\qquad\textbf{(E) }8$

Answer: 7


## Task 4 - 210514

A problem from a Leningrad Mathematical Olympiad:

An "October Child" (that is, a Young Pioneer up to 3rd grade), a Pioneer, and a Komsomol member went to a Pioneer camp. Their first names are (not necessarily in the same order) Kolya, Igor, and Sasha. From their conversations on the train, we learned:

(1) Kolya and the Komsomol member are two enthusiastic anglers.

(2) The October Child lives in Leningrad; Sasha also lives in Leningrad, but on a different street.

(3) Sasha is younger than the Komsomol member.

What is the first name of the October Child, the first name of the Pioneer, and the first name of the Komsomol member?

Answer: Kolya


A triangle's two altitudes are at least as long as the sides to which they are drawn. What are the angles of the triangle?

---

The translation maintains the original text's format and structure.

Answer: 45^\circ


## Task A-1.5.

Spouses Ana and Tomislav came to a party where four other couples were also present. Upon arrival, a certain number of handshakes occurred. No one shook hands with their own spouse or with themselves. Later, when Tomislav asked everyone how many people they had shaken hands with, he received nine different answers. How many people did Ana shake hands with?

Answer: 4


\section*{Problem 3B - 111043B}

Dirk explains to Jürgen the usefulness of differential calculus using the solution to the following problem: Let \(A B C D E\) be a planar convex pentagon such that \(A, B, C, E\) are the vertices of a rectangle and \(C, D, E\) are the vertices of an equilateral triangle. The area of the pentagon \(A B C D E\) is now prescribed to be a certain value \(\mathrm{F}\).

Determine whether among all such pentagons, there exists one with the smallest perimeter \(u\)! If this is the case, calculate for all such pentagons with the smallest perimeter the value \(a: b\), where \(A B=a\) and \(B C=b\).

The next day, Jürgen tells Dirk that he has found a solution to this problem without using differential calculus.

Provide a solution that Jürgen might have found.

Answer: \dfrac{3 + \sqrt{3}}{3}


75. Hope Middle School needs to select exchange students from Grade 7 to Grade 12, but due to the limited number of slots, the following rules are set:
(1) At most 3 students from Grade 7;
(2) At most 4 students from Grade 8;
(3) At most 5 students from Grade 9;
(4) At most 8 students from Grade 10;
(5) At most 10 students from Grade 11;
(6) At most 7 students from Grade 12.
If no matter how the selection is made, at least one of the above rules must be followed, then the maximum number of students that can be selected is $\qquad$.

Answer: 42


Problem 3. (15 points) In parallelogram $A B C D$, side $A D$ is divided into equal parts by points $A_{1}, A_{2}, \ldots, A_{2020}$. Point $E_{1}$ is the intersection point of lines $B A_{1}$ and $A C$. Determine what fraction of diagonal $A C$ segment $A E_{1}$ constitutes.

Answer: \dfrac{1}{2022}


Let \( n \) and \( b \) be positive integers. We say \( n \) is \( b \)-discerning if there exists a set consisting of \( n \) different positive integers less than \( b \) that has no two different subsets \( U \) and \( V \) such that the sum of all elements in \( U \) equals the sum of all elements in \( V \).

(a) Prove that 8 is 100-discerning.

(b) Prove that 9 is not 100-discerning.

Answer: 9


Let \( ABC \) be an equilateral triangle with side length 8. Let \( X \) be on side \( AB \) so that \( AX = 5 \) and \( Y \) be on side \( AC \) so that \( AY = 3 \). Let \( Z \) be on side \( BC \) so that \( AZ, BY, CX \) are concurrent. Let \( ZX, ZY \) intersect the circumcircle of \( AXY \) again at \( P, Q \) respectively. Let \( XQ \) and \( YP \) intersect at \( K \). Compute \( KX \cdot KQ \).

Answer: 304


In the quadrilateral pyramid $P-ABCD$ with a base $ABCD$ represented in Figure 7, it is given that $PA \perp$ to the base $ABCD$, $BC=CD=2$, $AC=4$, $\angle ACB = \angle ACD = \frac{\pi}{3}$. Let $F$ be the midpoint of $PC$, and let $AF \perp PB$.

Find:
1. The length of $PA$;
2. The sine of the dihedral angle $B-AF-D$.

Answer: \frac{\sqrt{63}}{8}


An equilateral triangle with a side length of 10 is divided into 100 smaller equilateral triangles with a side length of 1. Find the number of rhombuses composed of 8 small triangles (these rhombuses can be rotated).

Answer: 84


Given an $n \times n \times n$ cube consisting of $n^{3}$ unit cubes (henceforth referred to as "cells"), any two cells $A$ and $B$ are said to be "adjacent" if they share a common face, or if there exists a cell $C$ such that both $A$ and $B$ share a common face with $C$. Color each cell of an $n \times n \times n$ cube with one of $r$ colors such that any two adjacent cells have different colors. Find the minimum value of $r$.

Answer: 7


Let \( ABC \) be an equilateral triangle with \( AB = 3 \). Circle \( \omega \) with diameter 1 is drawn inside the triangle such that it is tangent to sides \( AB \) and \( AC \). Let \( P \) be a point on \( \omega \) and \( Q \) be a point on segment \( BC \). Find the minimum possible length of the segment \( PQ \).

Answer: \frac{3\sqrt{3}-3}{2}


A semicircle with a radius of $3 \text{ cm}$ contains a $1 \text{ cm}$ radius semicircle and a $2 \text{ cm}$ radius semicircle within it, as shown in the figure. Calculate the radius of the circle that is tangent to all three semicircular arcs.

Answer: \frac{6}{7}


A classroom has 30 students and 30 desks arranged in 5 rows of 6 desks. If the class has 15 boys and 15 girls, in how many ways can the students be placed in the chairs such that no boy is sitting in front of, behind, or next to another boy, and no girl is sitting in front of, behind, or next to another girl?

Answer: 2\cdot15!^2


Problem 11.5. Quadrilateral $ABCD$ is inscribed in a circle. It is known that $BC=CD, \angle BCA=$ $64^{\circ}, \angle ACD=70^{\circ}$. A point $O$ is marked on segment $AC$ such that $\angle ADO=32^{\circ}$. How many degrees does the angle $BOC$ measure?

![](https://cdn.mathpix.com/cropped/2024_05_06_8af0c885427e3e323cf9g-43.jpg?height=448&width=519&top_left_y=234&top_left_x=465)

Answer: 58


Answer: \left\{1 \frac{1}{16} ; 1 \frac{3}{4} ; 2 \frac{7}{16} ; 3 \frac{1}{8} ; 3 \frac{13}{16}\right\}


Prove that there exists a $k_0\in\mathbb{N}$ such that for every $k\in\mathbb{N},k>k_0$, there exists a finite number of lines in the plane not all parallel to one of them, that divide the plane exactly in $k$ regions. Find $k_0$.

Answer: 5


Problem 7.5. On an island, there live knights who always tell the truth, and liars who always lie. One day, 35 inhabitants of the island sat down at 7 tables, with 5 people at each table. Each of these 35 inhabitants was asked: "Are there more than three tables where at least 3 knights are sitting?"

(a) (1 point) What is the maximum number of inhabitants who could have answered "Yes"?

(b) (3 points) What is the maximum number of inhabitants who could have answered "No"?

Answer: 35


We denote by $\mathbb{N}^{*}$ the set of strictly positive integers. Find all $^{2}$ functions $f: \mathbb{N}^{*} \rightarrow \mathbb{N}^{*}$ such that

$$
m^{2}+f(n) \mid m f(m)+n
$$

for all strictly positive integers $m$ and $n$.

Answer: f(n) = n


5. Several people played a round-robin table tennis tournament. At the end of the tournament, it turned out that for any four participants, there would be two who scored the same number of points in the games between these four participants. What is the maximum number of tennis players that could have participated in this tournament? In table tennis, there are no ties; one point is awarded for a win, and zero points for a loss.

(from materials of international olympiads)

Answer: 7


21. Five participants of the competition became its prize winners, scoring 20, 19, and 18 points and taking first, second, and third places, respectively. How many participants won each prize place if together they scored 94 points?

Answer: 1


Consider $n$ lamps clockwise numbered from $1$ to $n$ on a circle.

