Example 2. Solve the equation $y^{\prime \prime \prime}-7 y^{\prime \prime}+15 y^{\prime}-9 y=0$.

Answer: y = C_1 e^{x} + (C_2 + C_3 x) e^{3x}


A $180 \mathrm{~cm}$ high, horizontally based, cylindrical fuel tank is equipped with a tap at the bottom and a filling nozzle at the top. The latter can fill the tank in 1 hour. If we open both the filling nozzle and the tap for 5 minutes, the fuel level in the tank rises by $10 \mathrm{~cm}$. How long will it take to empty a full tank through the tap?

Answer: 3


3. Let positive integers $a, b$ be such that $15a + 16b$ and $16a - 15b$ are both squares of positive integers. Find the smallest value that the smaller of these two squares can take. ${ }^{[3]}$
(1996, China Mathematical Olympiad)

Answer: 231361


12.319. Find the ratio of the volume of a regular $n$-sided pyramid to the volume of the circumscribed sphere, if the angle between the lateral edge and the plane of the base of the pyramid is $\alpha$.

Answer: \dfrac{n \sin\left(\dfrac{2\pi}{n}\right) \cos^2 \alpha \sin^4 \alpha}{\pi}


Proivolov V.V.

In an isosceles triangle $ABC (AB = AC)$, the angle $A$ is equal to $\alpha$. On the side $AB$, a point $D$ is taken such that $AD = AB / n$. Find the sum of $n-1$ angles under which the segment $AD$ is seen from the points dividing the side $BC$ into $n$ equal parts:

a) for $n=3$

b) for an arbitrary $n$.

Answer: \dfrac{\alpha}{2}


15. Let $f(x)=x^{2}+p x+q$. If the inequality $|f(x)|>2$ has no solution in the interval $[1,5]$. Try to find all real pairs $(p, q)$.

Translate the above text into English, please keep the original text's line breaks and format, and output the translation result directly.

(Note: The provided text is already in English, so no changes are necessary.)

Answer: (-6, 7)


## Task 2.

In a certain archipelago, there are 2017 islands named $1, 2, \ldots, 2017$. Two agencies, Red Dragon and Blue Eye, are negotiating the schedule of ferry routes between the islands. For each pair of islands, exactly one agency will organize a ferry route, and this route will only operate from the island with the smaller number to the island with the larger number.

A ferry route schedule is good if there do not exist two islands with labels $A < B$ such that it is possible to travel from island $A$ to island $B$ using only ferries from Red Dragon, and also using only ferries from Blue Eye.

Determine the total number of good ferry route schedules.

Answer: 2017!


5. Connecting the centers of the faces of a regular polyhedron, we get a new regular polyhedron, which we call the positive sub-polyhedron of the original polyhedron. A cube $T_{1}$ has a surface area of $a_{1}=16$, its positive sub-polyhedron is $T_{2}$, with a surface area of $a_{2}$, the positive sub-polyhedron of $T_{2}$ is $T_{3}$, with a surface area of $a_{3}, \cdots \cdots$ and so on. Let the surface area of the $n$-th positive sub-polyhedron be $a_{n}$. Then
$$
\lim _{n \rightarrow \infty}\left(a_{1}+a_{2}+\cdots+a_{n}\right)=
$$

Answer: 18 + 3\sqrt{3}


a) Let \( m \) and \( n \) be natural numbers. Prove that if for some non-negative integers \( k_{1}, k_{2}, \ldots, k_{n} \), the number \( 2^{k_{1}} + 2^{k_{2}} + \ldots + 2^{k_{n}} \) is divisible by \( 2^{m} - 1 \), then \( n \geq m \).

b) Does there exist a natural number that is divisible by a number composed entirely of ones (i.e., \( \underbrace{111 \ldots 1} \) ) and has a digit sum less than \( m \)?

Answer: n \geq m


A sequence consists of 20 different natural numbers. The product of each pair of consecutive numbers is a perfect square of a natural number. The first number is 42. Prove that at least one of the numbers is greater than 16000.

Answer: 16800


During training target practice, each soldier fired 10 times. One of them was successful and scored 90 points in total. How many times did he score 7 points if he scored 10 points 4 times and the results of the remaining shots were 7, 8, and 9 points? Note that there were no misses.

Answer: 1


In a grid rectangle of size $20210 \times 1505$, two diagonals were drawn and all cells through which they passed were painted. How many cells were painted?

(O. A. Pyayve, A. A. Tesler)

Answer: 42785


In the plane, there is a set of integer points \( S = \{ (a, b) \mid 1 \leqslant a, b \leqslant 5, a, b \in \mathbf{Z} \} \). Now consider a subset \( T \) of integer points in the plane such that for any point \( P \) in \( S \), there exists a distinct point \( Q \) in \( T \) such that the line segment \( PQ \) contains no other integer points except \( P \) and \( Q \). What is the minimum number of elements required in the set \( T \)?

Answer: 2


A $5 \times 5$ grid consists of 25 $1 \times 1$ small squares. Each small square is divided into four identical isosceles triangles, three of which are colored black. If a side of a small square is on a black part, it is called a black edge; otherwise, it is a white edge. In the $5 \times 5$ grid, the common edge of adjacent (sharing a common edge) small squares must be the same color. What is the minimum number of black edges on the four sides of the $5 \times 5$ grid?

Answer: 5


In the right triangle \(ABC\) as shown in the figure, the length of \(AB\) is 12 cm, and the length of \(AC\) is 24 cm. Points \(D\) and \(E\) are on \(AC\) and \(BC\), respectively. Determine the area of the isosceles right triangle \(BDE\) in square centimeters.

Answer: 80


In the expression \( x \cdot x + x \cdot x + \ldots + x \cdot x \) (50 terms), the placeholders have been replaced with numbers \( 1, \ldots, 100 \), each used exactly once. What is the maximum and minimum value that the resulting expression can have?

Answer: 169150


Starting with a positive integer $n$, a sequence is created by following this rule: each term is obtained from the previous one by subtracting the largest perfect square that is less than or equal to the previous term, continuing until reaching zero. For example, if $n=142$, the sequence of 5 terms is:

$$
a_{1}=142, a_{2}=21, a_{3}=5, a_{4}=1, a_{5}=0
$$

since $21=142-11^{2}, 5=21-4^{2}, 1=5-2^{2}$ and $0=1-1^{2}$.

a) Give an example of a sequence that has exactly 6 terms.

b) Find the smallest value of $n$ for which the sequence thus created has exactly 7 terms.

Answer: 167


After Natasha eats half of the peaches in the jar, the level of the compote decreases by one third. By what fraction (of the resulting level) will the compote level decrease if half of the remaining peaches are eaten?

Answer: \frac{1}{4}


A straight stick 2 meters long is cut into \( N \) smaller sticks, each with a length represented by a whole number of centimeters. What is the smallest \( N \) for which it is guaranteed that using all the resulting smaller sticks, without breaking any of them, you can form the outline of a rectangle?

Answer: 102


The figure below shows a target on a wall that is fixed and cannot be rotated. It is divided into 10 parts, including a central circle, a smaller ring, and a larger (outer) ring. We must distribute the numbers 1 through 10, assigning one number to each part, which will correspond to the scores obtained by hitting each part.

a) In how many ways can we distribute the numbers among the parts of the target?

b) In how many ways can we distribute the numbers such that numbers closer to the center are not smaller than numbers farther from the center?

c) In how many ways can we distribute the numbers so that the sum of the numbers in the outer ring is equal to the sum of the numbers in the smaller ring?

Answer: 34,560


The lateral edge of a regular triangular pyramid is \(\sqrt{5}\), and the height of the pyramid is 1. Find the dihedral angle at the base.

Answer: 45


In each cell of a $5 \times 5$ square grid, exactly one diagonal was drawn. A vertex of the grid is considered free if it is not an endpoint of any of the drawn diagonals. Find the maximum possible number of free vertices.

Answer: 18


On an island of knights and liars, a traveler visited his knight friend and saw him sitting at a round table with five guests.

- "I'm curious, how many of you are knights?" he asked.
- "Why don't you ask each one of us some question to find out?" suggested one of the guests.
- "Alright. Tell me, who are your neighbors?" asked the traveler.

Everyone answered this question in the same way.

- "This information is insufficient!" said the traveler.
- "But today is my birthday, don't forget that," said one of the guests.
- "Yes, today is his birthday!" confirmed his neighbor.

With this information, the traveler was able to deduce how many knights were at the table. How many knights are there?

