There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Bob`, `Carol`, `Arnold`, `Peter`, `Alice`
 - Everyone has a unique favorite cigar: `blends`, `prince`, `dunhill`, `yellow monster`, `blue master`, `pall mall`
 - People have unique hair colors: `auburn`, `gray`, `blonde`, `black`, `red`, `brown`
 - Each person has a unique favorite drink: `boba tea`, `root beer`, `water`, `tea`, `coffee`, `milk`
 - Each person has an occupation: `artist`, `nurse`, `teacher`, `doctor`, `engineer`, `lawyer`

## Clues:
1. Bob is the tea drinker.
2. The Dunhill smoker is not in the second house.
3. There is one house between Carol and Arnold.
4. The Prince smoker is the person who has black hair.
5. The person who has auburn hair is not in the third house.
6. Arnold is in the fourth house.
7. The Prince smoker is not in the fourth house.
8. The person who is an artist is the person partial to Pall Mall.
9. The person who is an engineer is directly left of the root beer lover.
10. The boba tea drinker is the person who has brown hair.
11. The person who is a lawyer is in the fifth house.
12. The person who is an engineer is the person who smokes Blue Master.
13. The person who likes milk is the person who has auburn hair.
14. Alice is somewhere to the left of the person who is a teacher.
15. The person who has blonde hair is the person who smokes Yellow Monster.
16. The person who has black hair is the person who is a doctor.
17. Arnold is somewhere to the right of the person who has gray hair.
18. The person who has auburn hair is not in the first house.
19. The one who only drinks water is the person who smokes many unique blends.
20. The person who smokes many unique blends is somewhere to the right of the person who has brown hair.
21. Arnold is the root beer lover.
22. The person who has brown hair is not in the third house.
23. The person who smokes many unique blends is somewhere to the left of Peter.
24. The person who likes milk is somewhere to the left of the person who has blonde hair.
 What is the value of attribute Drink for the person whose attribute HairColor is red? Please reason step by step, and put your final answer within \boxed{}

Answer: water


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`, `Carol`, `Bob`, `Eric`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`, `cruise`, `camping`, `cultural`
 - Everyone has a unique favorite cigar: `yellow monster`, `pall mall`, `prince`, `dunhill`, `blue master`, `blends`
 - People have unique favorite sports: `swimming`, `soccer`, `tennis`, `basketball`, `volleyball`, `baseball`

## Clues:
1. Arnold is the person who prefers city breaks.
2. There is one house between the person who loves volleyball and the person who loves swimming.
3. Alice is in the fourth house.
4. The person who likes going on cruises is the person who smokes many unique blends.
5. The person who enjoys camping trips is somewhere to the left of Eric.
6. The person who loves volleyball is the person who smokes many unique blends.
7. Arnold is the Prince smoker.
8. The person who loves baseball is Peter.
9. The Prince smoker and the person partial to Pall Mall are next to each other.
10. The person who loves beach vacations is in the sixth house.
11. Carol is the person who loves beach vacations.
12. Carol is the person who smokes Yellow Monster.
13. The person who loves tennis is somewhere to the right of the person who goes on cultural tours.
14. The person who goes on cultural tours is the person who smokes Blue Master.
15. The person who loves basketball is directly left of the person who smokes many unique blends.
16. The person who loves volleyball and Eric are next to each other.
17. The person who loves tennis is Arnold.
 What is the value of attribute Cigar for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: yellow monster


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`
 - Everyone has a unique favorite cigar: `pall mall`, `blue master`, `prince`
 - The people keep unique animals: `horse`, `cat`, `bird`
 - Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`
 - People have unique favorite book genres: `science fiction`, `romance`, `mystery`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `samsung galaxy s21`

## Clues:
1. The person who loves mystery books is the person's child is named Fred.
2. The cat lover is Eric.
3. The person partial to Pall Mall is in the second house.
4. The person who keeps horses is the person's child is named Meredith.
5. The person's child is named Bella is the Prince smoker.
6. The person who uses an iPhone 13 is directly left of the person who uses a Samsung Galaxy S21.
7. The person's child is named Fred is directly left of Arnold.
8. Peter is somewhere to the left of Eric.
9. The person who loves science fiction books is the person who uses a Samsung Galaxy S21.
10. The person who loves science fiction books is in the third house.
11. The person who loves mystery books is not in the second house.
 What is the value of attribute BookGenre for the person whose attribute PhoneModel is samsung galaxy s21? Please reason step by step, and put your final answer within \boxed{}

Answer: science fiction


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`
 - Each person has a unique hobby: `gardening`, `cooking`, `photography`
 - People have unique favorite sports: `tennis`, `soccer`, `basketball`
 - They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`
 - Everyone has a favorite smoothie: `desert`, `cherry`, `watermelon`