Let $\xi$ to be a configuration where $0 \le \ell \le n$ random lamps are turned on. A [i]cool procedure[/i] consists in perform, simultaneously, the following operations: for each one of the $\ell$ lamps which are turned on, we verify the number of the lamp; if $i$ is turned on, a [i]signal[/i] of range $i$ is sent by this lamp, and it will be received only by the next $i$ lamps which follow $i$, turned on or turned off, also considered clockwise. At the end of the operations we verify, for each lamp, turned on or turned off, how many signals it has received. If it was reached by an even number of signals, it remains on the same state(that is, if it was turned on, it will be turned on; if it was turned off, it will be turned off). Otherwise, it's state will be changed.

The example in attachment, for $n=4$, ilustrates a configuration where lamps $2$ and $4$  are initially turned on. Lamp $2$ sends signal only for the lamps $3$ e $4$, while lamp $4$ sends signal for lamps $1$, $2$, $3$ e $4$. Therefore, we verify that lamps $1$ e $2$ received only one signal, while lamps $3$ e $4$ received two signals. Therefore, in the next configuration, lamps $1$ e $4$ will be turned on, while lamps $2$ e $3$ will be turned off.

Let $\Psi$ to be the set of all $2^n$ possible configurations, where $0 \le \ell \le n$ random lamps are turned on. We define a function $f: \Psi \rightarrow \Psi$ where, if $\xi$ is a configuration of lamps, then $f(\xi)$ is the configurations obtained after we perform the [i]cool procedure[/i] described above.

Determine all values of $n$ for which $f$ is bijective.

Answer: 2^k


The brothers found a hoard of gold and silver. They divided it in such a way that each received 100 kg. The eldest received the most gold - 30 kg - and a fifth of all the silver. How much gold was in the hoard?

Answer: 50


3. Given the function $f(x)=\sin \omega x+\sin 2 x$, where $\omega \in \mathbf{N}_{+}, \omega \leqslant 2023$. If $f(x)<2$ always holds, then the number of constants $\omega$ that satisfy the condition is $\qquad$

Answer: 1770


7. Let the complex number $z$ satisfy: the real and imaginary parts of $\frac{z}{10}$ and $\frac{10}{\bar{z}}$ are positive numbers less than 1, then the area of the figure corresponding to the points of $z$ in the complex plane is $\qquad$ .

Answer: 75 - \dfrac{25}{2}\pi


## Task A-2.4.

In each field of a $10 \times 10$ table, a natural number is written, and all 20 sums of the numbers in its rows and columns are mutually different. What is the smallest possible sum of all the numbers in such a filled table?

Answer: 195


12.1.1. In a box, there are 6 identical pairs of black gloves and 4 identical pairs of beige gloves. Find the probability that two randomly drawn gloves form a pair.

Answer: \dfrac{47}{95}


7.5. Vasya had 101 real coins. One of them was replaced with a fake one (it differs in weight, but it is unknown whether it is lighter or heavier than a real coin). Vasya wants to find as many real coins as possible in one weighing on a balance scale without weights. What should he do and how many real coins will he be able to find?

Answer: 50


6. When the child was born, their parents were not yet 40 years old, but they were already adults. When the child turned 2 years old, the age of exactly one of the parents was divisible by 2; when the child turned 3 years old, the age of exactly one of the parents was divisible by 3, and so on. How long could such a pattern have continued?

Answer: 8


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Peter`
 - Each person has a unique level of education: `associate`, `bachelor`, `high school`
 - Each person has a unique favorite drink: `water`, `tea`, `milk`
 - People have unique favorite book genres: `science fiction`, `mystery`, `romance`
 - Each person has a unique hobby: `photography`, `cooking`, `gardening`
 - People own unique car models: `ford f150`, `tesla model 3`, `toyota camry`

## Clues:
1. The person who likes milk is somewhere to the right of Eric.
2. The person who loves science fiction books is directly left of the person who owns a Toyota Camry.
3. The person who loves cooking is Peter.
4. The person who loves romance books is the person with a bachelor's degree.
5. The person who owns a Tesla Model 3 is Peter.
6. The person with an associate's degree is the person who loves mystery books.
7. The person who loves mystery books is the photography enthusiast.
8. The one who only drinks water is not in the second house.
9. The person who owns a Toyota Camry is not in the third house.
10. The person who owns a Ford F-150 is the person who loves mystery books.
 What is the value of attribute Drink for the person whose attribute Education is bachelor? Please reason step by step, and put your final answer within \boxed{}

Answer: tea


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`, `Eric`, `Arnold`, `Bob`, `Alice`
 - The people are of nationalities: `german`, `swede`, `brit`, `dane`, `norwegian`

## Clues:
1. The British person is in the fifth house.
2. The Swedish person is somewhere to the left of Eric.
3. Alice is somewhere to the left of Bob.
4. Eric is somewhere to the left of the Norwegian.
5. Arnold is the Swedish person.
6. The Dane is in the first house.
7. Peter is in the fifth house.
 What is the value of attribute House for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Alice`, `Eric`
 - They all have a unique favorite flower: `roses`, `daffodils`, `carnations`, `lilies`
 - Each person has a unique hobby: `photography`, `painting`, `cooking`, `gardening`
 - Each person has a unique type of pet: `dog`, `fish`, `bird`, `cat`
 - Each person has a favorite color: `red`, `yellow`, `green`, `white`
 - Each person lives in a unique style of house: `craftsman`, `colonial`, `ranch`, `victorian`

## Clues:
1. The person in a Craftsman-style house is Arnold.
2. The person who loves the rose bouquet is somewhere to the right of Peter.
3. The photography enthusiast is the person who owns a dog.
4. The person who loves a bouquet of daffodils is not in the fourth house.
5. The person who loves the rose bouquet is the person whose favorite color is red.
6. The person in a Craftsman-style house is in the second house.
7. Eric is the person residing in a Victorian house.
8. The person with an aquarium of fish is the person who loves white.
9. The person who loves cooking is somewhere to the right of the person whose favorite color is red.
10. The person who loves white is the person who loves a carnations arrangement.
11. The person who loves white is somewhere to the right of the person who enjoys gardening.
12. The person who loves a bouquet of daffodils is the person who loves yellow.
13. The person living in a colonial-style house is the person whose favorite color is red.
14. The person who has a cat is Eric.
 What is the value of attribute Name for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
 - People have unique favorite music genres: `rock`, `jazz`, `pop`, `classical`
 - Everyone has a favorite smoothie: `dragonfruit`, `watermelon`, `desert`, `cherry`
 - People have unique hair colors: `red`, `black`, `brown`, `blonde`
 - People have unique favorite book genres: `science fiction`, `fantasy`, `romance`, `mystery`

## Clues:
1. The person who has red hair is not in the third house.
2. There is one house between Eric and the person who likes Cherry smoothies.
3. The person who loves science fiction books is Peter.
4. The person who loves fantasy books is Alice.
5. The Dragonfruit smoothie lover is the person who loves pop music.
6. The Dragonfruit smoothie lover is the person who has red hair.
7. The Watermelon smoothie lover is somewhere to the right of the person who loves classical music.
8. The person who has black hair is the person who likes Cherry smoothies.
9. There is one house between the person who loves pop music and the person who loves fantasy books.
10. The person who loves romance books is somewhere to the right of the person who loves jazz music.
11. The person who has red hair is directly left of the person who has black hair.
12. The person who has brown hair and the Dragonfruit smoothie lover are next to each other.
13. The person who loves science fiction books is the Dragonfruit smoothie lover.
 What is the value of attribute BookGenre for the person whose attribute MusicGenre is rock? Please reason step by step, and put your final answer within \boxed{}

Answer: fantasy


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`, `Peter`, `Bob`, `Eric`, `Carol`, `Alice`
 - The people keep unique animals: `horse`, `rabbit`, `fish`, `cat`, `bird`, `dog`
 - Each person has an occupation: `engineer`, `nurse`, `lawyer`, `teacher`, `artist`, `doctor`
 - People have unique favorite sports: `basketball`, `volleyball`, `soccer`, `tennis`, `baseball`, `swimming`
 - People have unique heights: `average`, `tall`, `short`, `very short`, `very tall`, `super tall`