Answer: 2


The host of a popular history podcast has invited you to discuss fictional portrayals of royal families. To prepare for the discussion, you decide to watch 3 different fictional series about royal families. Each series has 8 episodes. You plan to watch 2 episodes per day.

After watching the series, you also plan to read 4 articles per series about the historical accuracy of these portrayals. Each article takes you 30 minutes to read.

How many total hours will you spend preparing for the podcast, including both watching the series and reading the articles?

Answer: 30


Alex is a hardware enthusiast who loves collecting the latest VR headsets. Each year, Alex buys 2 new VR headsets to keep up with the latest trends. In 2021, Alex started with 5 VR headsets.

If Alex continues to buy 2 new VR headsets every year, how many VR headsets will Alex have at the end of 2025?

Answer: 15


Jamie is a parent living in Kintore and has two kids, Alex and Taylor, who attend Kintore Primary School. Every weekday, Jamie prepares lunchboxes for both kids. Each lunchbox contains 2 sandwiches, 3 fruit snacks, and a bottle of water. If Jamie spends 5 minutes making each sandwich, 2 minutes packing fruit snacks, and 1 minute packing a bottle of water, how much total time does Jamie spend preparing both lunchboxes for Alex and Taylor each day?

Answer: 26


Mr. Smith, known for his messy and disorganized desk, has a collection of paper stacks that frequently cause problems in his office. One morning, he tries to tidy up and finds 7 stacks of papers on his desk. Each stack contains 15 sheets of paper, but he accidentally knocks over 3 stacks, scattering 8 sheets from each of these stacks onto the floor. To make matters worse, he finds another 12 sheets under a pile of folders that he didn't notice before. How many sheets of paper does Mr. Smith have in total after cleaning up the scattered sheets?

Answer: 117


An investor is excited about an innovative desalination system that can convert seawater into fresh drinking water. The investor plans to fund the development of this system by investing in two different phases. In the first phase, they plan to invest $50,000. In the second phase, they want to increase their investment by 150% of the first phase's amount.

After the system is developed, the investor expects a return of 200% on their total investment.

How much money will the investor receive as a return after the system is developed?

Answer: 250000


Marco visits Ristorante Machiavelli every Thursday for dinner. He has been a regular customer for 5 years. Each visit, he orders his favorite pasta dish for $12 and a dessert for $5. Every third visit, he also orders a special appetizer for an additional $8. How much money has Marco spent on average at the restaurant each year, considering he visits every week without missing a Thursday?

Answer: 1020


Mr. Thompson, a secondary school history teacher, is planning a field trip to a local history museum for his class. He has 24 students in his class, and he wants to ensure there is at least one chaperone for every 6 students. If each student ticket costs $8 and each chaperone ticket costs $5, how much will the total cost be for the tickets if Mr. Thompson also goes as a chaperone?

Answer: 212


A retired professional drift racer named Alex spends his weekends watching drifting competitions and mentoring young drifters. During one weekend event, Alex watches 4 different drifting competitions. Each competition lasts 90 minutes. After each competition, Alex spends 30 minutes mentoring a group of young drifters. If Alex takes a 15-minute break after each mentoring session, how many total minutes does Alex spend at the event on that weekend?

Answer: 540


A political reporter is investigating the expenses of a legislator’s office to ensure transparency and accountability. The reporter finds that the legislator's office spent $2,500 on office supplies, $3,200 on travel, and $1,800 on meals for official events in one month. The reporter also discovers that the legislator claimed a reimbursement of $1,200 for additional travel expenses. If the legislator's total budget for the month was $10,000, how much of the budget remains after these expenses and the reimbursement claim?

Answer: 1300


Detective Smith, a retired NYPD detective, now teaches criminal justice courses at John Jay College. In his class, Detective Smith assigns a project where each student must solve a mock case. He plans to give each of his 24 students 3 different mock cases to work on, each requiring 5 hours of investigation. If Detective Smith spends an additional 2 hours per student to review and grade their work, how many total hours will Detective Smith need to spend on assigning, reviewing, and grading all the projects?

Answer: 48


Jamie is a young musician who is fascinated by incorporating engineering concepts into designing instruments. She decides to design a new type of guitar string that can produce unique sounds. Jamie has 4 different materials she can use for the strings, and she wants to test 3 different thicknesses for each material to find the best combination for her new guitar. If she wants to create a prototype with 6 strings, using the best combination she finds, how many total options does she have to test before choosing the final set of strings for her prototype?

Answer: 2985984


A prominent conservative lobbyist is planning a fundraising event to support a new policy initiative. The lobbyist has connections with 8 government officials, each of whom can bring 5 guests to the event. In addition, the lobbyist personally invites 12 influential community leaders. Each guest at the event is expected to donate $50. How much money will be raised in total if everyone invited attends and donates as expected?

Answer: 3000


A reliable vendor named Mr. Thompson runs a store where he sells high-quality notebooks. Each week, Mr. Thompson receives a shipment of 500 notebooks to maintain consistent inventory levels. Last week, he sold 320 notebooks. This week, he plans a special promotion and expects to sell 450 notebooks. At the end of this week, how many notebooks will Mr. Thompson have left in his inventory?

Answer: 230


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Eric`, `Arnold`
 - Everyone has a favorite smoothie: `desert`, `watermelon`, `dragonfruit`, `cherry`
 - Each person lives in a unique style of house: `craftsman`, `victorian`, `ranch`, `colonial`
 - The people are of nationalities: `dane`, `brit`, `norwegian`, `swede`
 - People use unique phone models: `google pixel 6`, `samsung galaxy s21`, `iphone 13`, `oneplus 9`

## Clues:
1. The person who uses a Samsung Galaxy S21 is Arnold.
2. There is one house between Alice and the Norwegian.
3. There are two houses between the person who uses a OnePlus 9 and the person living in a colonial-style house.
4. The person living in a colonial-style house is the British person.
5. The person who uses an iPhone 13 is somewhere to the right of Alice.
6. The Watermelon smoothie lover is the British person.
7. The person residing in a Victorian house is somewhere to the left of the person who uses a Samsung Galaxy S21.
8. The Dane is the person who uses a OnePlus 9.
9. The Desert smoothie lover is not in the second house.
10. The person who uses an iPhone 13 is the Dragonfruit smoothie lover.
11. Eric is the Norwegian.
12. The person who uses a Samsung Galaxy S21 is the person in a Craftsman-style house.
 What is the value of attribute PhoneModel for the person whose attribute HouseStyle is colonial? Please reason step by step, and put your final answer within \boxed{}

Answer: google pixel 6


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

Answer: pall mall


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Bob`, `Eric`, `Carol`, `Alice`, `Arnold`
 - The people keep unique animals: `rabbit`, `dog`, `horse`, `fish`, `bird`, `cat`
 - People have unique favorite sports: `basketball`, `swimming`, `tennis`, `soccer`, `baseball`, `volleyball`
 - People have unique hair colors: `blonde`, `gray`, `auburn`, `red`, `black`, `brown`
 - People have unique heights: `average`, `very short`, `very tall`, `tall`, `super tall`, `short`
 - Everyone has a unique favorite cigar: `pall mall`, `yellow monster`, `blue master`, `prince`, `dunhill`, `blends`

## Clues:
1. The person who is very tall and the dog owner are next to each other.
2. There are two houses between the person who loves tennis and the person who has an average height.
3. The cat lover is the person who loves baseball.
4. The person who is very short is not in the fifth house.
5. There is one house between the fish enthusiast and the person who has red hair.
6. The cat lover is somewhere to the left of the Dunhill smoker.
7. The rabbit owner is somewhere to the left of the person who is super tall.
8. The Dunhill smoker is Alice.
9. The person who has red hair is the Dunhill smoker.
10. The person who is super tall is not in the fifth house.
11. The Prince smoker is somewhere to the left of the person who smokes Yellow Monster.
12. The person who loves volleyball is somewhere to the right of the person who smokes Yellow Monster.
13. The person who smokes Blue Master is directly left of the person who has black hair.
14. There is one house between the person who loves basketball and the person who smokes Blue Master.
15. The person who smokes Yellow Monster is the person who is tall.
16. Bob and the fish enthusiast are next to each other.
17. The Dunhill smoker is the person who loves soccer.
18. The person who loves tennis is not in the third house.
19. Arnold is the person who smokes many unique blends.
20. The Prince smoker is Peter.
21. There is one house between the person who has blonde hair and the person who is tall.
22. The person who loves swimming is directly left of Alice.
23. The person who is super tall is Eric.
24. The person who is short is the rabbit owner.
25. The person who keeps horses is not in the fifth house.
26. The cat lover and the person who has brown hair are next to each other.
27. The person who is short and the person who has auburn hair are next to each other.
 What is the value of attribute House for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