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

Answer: photography


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Carol`, `Alice`, `Bob`, `Eric`
 - Each person has a unique level of education: `bachelor`, `high school`, `doctorate`, `trade school`, `associate`, `master`
 - Each person has an occupation: `teacher`, `artist`, `nurse`, `lawyer`, `engineer`, `doctor`
 - People own unique car models: `ford f150`, `toyota camry`, `honda civic`, `chevrolet silverado`, `bmw 3 series`, `tesla model 3`
 - Each person has a unique birthday month: `sept`, `jan`, `mar`, `april`, `feb`, `may`

## Clues:
1. The person with a bachelor's degree is somewhere to the right of the person who owns a Toyota Camry.
2. The person whose birthday is in February is the person with an associate's degree.
3. The person whose birthday is in September is not in the fifth house.
4. The person who owns a BMW 3 Series is somewhere to the right of the person who is an engineer.
5. The person whose birthday is in January is Arnold.
6. The person who is an artist is directly left of the person with a doctorate.
7. The person who owns a Ford F-150 is the person who is an engineer.
8. The person who attended trade school and Eric are next to each other.
9. There is one house between the person who attended trade school and the person with a bachelor's degree.
10. The person whose birthday is in May is the person who owns a BMW 3 Series.
11. The person who owns a Chevrolet Silverado is somewhere to the left of Alice.
12. The person who is an engineer is directly left of Bob.
13. The person who owns a Honda Civic is the person whose birthday is in April.
14. The person who is an artist is the person with a high school diploma.
15. Arnold is the person who owns a Toyota Camry.
16. The person who owns a Tesla Model 3 is in the first house.
17. The person who is a doctor is somewhere to the left of the person whose birthday is in April.
18. The person who is a nurse is directly left of the person whose birthday is in September.
19. The person who is a teacher is the person with a doctorate.
20. There is one house between the person who owns a Toyota Camry and the person who owns a Honda Civic.
21. The person who owns a Tesla Model 3 is Peter.
 What is the value of attribute Occupation for the person whose attribute CarModel is toyota camry? Please reason step by step, and put your final answer within \boxed{}

Answer: nurse


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

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

Answer: horse


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Eric`, `Arnold`, `Carol`, `Bob`
 - People have unique heights: `very short`, `very tall`, `short`, `super tall`, `tall`, `average`
 - Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `soup`, `stew`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Penny`, `Aniya`, `Kailyn`, `Sarah`
 - Each person has a unique favorite drink: `tea`, `water`, `milk`, `coffee`, `boba tea`, `root beer`
 - Each person has a unique type of pet: `rabbit`, `fish`, `bird`, `hamster`, `cat`, `dog`

## Clues:
1. Arnold is the person who loves the stew.
2. The person who owns a dog is directly left of the person who has a cat.
3. The person whose mother's name is Holly is in the sixth house.
4. The tea drinker is somewhere to the left of the boba tea drinker.
5. The tea drinker is in the second house.
6. The person who is very tall is Bob.
7. The person who has a cat is The person whose mother's name is Penny.
8. The person who is very short is directly left of Alice.
9. Carol is the person who is a pizza lover.
10. The person who has an average height is not in the sixth house.
11. The person who loves stir fry is Bob.
12. The person with a pet hamster is not in the third house.
13. The person whose mother's name is Janelle is somewhere to the left of the person with a pet hamster.
14. Eric is the person who loves the soup.
15. The person whose mother's name is Kailyn is directly left of the person who keeps a pet bird.
16. The one who only drinks water is somewhere to the right of the person who likes milk.
17. The person who owns a rabbit is the person who loves the stew.
18. The person who is tall is The person whose mother's name is Aniya.
19. The person who is very short is somewhere to the left of the person who likes milk.
20. The person who is tall is not in the fifth house.
21. The person who is very short is in the second house.
22. The person who loves the stew is the root beer lover.
23. The person whose mother's name is Kailyn is the boba tea drinker.
24. The person who is tall is not in the fourth house.
25. The person who is super tall is directly left of the person who loves eating grilled cheese.
26. Carol is directly left of the root beer lover.
 What is the value of attribute House for the person whose attribute Food is soup? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


5. Find all real numbers $x$ and $y$ that satisfy the equation

$$
(x+y)^{2}=(x+3)(y-3)
$$

Solve the problem independently. You have 150 minutes for solving.

The use of notes, literature, or a pocket calculator is not allowed.