## Clues:
1. The person who is an engineer is the dog owner.
2. The person who has an average height is somewhere to the left of the person who is short.
3. The person who has an average height is directly left of the rabbit owner.
4. The person who is tall is somewhere to the left of the person who is very short.
5. Arnold is the cat lover.
6. The person who keeps horses is the person who is a teacher.
7. Carol is the person who loves soccer.
8. The person who is tall is the person who loves volleyball.
9. The person who is a lawyer is in the fifth house.
10. The person who loves tennis is the person who is a teacher.
11. The person who has an average height is the person who loves swimming.
12. The person who loves baseball is directly left of the person who is an engineer.
13. Peter is the person who is a nurse.
14. Bob is somewhere to the right of the person who is an artist.
15. The person who is a teacher is directly left of the person who loves soccer.
16. The rabbit owner is Alice.
17. The fish enthusiast is Carol.
18. The person who loves baseball is in the first house.
19. The cat lover is somewhere to the right of the person who is very short.
20. The person who is super tall is in the fifth house.
 What is the value of attribute Animal for the person whose attribute Height is very short? Please reason step by step, and put your final answer within \boxed{}

Answer: horse


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`
 - The people keep unique animals: `horse`, `bird`, `cat`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`
 - People have unique favorite music genres: `pop`, `classical`, `rock`
 - Each person has a favorite color: `yellow`, `white`, `red`

## Clues:
1. The cat lover is in the third house.
2. There is one house between the person who loves yellow and the cat lover.
3. The person who loves classical music is directly left of Eric.
4. Arnold is the Desert smoothie lover.
5. The bird keeper is the Watermelon smoothie lover.
6. The person whose mother's name is Janelle is somewhere to the left of the person who loves white.
7. The person who loves yellow is the person who loves rock music.
8. The person whose mother's name is Holly is directly left of Peter.
 What is the value of attribute Mother for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: Janelle


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 Animal for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: fish


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Eric`, `Peter`, `Alice`, `Bob`, `Arnold`
 - Everyone has something unique for lunch: `spaghetti`, `soup`, `grilled cheese`, `stir fry`, `stew`, `pizza`
 - Each person has a favorite color: `green`, `purple`, `blue`, `red`, `white`, `yellow`
 - The mothers' names in different houses are unique: `Holly`, `Penny`, `Aniya`, `Kailyn`, `Sarah`, `Janelle`
 - Each person lives in a unique style of house: `colonial`, `craftsman`, `modern`, `ranch`, `victorian`, `mediterranean`

## Clues:
1. The person whose mother's name is Janelle is the person living in a colonial-style house.
2. Peter is the person whose favorite color is green.
3. The person who loves blue is directly left of the person who loves the spaghetti eater.
4. The person whose mother's name is Penny is directly left of the person whose favorite color is red.
5. The person who loves blue is The person whose mother's name is Penny.
6. The person whose mother's name is Aniya is directly left of the person whose favorite color is green.
7. The person who loves white is somewhere to the left of The person whose mother's name is Janelle.
8. Eric is the person who loves eating grilled cheese.
9. The person whose mother's name is Holly is directly left of Alice.
10. The person whose mother's name is Holly and the person who loves the stew are next to each other.
11. Alice is the person in a ranch-style home.
12. Carol is not in the sixth house.
13. The person who loves stir fry is the person who loves purple.
14. The person whose favorite color is red and the person living in a colonial-style house are next to each other.
15. The person who loves the soup is Peter.
16. The person who is a pizza lover is somewhere to the left of The person whose mother's name is Sarah.
17. The person residing in a Victorian house is the person who loves eating grilled cheese.
18. The person who loves the spaghetti eater is not in the fifth house.
19. There are two houses between the person who loves eating grilled cheese and The person whose mother's name is Aniya.
20. Arnold is the person whose favorite color is red.
21. The person in a modern-style house is Arnold.
22. The person who loves yellow is the person in a Mediterranean-style villa.
 What is the value of attribute HouseStyle for the person whose attribute Mother is Holly? Please reason step by step, and put your final answer within \boxed{}

Answer: mediterranean


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Carol`, `Peter`, `Eric`, `Bob`, `Alice`
 - Each person lives in a unique style of house: `ranch`, `colonial`, `modern`, `craftsman`, `mediterranean`, `victorian`
 - Everyone has something unique for lunch: `pizza`, `stew`, `spaghetti`, `grilled cheese`, `stir fry`, `soup`
 - Each person prefers a unique type of vacation: `cultural`, `cruise`, `mountain`, `camping`, `city`, `beach`
 - People have unique heights: `average`, `very tall`, `very short`, `short`, `tall`, `super tall`
 - Everyone has a unique favorite cigar: `yellow monster`, `prince`, `dunhill`, `pall mall`, `blue master`, `blends`

## Clues:
1. Alice is in the fifth house.
2. The person who loves stir fry is the person living in a colonial-style house.
3. Alice is the person who loves the spaghetti eater.
4. Arnold is the person who loves the stew.
5. There is one house between the person who has an average height and Peter.
6. The person in a Craftsman-style house is not in the third house.
7. The person who has an average height is the person who loves stir fry.
8. The person who loves beach vacations is the person in a ranch-style home.
9. Eric is in the fourth house.
10. There is one house between the person living in a colonial-style house and the person who enjoys camping trips.
11. The person who enjoys mountain retreats is the person who smokes Yellow Monster.
12. The person who enjoys mountain retreats is the person who is very tall.
13. The person who enjoys mountain retreats and the Dunhill smoker are next to each other.
14. The person who loves the spaghetti eater is the person residing in a Victorian house.
15. The person who is tall is the person who loves beach vacations.
16. The person who is tall is somewhere to the left of the person residing in a Victorian house.
17. The person who loves stir fry is directly left of Bob.
18. The person in a modern-style house is somewhere to the left of Alice.
19. The person in a Craftsman-style house is somewhere to the left of the person who is short.
20. The person who loves stir fry is somewhere to the left of the Prince smoker.
21. There are two houses between the person who loves eating grilled cheese and the person who is super tall.
22. The person in a ranch-style home is the person who smokes Blue Master.
23. The person who smokes many unique blends is directly left of the person who smokes Blue Master.
24. The person who goes on cultural tours is the person who is a pizza lover.
25. The person who is a pizza lover is somewhere to the left of the person who likes going on cruises.
 What is the value of attribute HouseStyle for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: ranch


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Bob`, `Arnold`, `Eric`, `Peter`
 - People have unique favorite book genres: `romance`, `mystery`, `biography`, `fantasy`, `science fiction`
 - Each person has a unique birthday month: `sept`, `feb`, `jan`, `mar`, `april`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`, `camping`, `cruise`
 - The people keep unique animals: `horse`, `bird`, `fish`, `dog`, `cat`

## Clues:
1. The person whose birthday is in April is the person who loves mystery books.
2. The person whose birthday is in March is somewhere to the left of the person who loves mystery books.
3. The person who loves beach vacations is Arnold.
4. The person who loves beach vacations is the person whose birthday is in January.
5. The bird keeper is directly left of Peter.
6. The person who loves science fiction books is somewhere to the left of the person whose birthday is in February.
7. The fish enthusiast is somewhere to the right of Bob.
8. The fish enthusiast is Eric.
9. The fish enthusiast is the person who loves fantasy books.
10. The person who enjoys mountain retreats is directly left of the person whose birthday is in April.
11. The person whose birthday is in April is the person who enjoys camping trips.
12. The person whose birthday is in September is the person who loves science fiction books.
13. The cat lover is the person who prefers city breaks.
14. The person who loves romance books is somewhere to the right of the person who loves science fiction books.
15. The cat lover is the person whose birthday is in February.
16. The person who keeps horses is Peter.
 What is the value of attribute House for the person whose attribute Vacation is mountain? 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: `Bob`, `Alice`, `Arnold`, `Peter`, `Eric`
 - The mothers' names in different houses are unique: `Penny`, `Aniya`, `Kailyn`, `Janelle`, `Holly`
 - The people keep unique animals: `cat`, `bird`, `dog`, `fish`, `horse`
 - Everyone has a favorite smoothie: `desert`, `dragonfruit`, `cherry`, `watermelon`, `lime`
 - Each person has an occupation: `doctor`, `engineer`, `artist`, `teacher`, `lawyer`