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: `Alice`, `Bob`, `Arnold`, `Carol`, `Eric`, `Peter`
 - People use unique phone models: `xiaomi mi 11`, `google pixel 6`, `samsung galaxy s21`, `oneplus 9`, `huawei p50`, `iphone 13`
 - People have unique favorite book genres: `romance`, `historical fiction`, `fantasy`, `mystery`, `science fiction`, `biography`
 - They all have a unique favorite flower: `tulips`, `roses`, `carnations`, `daffodils`, `iris`, `lilies`
 - The people keep unique animals: `dog`, `cat`, `bird`, `fish`, `rabbit`, `horse`
 - Each person has a unique level of education: `trade school`, `high school`, `master`, `associate`, `bachelor`, `doctorate`

## Clues:
1. The bird keeper is the person who uses a Google Pixel 6.
2. The person who loves a bouquet of daffodils is the person with an associate's degree.
3. The person who uses a OnePlus 9 is not in the fourth house.
4. There are two houses between the person with a master's degree and the rabbit owner.
5. The person who loves a carnations arrangement is Arnold.
6. The person who loves the boquet of lilies is not in the sixth house.
7. The person who loves the vase of tulips is Carol.
8. The person with a high school diploma is Bob.
9. The person who attended trade school is somewhere to the left of the person who keeps horses.
10. The person who loves mystery books is Eric.
11. The fish enthusiast is directly left of Carol.
12. Bob is the fish enthusiast.
13. Eric is the dog owner.
14. The person who loves a carnations arrangement is the person who uses a Google Pixel 6.
15. The person who loves fantasy books is in the second house.
16. The person who uses a Samsung Galaxy S21 is the person who loves the boquet of iris.
17. Alice is the person with an associate's degree.
18. The person who uses a Google Pixel 6 is not in the second house.
19. The dog owner is the person with a doctorate.
20. The fish enthusiast is the person who uses a Samsung Galaxy S21.
21. The person who uses an iPhone 13 is somewhere to the right of the person who loves fantasy books.
22. The person who loves mystery books is somewhere to the right of the person who loves the boquet of iris.
23. Alice is the person who uses an iPhone 13.
24. The person who attended trade school is not in the fourth house.
25. The person who loves biography books is directly left of Eric.
26. There is one house between the rabbit owner and the person who loves historical fiction books.
27. The person who loves the boquet of iris is somewhere to the right of the person who uses a Xiaomi Mi 11.
28. The person who loves science fiction books is the person who uses a Samsung Galaxy S21.
29. The person who loves the boquet of lilies is not in the second house.
 What is the value of attribute Animal for the person whose attribute BookGenre is historical fiction? 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: `Alice`, `Arnold`, `Eric`, `Peter`, `Bob`
 - Each person has a favorite color: `red`, `green`, `white`, `blue`, `yellow`
 - Each mother is accompanied by their child: `Bella`, `Timothy`, `Samantha`, `Meredith`, `Fred`
 - They all have a unique favorite flower: `tulips`, `daffodils`, `carnations`, `lilies`, `roses`

## Clues:
1. Alice is not in the fifth house.
2. Eric is the person who is the mother of Timothy.
3. Alice and Bob are next to each other.
4. The person who loves blue is not in the fourth house.
5. The person's child is named Samantha is the person who loves the vase of tulips.
6. The person who loves the vase of tulips is Alice.
7. The person's child is named Fred is the person whose favorite color is red.
8. The person's child is named Bella is in the first house.
9. There is one house between the person who loves blue and the person who loves yellow.
10. The person who loves yellow is the person who loves the rose bouquet.
11. The person's child is named Meredith is somewhere to the left of Bob.
12. The person who loves white is not in the second house.
13. The person who loves a carnations arrangement is not in the second house.
14. The person who loves white is Arnold.
15. The person who loves the boquet of lilies is in the first house.
 What is the value of attribute House for the person whose attribute Color is blue? 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: `Arnold`, `Eric`, `Peter`, `Alice`
 - People have unique heights: `very short`, `short`, `tall`, `average`
 - Each person prefers a unique type of vacation: `cruise`, `beach`, `city`, `mountain`
 - Each person has a favorite color: `green`, `red`, `yellow`, `white`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Meredith`, `Samantha`

## Clues:
1. The person who loves beach vacations is the person who is very short.
2. The person who is very short is the person who loves white.
3. The person who has an average height is the person's child is named Bella.
4. The person who has an average height is the person whose favorite color is red.
5. Peter is the person's child is named Samantha.
6. The person whose favorite color is green is directly left of the person who loves white.
7. Alice is in the third house.
8. The person who likes going on cruises is the person's child is named Bella.
9. The person who is short is the person who loves yellow.
10. The person who is very short is the person's child is named Fred.
11. Eric is the person who loves yellow.
12. The person who prefers city breaks is Eric.
13. The person who is short is somewhere to the left of the person who is tall.
 What is the value of attribute Color for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: white


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`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`
 - People have unique heights: `very short`, `average`, `short`
 - People have unique favorite sports: `basketball`, `tennis`, `soccer`

## Clues:
1. The person who loves tennis is somewhere to the left of The person whose mother's name is Aniya.
2. The person who is short is The person whose mother's name is Holly.
3. The person who loves tennis and the person who is very short are next to each other.
4. The person who loves soccer is somewhere to the right of Arnold.
5. Eric is not in the first house.
6. Arnold is in the second house.
7. The person whose mother's name is Holly is in the third house.
 What is the value of attribute House for the person whose attribute Mother is Janelle? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Peter`, `Bob`, `Arnold`
 - Each person has a unique type of pet: `hamster`, `fish`, `cat`, `dog`, `bird`
 - Each person has an occupation: `doctor`, `engineer`, `artist`, `lawyer`, `teacher`
 - Each person has a favorite color: `green`, `blue`, `yellow`, `red`, `white`
 - The people keep unique animals: `bird`, `cat`, `horse`, `fish`, `dog`

## Clues:
1. The person who owns a dog is Arnold.
2. The bird keeper is in the fourth house.
3. The person who keeps a pet bird is directly left of the dog owner.
4. The person who loves white is somewhere to the left of the person who is a lawyer.
5. The person who loves yellow is directly left of the person whose favorite color is green.
6. The cat lover is Bob.
7. The cat lover is somewhere to the left of Eric.
8. The person who keeps horses is in the fifth house.
9. The person who is a lawyer is directly left of the person who is a teacher.
10. The person who is a doctor is in the first house.
11. Alice is the person who loves yellow.
12. The person who loves blue is directly left of the person with an aquarium of fish.
13. The person who loves yellow is in the first house.
14. The person with a pet hamster is the person who is an artist.
15. Eric is the dog owner.
 What is the value of attribute Animal for the person whose attribute Color is red? Please reason step by step, and put your final answer within \boxed{}

Answer: horse


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

Answer: sept


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Arnold`, `Alice`, `Peter`, `Eric`
 - The people are of nationalities: `swede`, `german`, `dane`, `brit`, `chinese`, `norwegian`
 - Each person has a unique type of pet: `bird`, `cat`, `dog`, `rabbit`, `fish`, `hamster`
 - Each person has a favorite color: `red`, `green`, `purple`, `yellow`, `white`, `blue`

## Clues:
1. The person who has a cat is the British person.
2. The person with a pet hamster is in the fourth house.
3. The person who owns a rabbit is the person who loves purple.
4. Arnold is the person who loves white.
5. The Dane is somewhere to the left of the person who owns a dog.
6. Carol and Peter are next to each other.
7. The Swedish person is somewhere to the right of the person whose favorite color is green.
8. The person who loves blue is the person with a pet hamster.
9. There are two houses between the person whose favorite color is red and Bob.
10. The person who keeps a pet bird is in the second house.
11. Carol is in the first house.
12. The person who loves yellow and the German are next to each other.
13. Alice is the person who loves yellow.
14. The Dane is the person who loves yellow.
15. Bob is the Norwegian.
16. Alice is directly left of the person who loves white.
 What is the value of attribute 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: `Eric`, `Carol`, `Alice`, `Arnold`, `Peter`, `Bob`
 - People have unique favorite book genres: `historical fiction`, `science fiction`, `fantasy`, `romance`, `mystery`, `biography`
 - People use unique phone models: `iphone 13`, `google pixel 6`, `samsung galaxy s21`, `oneplus 9`, `huawei p50`, `xiaomi mi 11`
 - Each person has a unique favorite drink: `tea`, `water`, `boba tea`, `milk`, `root beer`, `coffee`