Mathematical Competition for High School Students in Slovenia

## Invitational Competition

March 28, 2003

## Problems for 4th Year

Answer: (-3, 3)


11. For every integer $n$, let $S(n)$ be the sum of the digits of $n$ (in base 10). What is the smallest integer $N$ for which $S(S(N)) \geq 10$?

Answer: 199


Suppose that $n$ is a positive integer and that the set $S$ contains exactly $n$ distinct positive integers. If the mean of the elements of $S$ is equal to $\frac{2}{5}$ of the largest element of $S$ and is also equal to $\frac{7}{4}$ of the smallest element of $S$, determine the minimum possible value of $n$.

Answer: 5


Example 3. Let the function $\mathrm{f}(\mathrm{x})$ have the properties:
i) It is defined for all $x$ except $x=0$ and $x=1$;
ii) $f(x)+f\left(\frac{x-1}{x}\right)=1+x$.

Try to find the analytical expression of the function $\mathrm{f}(\mathrm{x})$.

Answer: \dfrac{x^3 - x^2 - 1}{2x(x - 1)}


Example 3 If $a_{1}=1, a_{k}=k+a_{k-1}(2 \leqslant k \leqslant$ $n)$, then $a_{1}, a_{2}, \cdots, a_{n}$ is called a regular number. Question: How many numbers in the set $\{1,2, \cdots, 2001\}$ are either a regular number itself or the sum of several different regular numbers?

Answer: 1995


XXXVI OM - II - Problem 3

Let $ L $ be the set of all broken lines $ ABCDA $, where $ A, B, C, D $ are distinct vertices of a fixed regular 1985-gon. A broken line is randomly chosen from the set $ L $. Calculate the probability that it is the boundary of a convex quadrilateral.

Answer: \dfrac{1}{3}


We divide a solid cube with an edge length of \( n \) cm into 1 cm edge length cubes (\( n \) is a natural number). For which values of \( n \) is it possible to assemble a cube with an edge length of \( 2n \) cm from the obtained smaller cubes, if it is allowed to have a hollow interior in the assembled cube?

Answer: n \geq 23


Answer: -\dfrac{17}{19}


Given a grid strip (one cell wide), infinite in both directions. Two cells of the strip are traps, with $-N$ cells between them, one of which is occupied by a grasshopper. On each move, we call out a natural number, after which the grasshopper jumps that number of cells to the left or right (at its choice). For which $N$ can we call out numbers such that we can guarantee to drive the grasshopper into one of the traps, no matter where it initially is between the traps and how it chooses the directions of its jumps? (We always see where the grasshopper is sitting.)

Answer: N = 2^k - 1


Example. Solve the system of equations

$$
\left\{\begin{array}{r}
x_{1}+2 x_{2}+x_{3}=4 \\
3 x_{1}-5 x_{2}+3 x_{3}=1 \\
2 x_{1}+7 x_{2}-x_{3}=8
\end{array}\right.
$$

using Cramer's rule.

Answer: 1


5. On each of five cards, a number is written. The cards lie on the table numbers down. We can, by paying a ruble, point to any three cards, and we will be told the sum of the numbers written on them. For what minimum price can we surely find out the sum of all five numbers? (I. Rubanov)

Answer: 4


## Task B-2.6.

Rectangle $A B C D$, in which $|A B|>|A D|$, rotates around vertex $D$ to form rectangle $E F G D$ such that vertex $A$ maps to point $E$ on the diagonal $\overline{B D}$. The intersection of sides $\overline{D C}$ and $\overline{E F}$ is point $H$. The area of rectangle $A B C D$ is in the ratio 5 : 2 to the area of quadrilateral $B C H E$. If $\varphi=\varangle A D B$, calculate $\frac{\sin ^{2} \varphi+1}{\cos ^{2} \varphi+1}$.

Answer: \dfrac{11}{7}


Problem 4. A rectangular sheet of paper was folded, aligning a vertex with the midpoint of the opposite shorter side (Fig. 12). It turned out that triangles I and II are equal. Find the longer side of the rectangle if the shorter side is 8.

[6 points] (A. V. Khachatryan)

Answer: 12


4. Integers $a, b, c$ satisfy $a+b+c=2$, and
$$
S=(2 a+b c)(2 b+c a)(2 c+a b)>200 \text {. }
$$

Then the minimum value of $S$ is $\qquad$.

Answer: 256


7.3. On a board, all natural numbers $1,2,3, \ldots, 15$ are written. Determine the minimum number of numbers that can be erased from the board so that with the remaining numbers we can form two non-empty sets of numbers that simultaneously satisfy the following properties:

a) they have no common elements;

b) they have the same number of elements;

c) the product of the elements of the two sets is the same.