## Clues:
1. Bob is the Desert smoothie lover.
2. The cat lover is the person who is an engineer.
3. The person whose mother's name is Penny is the bird keeper.
4. The person who is a lawyer is the fish enthusiast.
5. The person who likes Cherry smoothies is directly left of Alice.
6. The Watermelon smoothie lover and the person who is an engineer are next to each other.
7. The person whose mother's name is Holly is the dog owner.
8. The person who is a teacher is in the first house.
9. The person whose mother's name is Penny is in the second house.
10. The person who drinks Lime smoothies is the person who is a doctor.
11. The person whose mother's name is Janelle is the person who is a lawyer.
12. Arnold is not in the third house.
13. The Dragonfruit smoothie lover is directly left of Peter.
14. The person whose mother's name is Kailyn is the Dragonfruit smoothie lover.
15. Arnold is somewhere to the right of Peter.
16. The dog owner is not in the fifth house.
17. The Watermelon smoothie lover is somewhere to the left of the Desert smoothie lover.
 What is the value of attribute Occupation for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}

Answer: teacher


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Peter`, `Bob`, `Alice`
 - Everyone has a favorite smoothie: `watermelon`, `lime`, `cherry`, `dragonfruit`, `desert`
 - The people keep unique animals: `fish`, `bird`, `horse`, `cat`, `dog`
 - Each person prefers a unique type of vacation: `camping`, `beach`, `mountain`, `city`, `cruise`
 - Each person has a unique favorite drink: `root beer`, `water`, `milk`, `tea`, `coffee`

## Clues:
1. The person who keeps horses is the person who drinks Lime smoothies.
2. There is one house between the Watermelon smoothie lover and the person who likes Cherry smoothies.
3. Bob and the coffee drinker are next to each other.
4. The fish enthusiast is the one who only drinks water.
5. The bird keeper is Bob.
6. The person who enjoys mountain retreats is directly left of the root beer lover.
7. The person who loves beach vacations is somewhere to the left of the dog owner.
8. Eric is the person who likes Cherry smoothies.
9. The tea drinker is Alice.
10. The person who prefers city breaks is somewhere to the right of the person who enjoys mountain retreats.
11. Peter is somewhere to the left of the coffee drinker.
12. Eric is the person who loves beach vacations.
13. The person who enjoys mountain retreats is Alice.
14. There are two houses between the Watermelon smoothie lover and Alice.
15. The person who enjoys camping trips is not in the first house.
16. The dog owner is not in the fifth house.
17. The fish enthusiast and the Dragonfruit smoothie lover are next to each other.
 What is the value of attribute House for the person whose attribute Vacation is city? 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`, `Bob`, `Peter`, `Eric`, `Alice`, `Arnold`
 - Everyone has something unique for lunch: `stir fry`, `grilled cheese`, `soup`, `spaghetti`, `stew`, `pizza`
 - Each person lives in a unique style of house: `colonial`, `victorian`, `craftsman`, `mediterranean`, `ranch`, `modern`

## Clues:
1. The person in a ranch-style home is in the fifth house.
2. The person in a modern-style house is not in the first house.
3. The person who loves stir fry is directly left of Peter.
4. There is one house between the person in a Craftsman-style house and Arnold.
5. The person who loves eating grilled cheese is the person residing in a Victorian house.
6. The person who loves the stew is the person living in a colonial-style house.
7. The person who loves the soup is directly left of the person who is a pizza lover.
8. Alice is the person who loves the stew.
9. There are two houses between the person in a modern-style house and Arnold.
10. The person who loves the stew is not in the sixth house.
11. The person who loves the spaghetti eater is Bob.
12. The person who loves eating grilled cheese is in the second house.
13. Carol is not in the fourth house.
 What is the value of attribute Food for the person whose attribute HouseStyle is modern? 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: `Arnold`, `Alice`, `Carol`, `Peter`, `Bob`, `Eric`
 - The people keep unique animals: `fish`, `bird`, `rabbit`, `cat`, `horse`, `dog`
 - Each person has a unique favorite drink: `tea`, `root beer`, `water`, `milk`, `boba tea`, `coffee`
 - People use unique phone models: `iphone 13`, `google pixel 6`, `samsung galaxy s21`, `huawei p50`, `xiaomi mi 11`, `oneplus 9`
 - Each mother is accompanied by their child: `Alice`, `Fred`, `Meredith`, `Samantha`, `Timothy`, `Bella`

## Clues:
1. The tea drinker is the person who uses an iPhone 13.
2. There is one house between the dog owner and the tea drinker.
3. The fish enthusiast is somewhere to the left of the tea drinker.
4. Eric and the person's child is named Alice are next to each other.
5. The one who only drinks water is not in the third house.
6. The root beer lover is directly left of the person's child is named Samantha.
7. The person who is the mother of Timothy is the coffee drinker.
8. The fish enthusiast is directly left of the person who likes milk.
9. Peter is the person who likes milk.
10. The person who uses a OnePlus 9 is directly left of the person's child is named Alice.
11. The person who keeps horses is not in the third house.
12. The person's child is named Meredith is directly left of Bob.
13. The person's child is named Bella is the person who uses a Google Pixel 6.
14. The bird keeper is directly left of the person's child is named Meredith.
15. The person who uses a Samsung Galaxy S21 is directly left of the person's child is named Bella.
16. The one who only drinks water is somewhere to the left of the person's child is named Fred.
17. Arnold is the tea drinker.
18. The person who keeps horses is somewhere to the left of the cat lover.
19. The person who uses a Huawei P50 and Alice are next to each other.
20. Bob is directly left of the root beer lover.
21. The person who is the mother of Timothy is Eric.
 What is the value of attribute House for the person whose attribute Children is Meredith? Please reason step by step, and put your final answer within \boxed{}

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`, `Eric`, `Alice`, `Arnold`, `Carol`, `Bob`
 - People have unique heights: `very tall`, `very short`, `tall`, `super tall`, `short`, `average`
 - Each person prefers a unique type of vacation: `cruise`, `mountain`, `camping`, `beach`, `city`, `cultural`
 - People have unique hair colors: `blonde`, `red`, `gray`, `brown`, `auburn`, `black`
 - Each person has a unique favorite drink: `tea`, `boba tea`, `milk`, `water`, `coffee`, `root beer`
 - They all have a unique favorite flower: `lilies`, `carnations`, `iris`, `tulips`, `roses`, `daffodils`

## Clues:
1. The person who loves the vase of tulips is the person who has auburn hair.
2. The person who is short is somewhere to the right of Arnold.
3. The person who goes on cultural tours is Arnold.
4. The person who has auburn hair is Bob.
5. The person who is very short is the person who loves a bouquet of daffodils.
6. The person who loves the boquet of iris is the person who is very tall.
7. Peter is somewhere to the right of the root beer lover.
8. The person who loves beach vacations is directly left of the person who prefers city breaks.
9. Bob is directly left of the coffee drinker.
10. The person who is very short is the person who has gray hair.
11. Eric is somewhere to the right of the tea drinker.
12. The person who has red hair is the person who is tall.
13. The person who is tall is somewhere to the right of the person who is short.
14. The person who has black hair is the person who enjoys mountain retreats.
15. The one who only drinks water is the person who prefers city breaks.
16. The person who has brown hair is Carol.
17. The person who has an average height is Arnold.
18. The person who has brown hair is directly left of the person who likes milk.
19. The root beer lover is the person who is very short.
20. The person who is short is somewhere to the left of the coffee drinker.
21. The person who enjoys camping trips is the person who loves a carnations arrangement.
22. The person who is super tall and Arnold are next to each other.
23. There is one house between the person who loves the boquet of lilies and Peter.
24. The person who loves the vase of tulips is directly left of the person who has black hair.
 What is the value of attribute Height for the person whose attribute Flower is carnations? Please reason step by step, and put your final answer within \boxed{}

Answer: tall


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 Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Bob`, `Eric`, `Arnold`
 - They all have a unique favorite flower: `tulips`, `daffodils`, `lilies`, `roses`, `carnations`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Timothy`, `Meredith`, `Samantha`
 - Each person has a unique level of education: `high school`, `bachelor`, `doctorate`, `master`, `associate`
 - The people keep unique animals: `cat`, `fish`, `dog`, `horse`, `bird`