## Clues:
1. The boba tea drinker is the person who uses a Xiaomi Mi 11.
2. Eric is the root beer lover.
3. The person who loves science fiction books is the person who likes milk.
4. The person who likes milk is somewhere to the right of Eric.
5. Arnold is the person who uses a Huawei P50.
6. The person who loves romance books is not in the fourth house.
7. Alice is the person who uses an iPhone 13.
8. The person who loves fantasy books is somewhere to the right of Bob.
9. There are two houses between the person who uses an iPhone 13 and the person who loves fantasy books.
10. The root beer lover is directly left of Peter.
11. The person who uses an iPhone 13 and the person who loves science fiction books are next to each other.
12. The person who uses a Samsung Galaxy S21 is the person who loves romance books.
13. The tea drinker is the person who uses a Huawei P50.
14. There is one house between the person who loves romance books and the person who uses a OnePlus 9.
15. There are two houses between the person who loves biography books and the boba tea drinker.
16. The person who loves historical fiction books is somewhere to the right of the root beer lover.
17. There is one house between the one who only drinks water and the person who uses a Huawei P50.
 What is the value of attribute PhoneModel for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: oneplus 9


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Bob`, `Arnold`, `Carol`, `Eric`, `Peter`
 - People use unique phone models: `xiaomi mi 11`, `google pixel 6`, `samsung galaxy s21`, `oneplus 9`, `huawei p50`, `iphone 13`
 - People have unique favorite book genres: `romance`, `historical fiction`, `fantasy`, `mystery`, `science fiction`, `biography`
 - They all have a unique favorite flower: `tulips`, `roses`, `carnations`, `daffodils`, `iris`, `lilies`
 - The people keep unique animals: `dog`, `cat`, `bird`, `fish`, `rabbit`, `horse`
 - Each person has a unique level of education: `trade school`, `high school`, `master`, `associate`, `bachelor`, `doctorate`

## Clues:
1. The bird keeper is the person who uses a Google Pixel 6.
2. The person who loves a bouquet of daffodils is the person with an associate's degree.
3. The person who uses a OnePlus 9 is not in the fourth house.
4. There are two houses between the person with a master's degree and the rabbit owner.
5. The person who loves a carnations arrangement is Arnold.
6. The person who loves the boquet of lilies is not in the sixth house.
7. The person who loves the vase of tulips is Carol.
8. The person with a high school diploma is Bob.
9. The person who attended trade school is somewhere to the left of the person who keeps horses.
10. The person who loves mystery books is Eric.
11. The fish enthusiast is directly left of Carol.
12. Bob is the fish enthusiast.
13. Eric is the dog owner.
14. The person who loves a carnations arrangement is the person who uses a Google Pixel 6.
15. The person who loves fantasy books is in the second house.
16. The person who uses a Samsung Galaxy S21 is the person who loves the boquet of iris.
17. Alice is the person with an associate's degree.
18. The person who uses a Google Pixel 6 is not in the second house.
19. The dog owner is the person with a doctorate.
20. The fish enthusiast is the person who uses a Samsung Galaxy S21.
21. The person who uses an iPhone 13 is somewhere to the right of the person who loves fantasy books.
22. The person who loves mystery books is somewhere to the right of the person who loves the boquet of iris.
23. Alice is the person who uses an iPhone 13.
24. The person who attended trade school is not in the fourth house.
25. The person who loves biography books is directly left of Eric.
26. There is one house between the rabbit owner and the person who loves historical fiction books.
27. The person who loves the boquet of iris is somewhere to the right of the person who uses a Xiaomi Mi 11.
28. The person who loves science fiction books is the person who uses a Samsung Galaxy S21.
29. The person who loves the boquet of lilies is not in the second house.
 What is the value of attribute Flower for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: tulips


There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`
 - Each person lives in a unique style of house: `colonial`, `victorian`
 - Each person has a unique birthday month: `april`, `sept`
 - People have unique favorite music genres: `rock`, `pop`

## Clues:
1. The person who loves pop music is directly left of Eric.
2. Eric is the person whose birthday is in September.
3. The person whose birthday is in April is the person living in a colonial-style house.
 What is the value of attribute Birthday for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: sept


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Carol`, `Peter`, `Bob`, `Eric`
 - People use unique phone models: `huawei p50`, `samsung galaxy s21`, `iphone 13`, `xiaomi mi 11`, `google pixel 6`, `oneplus 9`
 - Each person has a unique hobby: `photography`, `painting`, `gardening`, `woodworking`, `cooking`, `knitting`

## Clues:
1. The woodworking hobbyist is somewhere to the left of Bob.
2. The person who paints as a hobby is in the fifth house.
3. Arnold is directly left of the person who uses a Google Pixel 6.
4. The person who uses a Samsung Galaxy S21 is Arnold.
5. Carol is somewhere to the right of the person who uses a Samsung Galaxy S21.
6. The person who uses a Google Pixel 6 is directly left of the person who uses a OnePlus 9.
7. The person who uses a OnePlus 9 is somewhere to the right of Eric.
8. There are two houses between the person who loves cooking and Peter.
9. The person who enjoys knitting is Eric.
10. Peter is the person who paints as a hobby.
11. The person who enjoys gardening is somewhere to the right of Bob.
12. There is one house between Bob and the person who uses a Huawei P50.
13. The person who uses a Xiaomi Mi 11 is not in the first house.
14. Alice is in the sixth house.
 What is the value of attribute Hobby for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: painting


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Peter`, `Eric`
 - Each person prefers a unique type of vacation: `cruise`, `mountain`, `city`, `beach`
 - Each person has a unique favorite drink: `tea`, `coffee`, `milk`, `water`
 - The people are of nationalities: `brit`, `swede`, `dane`, `norwegian`

## Clues:
1. The person who prefers city breaks is the Swedish person.
2. The person who likes going on cruises is directly left of the person who loves beach vacations.
3. Arnold is in the second house.
4. Arnold is the person who likes milk.
5. The person who prefers city breaks is not in the fourth house.
6. The coffee drinker is the Norwegian.
7. The person who loves beach vacations and Peter are next to each other.
8. Eric is the one who only drinks water.
9. The person who loves beach vacations is directly left of the Dane.
 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: 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: `Eric`, `Alice`, `Peter`, `Arnold`
 - They all have a unique favorite flower: `lilies`, `carnations`, `roses`, `daffodils`
 - Each person has a favorite color: `white`, `green`, `yellow`, `red`
 - Each person has a unique level of education: `bachelor`, `associate`, `master`, `high school`
 - Each person has a unique hobby: `painting`, `photography`, `gardening`, `cooking`
 - Everyone has a unique favorite cigar: `dunhill`, `blue master`, `prince`, `pall mall`

## Clues:
1. The person partial to Pall Mall is the person with an associate's degree.
2. The person who loves white is the Prince smoker.
3. The person with a high school diploma is not in the fourth house.
4. The person with a master's degree is not in the second house.
5. Arnold is not in the fourth house.
6. The person whose favorite color is red is not in the third house.
7. The person whose favorite color is red is somewhere to the left of Eric.
8. The person who loves cooking is somewhere to the right of Peter.
9. The person who loves a bouquet of daffodils is somewhere to the left of the person who paints as a hobby.
10. The person who loves white is the person who loves the boquet of lilies.
11. Alice is the photography enthusiast.
12. Arnold is somewhere to the right of the person partial to Pall Mall.
13. The person who loves white is in the second house.
14. The person whose favorite color is green is directly left of the person who enjoys gardening.
15. The Dunhill smoker is the person with a high school diploma.
16. The person who loves the rose bouquet is somewhere to the right of the person whose favorite color is green.
 What is the value of attribute Hobby for the person whose attribute Education is master? Please reason step by step, and put your final answer within \boxed{}

Answer: gardening


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`, `Bob`, `Peter`, `Arnold`
 - People have unique favorite book genres: `fantasy`, `mystery`, `science fiction`, `biography`, `romance`
 - The mothers' names in different houses are unique: `Holly`, `Penny`, `Aniya`, `Kailyn`, `Janelle`
 - People use unique phone models: `oneplus 9`, `iphone 13`, `samsung galaxy s21`, `google pixel 6`, `huawei p50`
 - The people are of nationalities: `dane`, `brit`, `german`, `swede`, `norwegian`
 - Each person lives in a unique style of house: `ranch`, `modern`, `craftsman`, `victorian`, `colonial`