## Clues:
1. Peter is somewhere to the right of the dog owner.
2. There is one house between the person who loves a carnations arrangement and the person with a bachelor's degree.
3. There is one house between the person with a doctorate and the cat lover.
4. The person with an associate's degree is directly left of the person who loves the vase of tulips.
5. There is one house between the cat lover and the person who keeps horses.
6. The person's child is named Fred is somewhere to the left of the person with a bachelor's degree.
7. The person's child is named Meredith is not in the third house.
8. The person with a master's degree is the person's child is named Bella.
9. The person with a bachelor's degree is Bob.
10. The person who is the mother of Timothy is the person who loves a bouquet of daffodils.
11. The person's child is named Samantha is Bob.
12. Arnold is directly left of Peter.
13. The bird keeper is directly left of the person who loves a bouquet of daffodils.
14. The person who loves the rose bouquet is the bird keeper.
15. There is one house between the dog owner and the fish enthusiast.
16. The person who loves the vase of tulips is Eric.
 What is the value of attribute Children for the person whose attribute Animal is cat? Please reason step by step, and put your final answer within \boxed{}

Answer: Fred


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

Answer: romance


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Alice`, `Peter`
 - People have unique favorite sports: `swimming`, `soccer`, `tennis`, `basketball`
 - Each person has a unique type of pet: `bird`, `fish`, `cat`, `dog`
 - Everyone has a favorite smoothie: `dragonfruit`, `desert`, `watermelon`, `cherry`
 - People have unique hair colors: `brown`, `black`, `blonde`, `red`
 - Each person has a unique birthday month: `jan`, `feb`, `sept`, `april`

## Clues:
1. The person whose birthday is in September is the person who likes Cherry smoothies.
2. The person whose birthday is in February is not in the first house.
3. The Desert smoothie lover is the person who loves basketball.
4. Peter is the person who has black hair.
5. The person who loves tennis is somewhere to the right of the person who has a cat.
6. The person with an aquarium of fish is not in the fourth house.
7. Arnold is directly left of the person who has blonde hair.
8. There is one house between the person who has red hair and the person whose birthday is in January.
9. The person whose birthday is in September is directly left of the person who loves soccer.
10. Peter is directly left of the person who loves basketball.
11. The person who has blonde hair is the person whose birthday is in September.
12. Arnold is the person who keeps a pet bird.
13. The person whose birthday is in January is the Watermelon smoothie lover.
14. The person who has blonde hair is Eric.
 What is the value of attribute FavoriteSport for the person whose attribute Pet is fish? Please reason step by step, and put your final answer within \boxed{}

Answer: tennis


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

Answer: 2


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Arnold`, `Eric`, `Bob`
 - Each person has a unique hobby: `painting`, `cooking`, `knitting`, `gardening`, `photography`

## Clues:
1. Alice is directly left of the person who enjoys gardening.
2. Eric and the photography enthusiast are next to each other.
3. The person who loves cooking is directly left of the person who enjoys knitting.
4. Peter is somewhere to the left of Alice.
5. Eric is in the third house.
6. Arnold is directly left of the person who paints as a hobby.
7. The person who enjoys gardening is in the fifth house.
 What is the value of attribute Hobby for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: knitting


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`
 - They all have a unique favorite flower: `daffodils`, `lilies`, `carnations`
 - People have unique hair colors: `blonde`, `black`, `brown`
 - People have unique favorite music genres: `pop`, `rock`, `classical`
 - The mothers' names in different houses are unique: `Janelle`, `Holly`, `Aniya`
 - Each person has a favorite color: `yellow`, `red`, `white`

## Clues:
1. Peter is somewhere to the left of Arnold.
2. The person whose favorite color is red is not in the third house.
3. Peter and the person who has black hair are next to each other.
4. The person whose mother's name is Holly is somewhere to the right of the person who loves rock music.
5. The person who has blonde hair is the person who loves classical music.
6. The person who loves a carnations arrangement is somewhere to the right of the person who loves rock music.
7. Arnold is directly left of the person who loves a bouquet of daffodils.
8. The person who loves the boquet of lilies is the person who loves yellow.
9. The person whose mother's name is Janelle is directly left of the person who loves a bouquet of daffodils.
 What is the value of attribute MusicGenre for the person whose attribute Mother is Janelle? Please reason step by step, and put your final answer within \boxed{}

Answer: pop


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
 - The people keep unique animals: `cat`, `fish`, `bird`, `dog`, `horse`
 - Each person has a unique birthday month: `mar`, `jan`, `feb`, `april`, `sept`

## Clues:
1. The fish enthusiast and Arnold are next to each other.
2. The person whose birthday is in February is not in the fourth house.
3. The person who keeps horses is in the fourth house.
4. The person whose birthday is in March is somewhere to the left of the dog owner.
5. Peter is the person whose birthday is in September.
6. The dog owner is not in the fifth house.
7. The bird keeper is in the third house.
8. Peter and the person whose birthday is in February are next to each other.
9. Bob is not in the third house.
10. The dog owner is somewhere to the right of Alice.
11. The person whose birthday is in January is the bird keeper.
 What is the value of attribute House for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

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`, `Arnold`, `Bob`, `Carol`, `Alice`, `Eric`
 - People have unique heights: `very tall`, `very short`, `super tall`, `average`, `tall`, `short`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `blueberry`, `desert`, `dragonfruit`, `lime`
 - Everyone has a unique favorite cigar: `prince`, `blue master`, `yellow monster`, `dunhill`, `blends`, `pall mall`
 - Each person prefers a unique type of vacation: `camping`, `city`, `beach`, `cultural`, `mountain`, `cruise`

## Clues:
1. The person who is very short is directly left of the person who drinks Lime smoothies.
2. The person who smokes Yellow Monster is directly left of the person who drinks Lime smoothies.
3. The person who is short and the person who goes on cultural tours are next to each other.
4. The person who smokes many unique blends is the person who loves beach vacations.
5. There are two houses between the person who smokes Blue Master and the person who drinks Blueberry smoothies.
6. The Prince smoker is not in the fourth house.
7. The person who is tall is not in the first house.
8. The person who smokes Yellow Monster is the person who enjoys mountain retreats.
9. The person who is very tall is Alice.
10. The person who likes Cherry smoothies is the person who smokes Blue Master.
11. Bob is in the first house.
12. The person who smokes many unique blends is Alice.
13. The person who goes on cultural tours is the person partial to Pall Mall.
14. Eric is the person who drinks Blueberry smoothies.
15. The person who prefers city breaks is not in the sixth house.
16. The Prince smoker is the person who prefers city breaks.
17. The person who enjoys camping trips is somewhere to the left of Carol.
18. The person who has an average height is the person who prefers city breaks.
19. The Desert smoothie lover is in the fifth house.
20. The Watermelon smoothie lover is Arnold.
21. The person who is very tall is the person who drinks Lime smoothies.
22. Carol is the Dunhill smoker.
 What is the value of attribute House for the person whose attribute Height is average? 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: `Arnold`, `Peter`, `Alice`, `Eric`
 - Each person has a unique type of pet: `bird`, `fish`, `dog`, `cat`
 - Each person lives in a unique style of house: `colonial`, `craftsman`, `ranch`, `victorian`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Kailyn`, `Aniya`
 - Each mother is accompanied by their child: `Fred`, `Samantha`, `Meredith`, `Bella`

## Clues:
1. The person whose mother's name is Kailyn is in the second house.
2. The person living in a colonial-style house is the person's child is named Meredith.
3. There is one house between the person's child is named Samantha and The person whose mother's name is Janelle.
4. The person in a ranch-style home is the person's child is named Fred.
5. Eric is the person's child is named Bella.
6. The person whose mother's name is Janelle is the person with an aquarium of fish.
7. Arnold is the person in a Craftsman-style house.
8. The person who keeps a pet bird and the person with an aquarium of fish are next to each other.
9. The person whose mother's name is Holly is directly left of Peter.
10. The person who has a cat is the person living in a colonial-style house.
11. The person's child is named Fred is somewhere to the left of The person whose mother's name is Janelle.
 What is the value of attribute Children for the person whose attribute HouseStyle is craftsman? Please reason step by step, and put your final answer within \boxed{}

Answer: Samantha


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Carol`, `Arnold`, `Bob`, `Alice`
 - Each person has a favorite color: `blue`, `red`, `green`, `yellow`, `purple`, `white`
 - Each person prefers a unique type of vacation: `city`, `beach`, `cruise`, `cultural`, `mountain`, `camping`
 - People have unique hair colors: `blonde`, `black`, `gray`, `brown`, `red`, `auburn`
 - Each person has an occupation: `artist`, `lawyer`, `engineer`, `teacher`, `doctor`, `nurse`
 - They all have a unique favorite flower: `roses`, `iris`, `daffodils`, `carnations`, `tulips`, `lilies`

## Clues:
1. The person who loves a bouquet of daffodils is the person who is an artist.
2. The person who enjoys camping trips is the person whose favorite color is green.
3. The person who has brown hair is in the first house.
4. The person who loves blue is somewhere to the right of the person who enjoys mountain retreats.
5. The person who loves the vase of tulips is the person who enjoys mountain retreats.
6. Eric is in the second house.
7. The person who likes going on cruises and Arnold are next to each other.
8. The person who loves yellow and the person who enjoys camping trips are next to each other.
9. The person who loves yellow is somewhere to the left of Peter.
10. The person who is a lawyer and Arnold are next to each other.
11. The person who has red hair is Arnold.
12. Alice is the person who is a doctor.
13. The person who loves purple is directly left of the person who loves the vase of tulips.
14. The person who has brown hair is somewhere to the left of the person who is an engineer.
15. The person who has gray hair is somewhere to the left of the person whose favorite color is red.
16. The person who is an artist is somewhere to the right of Arnold.
17. Alice is the person who loves the boquet of lilies.
18. The person whose favorite color is red is directly left of the person who prefers city breaks.
19. The person who prefers city breaks is somewhere to the right of the person who has blonde hair.
20. There is one house between Alice and Bob.
21. The person who loves the rose bouquet is directly left of the person who is a nurse.
22. The person whose favorite color is green is in the fourth house.
23. The person who loves beach vacations is somewhere to the left of the person who has red hair.
24. The person who has black hair is Alice.
25. The person who loves blue is the person who loves a carnations arrangement.
 What is the value of attribute HairColor for the person whose attribute Occupation is lawyer? Please reason step by step, and put your final answer within \boxed{}

Answer: gray


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Bob`, `Carol`, `Alice`, `Eric`
 - People have unique heights: `very tall`, `very short`, `super tall`, `average`, `tall`, `short`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `blueberry`, `desert`, `dragonfruit`, `lime`
 - Everyone has a unique favorite cigar: `prince`, `blue master`, `yellow monster`, `dunhill`, `blends`, `pall mall`
 - Each person prefers a unique type of vacation: `camping`, `city`, `beach`, `cultural`, `mountain`, `cruise`

## Clues:
1. The person who is very short is directly left of the person who drinks Lime smoothies.
2. The person who smokes Yellow Monster is directly left of the person who drinks Lime smoothies.
3. The person who is short and the person who goes on cultural tours are next to each other.
4. The person who smokes many unique blends is the person who loves beach vacations.
5. There are two houses between the person who smokes Blue Master and the person who drinks Blueberry smoothies.
6. The Prince smoker is not in the fourth house.
7. The person who is tall is not in the first house.
8. The person who smokes Yellow Monster is the person who enjoys mountain retreats.
9. The person who is very tall is Alice.
10. The person who likes Cherry smoothies is the person who smokes Blue Master.
11. Bob is in the first house.
12. The person who smokes many unique blends is Alice.
13. The person who goes on cultural tours is the person partial to Pall Mall.
14. Eric is the person who drinks Blueberry smoothies.
15. The person who prefers city breaks is not in the sixth house.
16. The Prince smoker is the person who prefers city breaks.
17. The person who enjoys camping trips is somewhere to the left of Carol.
18. The person who has an average height is the person who prefers city breaks.
19. The Desert smoothie lover is in the fifth house.
20. The Watermelon smoothie lover is Arnold.
21. The person who is very tall is the person who drinks Lime smoothies.
22. Carol is the Dunhill smoker.
 What is the value of attribute Cigar for the person whose attribute Smoothie is blueberry? Please reason step by step, and put your final answer within \boxed{}

Answer: pall mall


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`
 - People have unique favorite music genres: `jazz`, `rock`, `pop`, `classical`
 - Each person has a unique hobby: `cooking`, `painting`, `gardening`, `photography`
 - Everyone has something unique for lunch: `stew`, `pizza`, `grilled cheese`, `spaghetti`

## Clues:
1. The person who is a pizza lover is somewhere to the left of the person who loves eating grilled cheese.
2. Arnold is not in the first house.
3. Peter is directly left of the person who enjoys gardening.
4. The person who loves eating grilled cheese and Peter are next to each other.
5. There are two houses between the person who loves jazz music and Arnold.
6. The person who loves cooking is the person who loves rock music.
7. The person who loves pop music is the person who paints as a hobby.
8. The person who paints as a hobby is Alice.
9. The person who enjoys gardening is the person who loves the spaghetti eater.
 What is the value of attribute Food for the person whose attribute Hobby is painting? Please reason step by step, and put your final answer within \boxed{}

Answer: grilled cheese


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Bob`, `Peter`, `Eric`, `Alice`, `Carol`
 - Each person has a unique birthday month: `april`, `feb`, `mar`, `jan`, `may`, `sept`
 - Each person prefers a unique type of vacation: `city`, `beach`, `mountain`, `cruise`, `cultural`, `camping`
 - Each person has a favorite color: `blue`, `white`, `green`, `purple`, `red`, `yellow`

## Clues:
1. The person whose birthday is in January is the person who loves blue.
2. The person whose birthday is in January is directly left of the person who loves white.
3. The person who enjoys camping trips is in the fourth house.
4. Eric is in the sixth house.
5. There are two houses between the person who likes going on cruises and the person whose birthday is in February.
6. The person whose birthday is in May is not in the sixth house.
7. Peter is directly left of the person who loves yellow.
8. The person who goes on cultural tours is Eric.
9. The person whose birthday is in September is directly left of the person whose favorite color is green.
10. Arnold and the person who loves purple are next to each other.
11. The person who loves beach vacations is the person whose birthday is in March.
12. The person whose favorite color is green is somewhere to the left of Carol.
13. The person whose birthday is in May is somewhere to the right of Peter.
14. The person who loves blue is Bob.
15. The person who enjoys mountain retreats is in the fifth house.
16. The person who loves purple is in the third house.
17. Carol is in the fourth house.
 What is the value of attribute House for the person whose attribute Birthday is sept? 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`, `Carol`, `Alice`, `Bob`, `Peter`, `Arnold`
 - Each person prefers a unique type of vacation: `cultural`, `city`, `cruise`, `mountain`, `camping`, `beach`
 - Everyone has a favorite smoothie: `blueberry`, `watermelon`, `lime`, `desert`, `dragonfruit`, `cherry`
 - People have unique favorite book genres: `fantasy`, `mystery`, `science fiction`, `biography`, `historical fiction`, `romance`

## Clues:
1. The person who loves science fiction books is the person who enjoys camping trips.
2. Arnold is not in the fifth house.
3. The person who loves fantasy books is Peter.
4. The Dragonfruit smoothie lover is the person who loves beach vacations.
5. Alice is somewhere to the left of Eric.
6. The person who drinks Blueberry smoothies is somewhere to the left of the person who enjoys mountain retreats.
7. The person who likes Cherry smoothies is in the fifth house.
8. The person who loves fantasy books is the person who prefers city breaks.
9. There is one house between Peter and the person who loves mystery books.
10. There is one house between the Dragonfruit smoothie lover and the person who drinks Lime smoothies.
11. The person who likes Cherry smoothies is directly left of the person who loves romance books.
12. The person who loves science fiction books is directly left of Eric.
13. The person who loves mystery books is somewhere to the left of Carol.
14. Carol is somewhere to the right of the person who enjoys mountain retreats.
15. The person who likes going on cruises is the person who likes Cherry smoothies.
16. Eric is the person who loves historical fiction books.
17. The person who prefers city breaks is the Desert smoothie lover.
18. The Desert smoothie lover is somewhere to the right of the Dragonfruit smoothie lover.
 What is the value of attribute House for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}

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: `Eric`, `Arnold`, `Peter`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `lilies`
 - People have unique favorite music genres: `rock`, `classical`, `pop`
 - Each person has a unique favorite drink: `water`, `milk`, `tea`
 - Everyone has a unique favorite cigar: `pall mall`, `blue master`, `prince`
 - Each person has a unique birthday month: `april`, `jan`, `sept`