## Clues:
1. The person in a ranch-style home is somewhere to the right of the person residing in a Victorian house.
2. The Dane and the person who uses a Samsung Galaxy S21 are next to each other.
3. The person who uses a Google Pixel 6 is not in the second house.
4. There are two houses between the person who loves fantasy books and the person in a modern-style house.
5. The person whose mother's name is Kailyn is the Swedish person.
6. The Swedish person is Arnold.
7. The British person is somewhere to the left of the person who uses an iPhone 13.
8. The Dane is The person whose mother's name is Penny.
9. The person who uses a Samsung Galaxy S21 is the Norwegian.
10. The Norwegian is The person whose mother's name is Holly.
11. The person who loves fantasy books is Bob.
12. Alice is directly left of the Swedish person.
13. The person who loves romance books is Arnold.
14. The person who loves science fiction books is Peter.
15. The person whose mother's name is Aniya is directly left of the person who loves science fiction books.
16. The person who loves science fiction books is the person who uses a OnePlus 9.
17. The person residing in a Victorian house is the person who loves biography books.
18. The person who loves fantasy books is somewhere to the left of the German.
19. The person who uses an iPhone 13 is the person in a Craftsman-style house.
 What is the value of attribute Nationality for the person whose attribute Mother is Kailyn? Please reason step by step, and put your final answer within \boxed{}

Answer: swede


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 prefers a unique type of vacation: `beach`, `mountain`, `city`
 - They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`
 - Each person has a unique birthday month: `april`, `jan`, `sept`

## Clues:
1. Eric is the person who prefers city breaks.
2. Peter is the person who loves beach vacations.
3. Arnold is somewhere to the right of the person who loves a carnations arrangement.
4. The person whose birthday is in April is the person who loves a bouquet of daffodils.
5. The person who loves a carnations arrangement is Peter.
6. The person whose birthday is in September is somewhere to the left of Peter.
 What is the value of attribute Birthday for the person whose attribute Flower is carnations? Please reason step by step, and put your final answer within \boxed{}

Answer: jan


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

Answer: tea


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Peter`
 - People have unique favorite book genres: `mystery`, `romance`, `science fiction`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `samsung galaxy s21`
 - People have unique heights: `short`, `very short`, `average`
 - They all have a unique favorite flower: `daffodils`, `lilies`, `carnations`
 - Everyone has something unique for lunch: `pizza`, `grilled cheese`, `spaghetti`

## Clues:
1. The person who uses a Samsung Galaxy S21 is the person who is short.
2. The person who loves a carnations arrangement is directly left of the person who uses an iPhone 13.
3. Peter is the person who loves romance books.
4. The person who loves eating grilled cheese is not in the first house.
5. Arnold is the person who loves science fiction books.
6. The person who loves a bouquet of daffodils is the person who is very short.
7. The person who uses a Samsung Galaxy S21 is the person who loves science fiction books.
8. The person who loves science fiction books is the person who is a pizza lover.
9. Arnold is in the third house.
10. Peter is the person who is very short.
 What is the value of attribute BookGenre for the person whose attribute Height is very short? Please reason step by step, and put your final answer within \boxed{}

Answer: romance


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`
 - Each person prefers a unique type of vacation: `beach`, `mountain`, `city`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`
 - Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `pizza`
 - The people keep unique animals: `bird`, `cat`, `horse`

## Clues:
1. The bird keeper is not in the second house.
2. The person who loves beach vacations is somewhere to the left of Arnold.
3. The bird keeper and the person who keeps horses are next to each other.
4. The bird keeper is not in the third house.
5. The person who is a pizza lover is not in the second house.
6. The person who prefers city breaks is the bird keeper.
7. The person who smokes Blue Master is not in the second house.
8. The person who loves the spaghetti eater is in the third house.
9. Eric is the person who smokes Blue Master.
10. The person who loves eating grilled cheese is directly left of the Prince smoker.
 What is the value of attribute Food for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: pizza


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`
 - Everyone has something unique for lunch: `pizza`, `grilled cheese`, `spaghetti`
 - Each person has a unique birthday month: `april`, `jan`, `sept`
 - Everyone has a favorite smoothie: `cherry`, `watermelon`, `desert`
 - People own unique car models: `toyota camry`, `ford f150`, `tesla model 3`
 - People have unique favorite music genres: `pop`, `classical`, `rock`

## Clues:
1. The person whose birthday is in January is not in the second house.
2. Arnold is directly left of the person who loves eating grilled cheese.
3. The person who owns a Tesla Model 3 is the person who loves pop music.
4. The Watermelon smoothie lover and the person who owns a Tesla Model 3 are next to each other.
5. The person whose birthday is in April is not in the third house.
6. The person who loves eating grilled cheese is the Desert smoothie lover.
7. The person who owns a Toyota Camry is the person who is a pizza lover.
8. The person who owns a Tesla Model 3 is the person who loves eating grilled cheese.
9. The person whose birthday is in January is the person who loves classical music.
10. The person who is a pizza lover is Eric.
11. Eric is not in the third house.
 What is the value of attribute Birthday for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: sept


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Bob`, `Alice`, `Carol`
 - The people keep unique animals: `rabbit`, `dog`, `fish`, `bird`, `cat`, `horse`
 - Each person has a unique hobby: `cooking`, `knitting`, `painting`, `woodworking`, `photography`, `gardening`
 - People have unique favorite sports: `basketball`, `soccer`, `swimming`, `tennis`, `baseball`, `volleyball`
 - Each person prefers a unique type of vacation: `cruise`, `cultural`, `city`, `camping`, `mountain`, `beach`
 - Each person has a unique favorite drink: `water`, `root beer`, `boba tea`, `tea`, `milk`, `coffee`

## Clues:
1. The person who enjoys camping trips is the person who loves cooking.
2. The person who loves baseball is the photography enthusiast.
3. The person who loves volleyball is somewhere to the left of the person who prefers city breaks.
4. Carol is the person who loves tennis.
5. The dog owner is the person who loves swimming.
6. The photography enthusiast is the tea drinker.
7. The person who loves baseball is directly left of the person who goes on cultural tours.
8. Peter is the person who enjoys camping trips.
9. The person who enjoys knitting is the person who keeps horses.
10. The coffee drinker is directly left of the person who loves soccer.
11. The person who enjoys mountain retreats is the person who loves soccer.
12. The boba tea drinker is not in the fourth house.
13. The cat lover is somewhere to the left of the dog owner.
14. The person who loves beach vacations is Bob.
15. The coffee drinker is somewhere to the right of Alice.
16. The tea drinker is the fish enthusiast.
17. The person who likes milk is Carol.
18. There is one house between the rabbit owner and the woodworking hobbyist.
19. The person who loves cooking is not in the third house.
20. The person who loves tennis is the rabbit owner.
21. The dog owner is directly left of the person who likes going on cruises.
22. The woodworking hobbyist is the dog owner.
23. There are two houses between the person who paints as a hobby and the person who keeps horses.
24. Arnold is the root beer lover.
 What is the value of attribute Animal for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: fish


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`
 - Each person lives in a unique style of house: `victorian`, `ranch`, `craftsman`, `colonial`
 - Everyone has a unique favorite cigar: `pall mall`, `dunhill`, `blue master`, `prince`
 - Each person has an occupation: `doctor`, `teacher`, `engineer`, `artist`
 - They all have a unique favorite flower: `lilies`, `daffodils`, `roses`, `carnations`
 - The people keep unique animals: `horse`, `bird`, `fish`, `cat`