## Clues:
1. The Prince smoker is not in the first house.
2. The person who likes milk is the person whose birthday is in April.
3. The person whose birthday is in January is somewhere to the right of Eric.
4. The person who loves pop music is directly left of the person who loves a bouquet of daffodils.
5. The one who only drinks water is the person who loves a bouquet of daffodils.
6. The person who likes milk is the person who smokes Blue Master.
7. Arnold is in the second house.
8. The person who loves rock music is the person whose birthday is in September.
9. The person who loves the boquet of lilies is somewhere to the left of the person whose birthday is in April.
 What is the value of attribute Drink for the person whose attribute Cigar is pall mall? Please reason step by step, and put your final answer within \boxed{}

Answer: tea


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Alice`, `Eric`, `Peter`, `Arnold`
 - People have unique heights: `average`, `short`, `very tall`, `very short`, `tall`
 - Each person has an occupation: `engineer`, `artist`, `doctor`, `lawyer`, `teacher`
 - The mothers' names in different houses are unique: `Janelle`, `Aniya`, `Holly`, `Penny`, `Kailyn`
 - Each person has a unique birthday month: `mar`, `april`, `jan`, `feb`, `sept`
 - Each person has a unique type of pet: `hamster`, `fish`, `bird`, `dog`, `cat`

## Clues:
1. The person who is a doctor is somewhere to the left of the person with a pet hamster.
2. Arnold is in the first house.
3. The person who is an engineer is the person who owns a dog.
4. The person whose birthday is in March is somewhere to the left of Peter.
5. The person who is an artist is in the third house.
6. The person who is a lawyer is in the fifth house.
7. The person who has a cat is The person whose mother's name is Kailyn.
8. Alice is directly left of Eric.
9. The person whose birthday is in February is directly left of The person whose mother's name is Holly.
10. The person whose birthday is in April is somewhere to the right of the person who is a teacher.
11. The person whose birthday is in February is The person whose mother's name is Kailyn.
12. Peter is in the fourth house.
13. The person with an aquarium of fish is the person who is very short.
14. The person whose mother's name is Kailyn and the person with an aquarium of fish are next to each other.
15. The person who is short is directly left of the person who is a lawyer.
16. The person whose mother's name is Aniya and the person who is a lawyer are next to each other.
17. The person whose birthday is in January is The person whose mother's name is Penny.
18. The person who has an average height is the person who keeps a pet bird.
19. The person who is tall is the person who is an engineer.
 What is the value of attribute Height for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}

Answer: very tall


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 Animal for the person whose attribute Color is yellow? Please reason step by step, and put your final answer within \boxed{}

Answer: horse


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
 - The people keep unique animals: `cat`, `fish`, `bird`, `dog`, `horse`
 - Each person has a unique birthday month: `mar`, `jan`, `feb`, `april`, `sept`

## Clues:
1. The fish enthusiast and Arnold are next to each other.
2. The person whose birthday is in February is not in the fourth house.
3. The person who keeps horses is in the fourth house.
4. The person whose birthday is in March is somewhere to the left of the dog owner.
5. Peter is the person whose birthday is in September.
6. The dog owner is not in the fifth house.
7. The bird keeper is in the third house.
8. Peter and the person whose birthday is in February are next to each other.
9. Bob is not in the third house.
10. The dog owner is somewhere to the right of Alice.
11. The person whose birthday is in January is the bird keeper.
 What is the value of attribute House for the person whose attribute Name is Alice? 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`, `Eric`, `Arnold`, `Peter`
 - People have unique favorite sports: `tennis`, `soccer`, `basketball`, `swimming`
 - People have unique hair colors: `red`, `black`, `brown`, `blonde`

## Clues:
1. Peter and the person who has blonde hair are next to each other.
2. The person who has black hair is not in the second house.
3. The person who loves soccer is somewhere to the right of the person who has brown hair.
4. Eric is in the second house.
5. The person who loves tennis is the person who has blonde hair.
6. The person who has brown hair is the person who loves basketball.
7. Arnold is somewhere to the right of the person who has black hair.
8. The person who has brown hair is directly left of the person who has black hair.
 What is the value of attribute FavoriteSport for the person whose attribute HairColor is black? Please reason step by step, and put your final answer within \boxed{}

Answer: soccer


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Eric`, `Arnold`, `Bob`, `Peter`
 - They all have a unique favorite flower: `tulips`, `roses`, `lilies`, `daffodils`, `carnations`
 - The people keep unique animals: `dog`, `horse`, `cat`, `bird`, `fish`

## Clues:
1. Alice is in the second house.
2. The person who loves the boquet of lilies is the bird keeper.
3. Peter is somewhere to the right of the person who loves the vase of tulips.
4. The fish enthusiast is the person who loves a bouquet of daffodils.
5. The person who keeps horses is Eric.
6. There are two houses between the dog owner and Bob.
7. The fish enthusiast is directly left of Bob.
8. Alice is directly left of the person who keeps horses.
9. The person who loves a carnations arrangement is directly left of the person who loves the vase of tulips.
10. The cat lover is not in the first house.
 What is the value of attribute Flower for the person whose attribute Animal is bird? Please reason step by step, and put your final answer within \boxed{}

Answer: lilies


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 Education for the person whose attribute Nationality is swede? Please reason step by step, and put your final answer within \boxed{}

Answer: master


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Bob`, `Alice`, `Eric`, `Carol`
 - The mothers' names in different houses are unique: `Holly`, `Aniya`, `Kailyn`, `Janelle`, `Penny`, `Sarah`
 - Everyone has something unique for lunch: `stir fry`, `stew`, `spaghetti`, `soup`, `pizza`, `grilled cheese`
 - The people keep unique animals: `dog`, `horse`, `cat`, `fish`, `rabbit`, `bird`
 - Everyone has a favorite smoothie: `watermelon`, `desert`, `lime`, `cherry`, `blueberry`, `dragonfruit`
 - Each person lives in a unique style of house: `mediterranean`, `craftsman`, `victorian`, `colonial`, `modern`, `ranch`

## Clues:
1. The person whose mother's name is Penny is the person residing in a Victorian house.
2. The person in a modern-style house is The person whose mother's name is Kailyn.
3. The person in a modern-style house is somewhere to the right of the person residing in a Victorian house.
4. The person who drinks Blueberry smoothies is not in the sixth house.
5. The person whose mother's name is Sarah is the person who drinks Blueberry smoothies.
6. The person who likes Cherry smoothies is not in the third house.
7. The person who likes Cherry smoothies is Eric.
8. The person whose mother's name is Janelle is not in the third house.
9. The person who loves the spaghetti eater is in the third house.
10. The fish enthusiast is The person whose mother's name is Holly.
11. The person who keeps horses is in the first house.
12. The person in a Mediterranean-style villa is the person who loves the stew.
13. The bird keeper is in the third house.
14. The person living in a colonial-style house is the person who drinks Blueberry smoothies.
15. Carol is the person who keeps horses.
16. There are two houses between the Desert smoothie lover and Peter.
17. The person who loves eating grilled cheese is the Dragonfruit smoothie lover.
18. The person who is a pizza lover is somewhere to the right of the Dragonfruit smoothie lover.
19. The person whose mother's name is Janelle is somewhere to the left of Arnold.
20. Carol is directly left of The person whose mother's name is Aniya.
21. The person in a ranch-style home is The person whose mother's name is Aniya.
22. Arnold is somewhere to the right of the person in a Craftsman-style house.
23. The cat lover is Bob.
24. There is one house between the Watermelon smoothie lover and the person who is a pizza lover.
25. There are two houses between the cat lover and the person who loves stir fry.
26. Arnold is the rabbit owner.
27. Peter is The person whose mother's name is Janelle.
 What is the value of attribute HouseStyle for the person whose attribute Smoothie is dragonfruit? Please reason step by step, and put your final answer within \boxed{}

Answer: ranch


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Bob`, `Alice`, `Eric`, `Peter`
 - The people are of nationalities: `dane`, `swede`, `german`, `brit`, `norwegian`
 - Each person has a unique hobby: `gardening`, `painting`, `knitting`, `photography`, `cooking`
 - Everyone has a favorite smoothie: `dragonfruit`, `lime`, `watermelon`, `desert`, `cherry`
 - People have unique hair colors: `brown`, `gray`, `black`, `blonde`, `red`
 - People have unique favorite sports: `baseball`, `soccer`, `swimming`, `tennis`, `basketball`

## Clues:
1. The person who loves cooking is not in the second house.
2. The Watermelon smoothie lover is not in the fourth house.
3. The person who loves baseball is somewhere to the right of the Desert smoothie lover.
4. The person who drinks Lime smoothies is the person who has brown hair.
5. The person who has gray hair is somewhere to the right of the Swedish person.
6. The photography enthusiast is not in the fifth house.
7. The Swedish person is not in the first house.
8. The German is the person who has blonde hair.
9. There is one house between the Watermelon smoothie lover and the photography enthusiast.
10. Alice and the person who drinks Lime smoothies are next to each other.
11. The British person and the person who enjoys knitting are next to each other.
12. The person who has black hair is the Swedish person.
13. The British person is the person who enjoys gardening.
14. The person who loves swimming is the person who loves cooking.
15. The Dragonfruit smoothie lover is not in the third house.
16. The Watermelon smoothie lover is not in the second house.
17. Eric is somewhere to the left of the person who drinks Lime smoothies.
18. The person who loves soccer is Alice.
19. Peter is the photography enthusiast.
20. The person who enjoys gardening is directly left of the person who loves tennis.
21. The Norwegian and the photography enthusiast are next to each other.
22. The British person is Alice.
23. Bob is the person who has blonde hair.
 What is the value of attribute Nationality for the person whose attribute HairColor is blonde? Please reason step by step, and put your final answer within \boxed{}

Answer: german


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 a unique favorite drink: `water`, `tea`
 - Everyone has a favorite smoothie: `desert`, `cherry`
 - Each person has a favorite color: `yellow`, `red`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`
 - People own unique car models: `tesla model 3`, `ford f150`

## Clues:
1. Eric is not in the second house.
2. The person partial to Pall Mall is not in the first house.
3. The person who owns a Ford F-150 is the one who only drinks water.
4. The Desert smoothie lover is somewhere to the left of the person who owns a Tesla Model 3.
5. The person whose favorite color is red is Eric.
 What is the value of attribute Drink for the person whose attribute Cigar is prince? Please reason step by step, and put your final answer within \boxed{}

Answer: water


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`
 - They all have a unique favorite flower: `roses`, `carnations`, `daffodils`, `lilies`
 - Each person lives in a unique style of house: `victorian`, `craftsman`, `colonial`, `ranch`
 - Everyone has a unique favorite cigar: `prince`, `dunhill`, `blue master`, `pall mall`

## Clues:
1. The person in a ranch-style home is in the third house.
2. The person who smokes Blue Master is somewhere to the left of the person residing in a Victorian house.
3. There are two houses between Eric and the person who loves the rose bouquet.
4. The Prince smoker is Peter.
5. The person in a Craftsman-style house is the Dunhill smoker.
6. The Dunhill smoker is the person who loves a carnations arrangement.
7. Arnold is in the fourth house.
8. The Prince smoker is in the second house.
9. The person who loves the boquet of lilies is the person who smokes Blue Master.
 What is the value of attribute House for the person whose attribute Flower is lilies? 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: `Bob`, `Arnold`, `Alice`, `Eric`, `Peter`
 - Everyone has something unique for lunch: `stew`, `spaghetti`, `grilled cheese`, `pizza`, `stir fry`
 - Each person has a favorite color: `green`, `blue`, `yellow`, `red`, `white`
 - The people are of nationalities: `swede`, `brit`, `dane`, `german`, `norwegian`
 - People have unique favorite book genres: `fantasy`, `biography`, `romance`, `mystery`, `science fiction`
 - Each mother is accompanied by their child: `Timothy`, `Samantha`, `Meredith`, `Fred`, `Bella`

## Clues:
1. The Swedish person is the person's child is named Bella.
2. There is one house between the person who loves science fiction books and the person who loves the stew.
3. The person who is a pizza lover is the person's child is named Fred.
4. The person who loves white is not in the fourth house.
5. The person who loves yellow is Peter.
6. The person who loves eating grilled cheese is directly left of the person's child is named Meredith.
7. The German is the person who loves the spaghetti eater.
8. The person who loves romance books is the person who loves the stew.
9. The person's child is named Samantha is directly left of the German.
10. Alice is the Swedish person.
11. Arnold is the person whose favorite color is green.
12. Arnold is in the third house.
13. The person's child is named Meredith is the person who loves biography books.
14. The Norwegian is the person whose favorite color is red.
15. The person who loves romance books is not in the third house.
16. The person who loves the spaghetti eater is Eric.
17. The Dane is somewhere to the left of the person who loves yellow.
18. The person who loves mystery books is directly left of the person whose favorite color is red.
19. The person's child is named Fred is not in the third house.
 What is the value of attribute Food for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


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 have unique favorite sports: `soccer`, `basketball`, `tennis`
 - The people keep unique animals: `cat`, `bird`, `horse`
 - Each person has a unique favorite drink: `water`, `tea`, `milk`
 - The people are of nationalities: `swede`, `dane`, `brit`

## Clues:
1. The person who likes milk is not in the first house.
2. The person who keeps horses is somewhere to the left of Eric.
3. The person who loves basketball is Peter.
4. The Swedish person is somewhere to the left of the one who only drinks water.
5. The person who loves tennis is the tea drinker.
6. The person who loves soccer is the bird keeper.
7. The cat lover is the British person.
8. Peter is not in the third house.
9. The person who likes milk is the person who loves soccer.
 What is the value of attribute FavoriteSport for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: soccer


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Peter`, `Eric`, `Alice`, `Carol`
 - People have unique favorite music genres: `jazz`, `rock`, `pop`, `hip hop`, `classical`, `country`
 - Each person has a unique birthday month: `april`, `feb`, `jan`, `mar`, `sept`, `may`
 - Each person has a unique favorite drink: `root beer`, `coffee`, `tea`, `boba tea`, `water`, `milk`
 - Each person has an occupation: `nurse`, `doctor`, `teacher`, `lawyer`, `artist`, `engineer`

## Clues:
1. The person who loves pop music is not in the fourth house.
2. The boba tea drinker is the person whose birthday is in April.
3. The person whose birthday is in January is somewhere to the right of the person whose birthday is in May.
4. Arnold is not in the third house.
5. Eric is in the first house.
6. Carol is the person who loves jazz music.
7. The person who loves classical music is directly left of the root beer lover.
8. The person who loves country music is somewhere to the left of the person who is a teacher.
9. The person who is a teacher is somewhere to the left of the person who is a nurse.
10. The person who is a doctor is somewhere to the left of the person who is a teacher.
11. The root beer lover is the person who loves hip-hop music.
12. Arnold is the person who is a lawyer.
13. Carol is not in the fourth house.
14. The person who is an artist is somewhere to the left of the person who loves pop music.
15. The person whose birthday is in April is Bob.
16. The person who likes milk is not in the second house.
17. The one who only drinks water is somewhere to the right of the person whose birthday is in March.
18. The tea drinker is the person whose birthday is in September.
19. The person whose birthday is in January is the person who loves pop music.
20. The person who loves jazz music is directly left of the person who loves rock music.
21. Alice is the person who is a nurse.
22. The tea drinker is not in the sixth house.
23. The person who is a doctor is the root beer lover.
 What is the value of attribute House for the person whose attribute Birthday is feb? Please reason step by step, and put your final answer within \boxed{}

Answer: 6


Answer: 1


Let \( n \geq 2 \), and \( x_{1}, x_{2}, \cdots, x_{n} \) be \( n \) distinct real numbers in the open interval \( (0,1) \). Prove:
$$
\sum_{i=1}^{n} \sum_{j=1}^{n}\left\{x_{i}-x_{j}\right\}^{2} \geq \frac{(n-1)(2n-1)}{6},
$$
where \(\{x\} = x - \lfloor x \rfloor\) and \(\lfloor x \rfloor\) denotes the greatest integer less than or equal to \( x \).

Answer: \frac{(n-1)(2n-1)}{6}


Example 6 Suppose a circle satisfies: (1) the length of the chord intercepted on the $y$-axis is 2; (2) it is divided into two arcs by the $x$-axis, with the ratio of their arc lengths being $3: 1$. Among all circles satisfying (1) and (2), find the equation of the circle whose center is closest to the line $l: x-2y=0$.

Answer: (x-1)^2 + (y-1)^2 = 2


15. Given that 15 rays share a common endpoint. Question: What is the maximum number of obtuse angles (considering the angle between any two rays to be the one not greater than $180^{\circ}$) that these 15 rays can form?

Answer: 75