## Clues:
1. The fish enthusiast is somewhere to the right of Eric.
2. The person who is an engineer is Arnold.
3. The person who loves a carnations arrangement is the person in a ranch-style home.
4. Alice is the person in a Craftsman-style house.
5. The person partial to Pall Mall is the person who loves a bouquet of daffodils.
6. The cat lover is Arnold.
7. The Dunhill smoker is Peter.
8. The person living in a colonial-style house is not in the fourth house.
9. The person who is a teacher is the bird keeper.
10. The person residing in a Victorian house is Peter.
11. The person who loves the boquet of lilies is the person who smokes Blue Master.
12. Peter is somewhere to the right of the person who is an artist.
13. The person who is an engineer and the person who is a teacher are next to each other.
14. The person who is a doctor is the person who loves a carnations arrangement.
15. The person partial to Pall Mall is the person living in a colonial-style house.
 What is the value of attribute House for the person whose attribute Animal is fish? 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: `Peter`, `Bob`, `Arnold`, `Eric`, `Alice`
 - Each person has a favorite color: `red`, `white`, `green`, `blue`, `yellow`
 - Each person has a unique hobby: `gardening`, `cooking`, `painting`, `photography`, `knitting`
 - People have unique heights: `very tall`, `tall`, `average`, `short`, `very short`
 - People have unique hair colors: `black`, `blonde`, `brown`, `gray`, `red`

## Clues:
1. The person whose favorite color is green is somewhere to the right of the person who has black hair.
2. The person who has an average height is somewhere to the right of the person who loves blue.
3. The person who has red hair is Alice.
4. The person who loves cooking is not in the first house.
5. The person who loves yellow is the person who has gray hair.
6. The person who is short is somewhere to the left of the person who loves yellow.
7. The person who enjoys gardening is the person who loves white.
8. Arnold is somewhere to the left of the person who has black hair.
9. The person who is short is somewhere to the right of the person who has blonde hair.
10. Eric and the person who loves cooking are next to each other.
11. The person who has black hair is directly left of the person who loves blue.
12. The person who is very short is the person who has black hair.
13. Bob is the person who loves blue.
14. The person who is tall is directly left of the photography enthusiast.
15. The person who loves white is not in the first house.
16. The person who loves yellow is the person who enjoys knitting.
17. The person who loves blue is the person who has blonde hair.
 What is the value of attribute House for the person whose attribute HairColor is blonde? 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: `Eric`, `Arnold`, `Alice`, `Peter`
 - Each person lives in a unique style of house: `craftsman`, `ranch`, `victorian`, `colonial`
 - Each person has a unique favorite drink: `water`, `tea`, `milk`, `coffee`

## Clues:
1. Eric is the one who only drinks water.
2. The person who likes milk is the person residing in a Victorian house.
3. The person in a ranch-style home is somewhere to the left of the person in a Craftsman-style house.
4. Eric is in the third house.
5. Arnold is somewhere to the right of Alice.
6. The person in a ranch-style home is Arnold.
7. Eric and the person residing in a Victorian house are next to each other.
8. The tea drinker is not in the first house.
 What is the value of attribute Drink for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: milk


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`, `Alice`
 - Each person has a unique hobby: `painting`, `gardening`, `photography`, `cooking`
 - The people keep unique animals: `horse`, `bird`, `fish`, `cat`

## Clues:
1. Peter is the cat lover.
2. There is one house between the person who paints as a hobby and Peter.
3. Alice is the fish enthusiast.
4. The person who enjoys gardening is somewhere to the right of the person who paints as a hobby.
5. Arnold is not in the second house.
6. The photography enthusiast is not in the third house.
7. The bird keeper is the person who enjoys gardening.
8. Eric is the bird keeper.
9. Alice is in the first house.
 What is the value of attribute House for the person whose attribute Animal is horse? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Alice`, `Arnold`, `Eric`, `Peter`
 - Each person prefers a unique type of vacation: `camping`, `cultural`, `beach`, `city`, `mountain`, `cruise`
 - People have unique favorite sports: `swimming`, `volleyball`, `baseball`, `basketball`, `tennis`, `soccer`

## Clues:
1. The person who loves tennis is somewhere to the left of Peter.
2. Arnold is not in the fifth house.
3. The person who prefers city breaks and Peter are next to each other.
4. The person who enjoys camping trips is the person who loves basketball.
5. The person who likes going on cruises is Carol.
6. The person who enjoys mountain retreats is the person who loves swimming.
7. The person who loves baseball is the person who loves beach vacations.
8. Bob is the person who loves swimming.
9. The person who goes on cultural tours is the person who loves soccer.
10. The person who loves tennis is directly left of the person who enjoys mountain retreats.
11. The person who enjoys camping trips is Alice.
12. There are two houses between the person who loves tennis and Alice.
13. The person who goes on cultural tours is not in the fifth house.
14. The person who loves beach vacations is in the third house.
 What is the value of attribute FavoriteSport for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: volleyball


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`
 - Everyone has a unique favorite cigar: `dunhill`, `prince`, `blue master`, `pall mall`
 - People have unique favorite book genres: `mystery`, `romance`, `science fiction`, `fantasy`

## Clues:
1. There is one house between the person partial to Pall Mall and the person who loves mystery books.
2. There is one house between Eric and the person who loves mystery books.
3. The person who loves romance books is the Dunhill smoker.
4. Peter is not in the fourth house.
5. The person who loves science fiction books is Eric.
6. The person who loves fantasy books is not in the fourth house.
7. The Prince smoker and the Dunhill smoker are next to each other.
8. Arnold is the person who loves mystery books.
9. The Prince smoker is not in the fourth house.
10. The person who loves science fiction books is somewhere to the left of Arnold.
 What is the value of attribute BookGenre for the person whose attribute Cigar is dunhill? Please reason step by step, and put your final answer within \boxed{}

Answer: romance


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Peter`, `Bob`, `Eric`, `Carol`
 - Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `watermelon`, `lime`, `desert`, `blueberry`
 - Each person has a unique birthday month: `mar`, `april`, `jan`, `may`, `sept`, `feb`
 - The people keep unique animals: `cat`, `rabbit`, `horse`, `bird`, `fish`, `dog`

## Clues:
1. The bird keeper is in the third house.
2. The person whose birthday is in May is somewhere to the left of Eric.
3. Eric is the Desert smoothie lover.
4. The rabbit owner is the person whose birthday is in January.
5. The fish enthusiast is directly left of the person who likes Cherry smoothies.
6. The person whose birthday is in September is Peter.
7. There is one house between Peter and the rabbit owner.
8. The person who drinks Lime smoothies is not in the sixth house.
9. The Watermelon smoothie lover is the dog owner.
10. The person whose birthday is in April is somewhere to the right of Carol.
11. The bird keeper is somewhere to the left of the person who keeps horses.
12. The person who drinks Lime smoothies is Alice.
13. The Dragonfruit smoothie lover is directly left of Carol.
14. The person who drinks Blueberry smoothies is the person whose birthday is in February.
15. The person whose birthday is in September is in the third house.
16. Bob is the Dragonfruit smoothie lover.
17. The person who likes Cherry smoothies is somewhere to the left of the person whose birthday is in May.
18. The rabbit owner is the Desert smoothie lover.
 What is the value of attribute Smoothie for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: watermelon


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`, `Eric`, `Alice`
 - Each person prefers a unique type of vacation: `mountain`, `cruise`, `beach`, `city`
 - Each person lives in a unique style of house: `craftsman`, `ranch`, `victorian`, `colonial`
 - The mothers' names in different houses are unique: `Kailyn`, `Holly`, `Aniya`, `Janelle`
 - They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `carnations`
 - Each person has a favorite color: `green`, `white`, `yellow`, `red`

## Clues:
1. Alice is directly left of the person whose favorite color is red.
2. The person who loves a bouquet of daffodils is The person whose mother's name is Janelle.
3. Eric is not in the first house.
4. The person who loves the boquet of lilies is directly left of the person living in a colonial-style house.
5. The person residing in a Victorian house is in the second house.
6. The person who loves the rose bouquet is the person who loves yellow.
7. The person whose mother's name is Aniya is the person who loves yellow.
8. The person who enjoys mountain retreats is in the first house.
9. The person who likes going on cruises is the person whose favorite color is red.
10. The person who loves yellow is in the second house.
11. The person who loves white is the person who prefers city breaks.
12. The person whose mother's name is Holly is not in the fourth house.
13. The person whose favorite color is red is directly left of Peter.
14. The person who loves a bouquet of daffodils is the person in a ranch-style home.
 What is the value of attribute Flower for the person whose attribute HouseStyle is victorian? Please reason step by step, and put your final answer within \boxed{}

Answer: roses


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`, `Alice`, `Eric`, `Peter`, `Arnold`, `Bob`
 - The mothers' names in different houses are unique: `Penny`, `Janelle`, `Aniya`, `Sarah`, `Holly`, `Kailyn`
 - Everyone has a unique favorite cigar: `blends`, `dunhill`, `blue master`, `prince`, `yellow monster`, `pall mall`
 - Each person has a unique type of pet: `cat`, `dog`, `rabbit`, `hamster`, `bird`, `fish`
 - The people keep unique animals: `bird`, `horse`, `cat`, `rabbit`, `dog`, `fish`
 - Everyone has a favorite smoothie: `desert`, `watermelon`, `lime`, `cherry`, `blueberry`, `dragonfruit`

## Clues:
1. The dog owner is not in the third house.
2. The fish enthusiast is not in the fourth house.
3. The person who owns a dog is Eric.
4. The cat lover is not in the second house.
5. The person who smokes Blue Master is somewhere to the right of The person whose mother's name is Sarah.
6. The cat lover is not in the fourth house.
7. There are two houses between Carol and the person who owns a rabbit.
8. The person whose mother's name is Penny is the person with a pet hamster.
9. The person whose mother's name is Kailyn is somewhere to the right of the person with a pet hamster.
10. The dog owner and the person who drinks Lime smoothies are next to each other.
11. The Prince smoker is somewhere to the right of The person whose mother's name is Janelle.
12. There is one house between The person whose mother's name is Penny and Bob.
13. There are two houses between the person partial to Pall Mall and The person whose mother's name is Penny.
14. Peter is somewhere to the left of the person who drinks Lime smoothies.
15. The bird keeper is the Watermelon smoothie lover.
16. The person with a pet hamster is the Prince smoker.
17. The person who smokes Yellow Monster is the person who drinks Lime smoothies.
18. The person whose mother's name is Sarah is the person who smokes Yellow Monster.
19. The Dunhill smoker is somewhere to the left of the Watermelon smoothie lover.
20. The person whose mother's name is Holly is directly left of the person who owns a dog.
21. The bird keeper is The person whose mother's name is Kailyn.
22. The person whose mother's name is Sarah is not in the third house.
23. The person who smokes many unique blends is the rabbit owner.
24. The person who has a cat is somewhere to the right of the person with an aquarium of fish.
25. The person who smokes Yellow Monster is Eric.
26. The person who keeps a pet bird is the Desert smoothie lover.
27. Alice is The person whose mother's name is Kailyn.
28. The Dragonfruit smoothie lover is Carol.
29. The person who keeps horses is the person who likes Cherry smoothies.
 What is the value of attribute Smoothie for the person whose attribute Pet is dog? Please reason step by step, and put your final answer within \boxed{}

Answer: lime


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

Answer: Peter


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`
 - The people are of nationalities: `brit`, `dane`
 - Each person has a unique level of education: `associate`, `high school`
 - Each person has a unique birthday month: `april`, `sept`
 - Each person has an occupation: `engineer`, `doctor`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`

## Clues:
1. The Dane is the person who uses an iPhone 13.
2. The person who is a doctor is the person with a high school diploma.
3. The Dane is Eric.
4. The person who is a doctor is the person whose birthday is in April.
5. The British person is in the first house.
6. The person who uses a Samsung Galaxy S21 is the person whose birthday is in September.
 What is the value of attribute Birthday for the person whose attribute Education is associate? Please reason step by step, and put your final answer within \boxed{}

Answer: sept


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Peter`, `Alice`, `Eric`
 - Each person has a unique birthday month: `sept`, `april`, `feb`, `jan`, `mar`
 - They all have a unique favorite flower: `daffodils`, `lilies`, `tulips`, `carnations`, `roses`

## Clues:
1. The person who loves the vase of tulips is somewhere to the left of the person whose birthday is in January.
2. The person whose birthday is in March and Alice are next to each other.
3. The person whose birthday is in April is Bob.
4. The person whose birthday is in January is not in the fourth house.
5. The person who loves the vase of tulips is not in the first house.
6. The person whose birthday is in February is in the fifth house.
7. The person who loves a carnations arrangement is not in the third house.
8. The person whose birthday is in September is somewhere to the right of Peter.
9. The person who loves the boquet of lilies is the person whose birthday is in February.
10. Eric is not in the third house.
11. The person who loves the rose bouquet is directly left of Alice.
 What is the value of attribute Birthday for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: mar


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Alice`, `Bob`, `Peter`, `Eric`
 - People have unique hair colors: `blonde`, `black`, `gray`, `brown`, `red`
 - They all have a unique favorite flower: `tulips`, `carnations`, `daffodils`, `lilies`, `roses`
 - Each person has a favorite color: `white`, `red`, `green`, `blue`, `yellow`

## Clues:
1. The person who loves the rose bouquet and the person who loves yellow are next to each other.
2. The person who loves a carnations arrangement is Peter.
3. The person who loves the rose bouquet is not in the third house.
4. The person whose favorite color is green is not in the fifth house.
5. The person who loves a bouquet of daffodils is Alice.
6. The person who loves yellow is Eric.
7. The person who has blonde hair is in the fifth house.
8. The person who has black hair is directly left of Arnold.
9. The person who loves yellow is the person who has brown hair.
10. Alice is the person whose favorite color is green.
11. The person who has red hair is the person who loves blue.
12. The person whose favorite color is red is somewhere to the right of the person who loves blue.
13. The person who has black hair is the person who loves the vase of tulips.
 What is the value of attribute Flower for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}

Answer: tulips


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Alice`, `Eric`
 - Each person has a favorite color: `yellow`, `red`, `white`, `green`
 - Everyone has a unique favorite cigar: `dunhill`, `blue master`, `pall mall`, `prince`
 - Each person has a unique level of education: `high school`, `associate`, `master`, `bachelor`

## Clues:
1. The person whose favorite color is green is somewhere to the left of the person with a high school diploma.
2. Eric is the person whose favorite color is red.
3. There are two houses between Alice and the person who loves white.
4. The person who smokes Blue Master and the person partial to Pall Mall are next to each other.
5. The person who loves white is the person with a master's degree.
6. Arnold is in the fourth house.
7. The person who loves yellow is the person who smokes Blue Master.
8. The Dunhill smoker is Alice.
9. The person partial to Pall Mall is the person with a master's degree.
10. The person who loves yellow is the person with a bachelor's degree.
 What is the value of attribute Cigar for the person whose attribute Education is high school? Please reason step by step, and put your final answer within \boxed{}

Answer: prince


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Alice`
 - People have unique favorite sports: `basketball`, `swimming`, `soccer`, `tennis`
 - People have unique hair colors: `black`, `brown`, `blonde`, `red`
 - Each person has a favorite color: `yellow`, `red`, `white`, `green`
 - The people are of nationalities: `dane`, `norwegian`, `brit`, `swede`
 - Each person has a unique birthday month: `april`, `feb`, `jan`, `sept`

## Clues:
1. The person who has brown hair is in the first house.
2. The person who loves soccer is directly left of the person who loves tennis.
3. The person who has brown hair is directly left of Eric.
4. The person who has blonde hair is somewhere to the left of the British person.
5. The person who loves white is directly left of the Norwegian.
6. The person who has blonde hair and Arnold are next to each other.
7. The person whose birthday is in January is the Swedish person.
8. The person whose birthday is in April is the British person.
9. The person who loves basketball is somewhere to the right of the person who has black hair.
10. The person who has brown hair and the person who loves yellow are next to each other.
11. The person who loves swimming is Peter.
12. The person whose favorite color is red is Peter.
13. The person who has blonde hair is the Swedish person.
14. Eric is the person whose birthday is in February.
 What is the value of attribute 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: `Alice`, `Arnold`, `Carol`, `Peter`, `Bob`, `Eric`
 - People use unique phone models: `huawei p50`, `samsung galaxy s21`, `iphone 13`, `xiaomi mi 11`, `google pixel 6`, `oneplus 9`
 - Each person has a unique hobby: `photography`, `painting`, `gardening`, `woodworking`, `cooking`, `knitting`

## Clues:
1. The woodworking hobbyist is somewhere to the left of Bob.
2. The person who paints as a hobby is in the fifth house.
3. Arnold is directly left of the person who uses a Google Pixel 6.
4. The person who uses a Samsung Galaxy S21 is Arnold.
5. Carol is somewhere to the right of the person who uses a Samsung Galaxy S21.
6. The person who uses a Google Pixel 6 is directly left of the person who uses a OnePlus 9.
7. The person who uses a OnePlus 9 is somewhere to the right of Eric.
8. There are two houses between the person who loves cooking and Peter.
9. The person who enjoys knitting is Eric.
10. Peter is the person who paints as a hobby.
11. The person who enjoys gardening is somewhere to the right of Bob.
12. There is one house between Bob and the person who uses a Huawei P50.
13. The person who uses a Xiaomi Mi 11 is not in the first house.
14. Alice is in the sixth house.
 What is the value of attribute PhoneModel for the person whose attribute House is 5? Please reason step by step, and put your final answer within \boxed{}

Answer: xiaomi mi 11


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

## Clues:
1. Alice is the person who loves swimming.
2. The person's child is named Alice is directly left of the person who loves historical fiction books.
3. The person who loves the stew is the person who loves historical fiction books.
4. The person with a doctorate is the person who loves the soup.
5. The person who loves science fiction books is in the sixth house.
6. The person who attended trade school is directly left of the person who loves historical fiction books.
7. The person who loves baseball and the person's child is named Bella are next to each other.
8. The person with a master's degree is somewhere to the left of the person who loves mystery books.
9. The person who loves soccer is somewhere to the left of the person who loves fantasy books.
10. The person who loves stir fry is the person with an associate's degree.
11. The person who is a pizza lover is Peter.
12. Bob is not in the sixth house.
13. The person's child is named Meredith is directly left of the person who loves fantasy books.
14. The person's child is named Samantha is Eric.
15. There is one house between the person who loves eating grilled cheese and Bob.
16. The person who loves eating grilled cheese is the person's child is named Samantha.
17. The person who loves volleyball is the person's child is named Samantha.
18. The person's child is named Fred is somewhere to the left of the person's child is named Samantha.
19. Bob is the person who loves tennis.
20. The person who loves soccer is directly left of Carol.
21. The person who loves eating grilled cheese is somewhere to the left of the person who loves mystery books.
22. The person's child is named Meredith is the person who loves biography books.
23. The person's child is named Meredith is the person who loves the soup.
24. Carol is the person with a high school diploma.
 What is the value of attribute BookGenre for the person whose attribute Food is grilled cheese? 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: `Arnold`, `Eric`, `Peter`, `Alice`
 - Each person has a unique level of education: `master`, `high school`, `associate`, `bachelor`
 - Everyone has something unique for lunch: `stew`, `grilled cheese`, `pizza`, `spaghetti`
 - People have unique favorite sports: `soccer`, `swimming`, `tennis`, `basketball`
 - People have unique hair colors: `blonde`, `black`, `brown`, `red`
 - People have unique favorite book genres: `mystery`, `fantasy`, `science fiction`, `romance`

## Clues:
1. The person who loves the stew is in the first house.
2. The person who loves science fiction books is the person who has black hair.
3. The person who has blonde hair is not in the second house.
4. The person with a master's degree is in the first house.
5. Eric is the person who loves soccer.
6. The person with a master's degree and the person who loves mystery books are next to each other.
7. The person who loves tennis is the person with a high school diploma.
8. The person who loves the spaghetti eater is the person who loves science fiction books.
9. The person who is a pizza lover is the person with an associate's degree.
10. The person who has blonde hair is not in the fourth house.
11. The person with a master's degree is directly left of Eric.
12. The person with a bachelor's degree is directly left of the person who loves fantasy books.
13. The person who has red hair is Peter.
14. The person who loves swimming is directly left of the person who is a pizza lover.
15. Alice is not in the first house.
 What is the value of attribute House for the person whose attribute Education is master? 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: `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 House for the person whose attribute HouseStyle is mediterranean? Please reason step by step, and put your final answer within \boxed{}

Answer: 6


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Peter`, `Eric`
 - Each person prefers a unique type of vacation: `cruise`, `mountain`, `city`, `beach`
 - Each person has a unique favorite drink: `tea`, `coffee`, `milk`, `water`
 - The people are of nationalities: `brit`, `swede`, `dane`, `norwegian`

## Clues:
1. The person who prefers city breaks is the Swedish person.
2. The person who likes going on cruises is directly left of the person who loves beach vacations.
3. Arnold is in the second house.
4. Arnold is the person who likes milk.
5. The person who prefers city breaks is not in the fourth house.
6. The coffee drinker is the Norwegian.
7. The person who loves beach vacations and Peter are next to each other.
8. Eric is the one who only drinks water.
9. The person who loves beach vacations is directly left of the Dane.
 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: 3


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`
 - Each mother is accompanied by their child: `Meredith`, `Fred`, `Bella`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`
 - Each person prefers a unique type of vacation: `mountain`, `city`, `beach`
 - Each person has a favorite color: `white`, `red`, `yellow`

## Clues:
1. There is one house between the person's child is named Bella and the person's child is named Meredith.
2. The person who likes Cherry smoothies is the person who loves beach vacations.
3. The person who prefers city breaks is Arnold.
4. The person whose favorite color is red is the person's child is named Fred.
5. The person's child is named Fred is the Watermelon smoothie lover.
6. Eric is not in the first house.
7. The person's child is named Meredith is the person who loves white.
8. The person who loves white is the Desert smoothie lover.
9. The Desert smoothie lover is Eric.
 What is the value of attribute Name for the person whose attribute Children is Bella? 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: `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 BookGenre for the person whose attribute Mother is Janelle? Please reason step by step, and put your final answer within \boxed{}

Answer: romance


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`, `Peter`, `Eric`, `Arnold`
 - People have unique favorite sports: `swimming`, `basketball`, `soccer`, `tennis`, `baseball`
 - Each mother is accompanied by their child: `Meredith`, `Bella`, `Fred`, `Samantha`, `Timothy`
 - Each person has a unique birthday month: `april`, `feb`, `sept`, `jan`, `mar`

## Clues:
1. The person who loves soccer is the person's child is named Fred.
2. The person whose birthday is in April is somewhere to the left of the person who loves soccer.
3. The person whose birthday is in January is Peter.
4. The person who loves baseball is the person whose birthday is in September.
5. The person who is the mother of Timothy is the person who loves baseball.
6. There are two houses between the person whose birthday is in February and Peter.
7. Eric is directly left of the person who loves basketball.
8. Eric is the person who loves tennis.
9. The person's child is named Meredith is directly left of Peter.
10. Alice is directly left of the person whose birthday is in September.
11. The person's child is named Bella is somewhere to the left of the person's child is named Samantha.
12. Eric is in the third house.
13. The person who loves soccer is Arnold.
 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 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`
 - The people keep unique animals: `fish`, `dog`, `horse`, `bird`, `cat`
 - People own unique car models: `honda civic`, `bmw 3 series`, `ford f150`, `toyota camry`, `tesla model 3`
 - Each person has a unique favorite drink: `coffee`, `tea`, `root beer`, `milk`, `water`

## Clues:
1. Arnold is not in the fifth house.
2. Alice and Bob are next to each other.
3. The person who owns a Tesla Model 3 is the person who keeps horses.
4. There are two houses between Arnold and the root beer lover.
5. Eric is in the second house.
6. The person who likes milk is the dog owner.
7. Arnold is the person who owns a Tesla Model 3.
8. The bird keeper is the person who owns a Honda Civic.
9. The one who only drinks water and the person who owns a Toyota Camry are next to each other.
10. The one who only drinks water is directly left of the cat lover.
11. There is one house between the person who owns a Ford F-150 and the fish enthusiast.
12. The dog owner is not in the fifth house.
13. The tea drinker is Bob.
 What is the value of attribute Drink for the person whose attribute Animal is horse? Please reason step by step, and put your final answer within \boxed{}

Answer: water


We mean a traingle in $\mathbb Q^{n}$, 3 points that are not collinear in $\mathbb Q^{n}$

a) Suppose that $ABC$ is triangle in $\mathbb Q^{n}$. Prove that there is a triangle $A'B'C'$ in $\mathbb Q^{5}$ that $\angle B'A'C'=\angle BAC$.
b) Find a natural $m$ that for each traingle that can be embedded in $\mathbb Q^{n}$ it can be embedded in $\mathbb Q^{m}$.
c) Find a triangle that can be embedded in $\mathbb Q^{n}$ and no triangle similar to it can be embedded in $\mathbb Q^{3}$.
d) Find a natural $m'$ that for each traingle that can be embedded in $\mathbb Q^{n}$ then there is a triangle similar to it, that can be embedded in $\mathbb Q^{m}$.
You must prove the problem for $m=9$ and $m'=6$ to get complete mark. (Better results leads to additional mark.)

Answer: 5


2. A regular tetrahedral box with an edge length of 6 contains a smaller regular tetrahedron. If the smaller tetrahedron can rotate freely within the box, then the maximum edge length of the smaller tetrahedron is $\qquad$ .

Answer: 2