Answer: 3


Let $x,$ $y,$ and $z$ be positive real numbers such that
\[\frac{1}{x^4} + \frac{1}{y^4} + \frac{1}{z^4} = 1.\]Find the minimum value of
\[\frac{x^4 y^4 + x^4 z^4 + y^4 z^4}{x^3 y^2 z^3}.\]The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Answer: 4


The real number $x$ satisfies
\[3x + \frac{1}{2x} = 3.\]Find
\[64x^6 + \frac{1}{729x^6}.\]The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Answer: 443


$ABCDE$ is inscribed in a circle with $AB = BC = CD = DE = 4$ and $AE = 1.$  Compute $(1 - \cos \angle B)(1 - \cos \angle ACE).$The answer is in the form rac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Answer: 65


Exercise 11. In a classroom, there are ten students. Aline writes ten consecutive integers on the board. Each student chooses one of the ten integers written on the board, such that any two students always choose two different integers. Each student then calculates the sum of the nine integers chosen by the other nine students. Each student whose result is a perfect square then receives a gift.

What is the maximum number of students who will receive a gift?

A perfect square is an integer of the form $n^{2}$, where $n$ is a natural number.

Answer: 4


2. Find the ordered integer pairs $(x, y)$ that satisfy $(|x|-2)^{2}+(|y|-2)^{2}<5$.

 untranslated text remains unchanged.

Answer: 48


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Arnold`, `Bob`, `Eric`, `Carol`
 - Each person has a unique hobby: `cooking`, `gardening`, `painting`, `knitting`, `photography`, `woodworking`
 - Each person has a unique birthday month: `april`, `sept`, `mar`, `jan`, `feb`, `may`
 - Everyone has a unique favorite cigar: `blends`, `prince`, `pall mall`, `dunhill`, `yellow monster`, `blue master`

## Clues:
1. The person whose birthday is in April is Eric.
2. Arnold is in the first house.
3. The person whose birthday is in January is the person who smokes many unique blends.
4. The Dunhill smoker is Alice.
5. Bob is the person whose birthday is in May.
6. The person whose birthday is in September and the photography enthusiast are next to each other.
7. Bob is the person who smokes Blue Master.
8. The person who loves cooking is the person whose birthday is in May.
9. The woodworking hobbyist and the person whose birthday is in March are next to each other.
10. The person who enjoys knitting is directly left of the person who smokes Yellow Monster.
11. Peter and the person who paints as a hobby are next to each other.
12. The person whose birthday is in March is somewhere to the left of the Prince smoker.
13. The person whose birthday is in February is somewhere to the left of the person who smokes many unique blends.
14. The person whose birthday is in March is somewhere to the right of the person whose birthday is in September.
15. The person who smokes many unique blends is directly left of the person whose birthday is in May.
16. The photography enthusiast and Peter are next to each other.
 What is the value of attribute House for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `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 FavoriteSport for the person whose attribute House is 6? Please reason step by step, and put your final answer within \boxed{}

Answer: soccer


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Arnold`, `Carol`, `Bob`, `Peter`
 - Each person has a unique level of education: `master`, `bachelor`, `high school`, `doctorate`, `associate`, `trade school`
 - People use unique phone models: `huawei p50`, `google pixel 6`, `oneplus 9`, `xiaomi mi 11`, `iphone 13`, `samsung galaxy s21`

## Clues:
1. The person with a bachelor's degree is somewhere to the left of the person with a master's degree.
2. The person with an associate's degree is the person who uses a Samsung Galaxy S21.
3. The person who uses a Google Pixel 6 is Alice.
4. The person who uses a Xiaomi Mi 11 is the person with a bachelor's degree.
5. The person who uses a Huawei P50 is in the third house.
6. There is one house between Arnold and Bob.
7. Arnold is in the second house.
8. Peter is somewhere to the left of the person who uses a Huawei P50.
9. There is one house between the person who uses an iPhone 13 and Eric.
10. The person with a doctorate is directly left of the person with an associate's degree.
11. The person with a master's degree is the person who uses a Huawei P50.
12. The person with a high school diploma is Arnold.
 What is the value of attribute Education for the person whose attribute PhoneModel is huawei p50? Please reason step by step, and put your final answer within \boxed{}

Answer: master


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Peter`, `Eric`, `Carol`, `Alice`
 - They all have a unique favorite flower: `lilies`, `daffodils`, `carnations`, `tulips`, `iris`, `roses`

## Clues:
1. Alice and Bob are next to each other.
2. Carol is not in the first house.
3. There are two houses between Peter and the person who loves the rose bouquet.
4. The person who loves a bouquet of daffodils is somewhere to the left of the person who loves the vase of tulips.
5. The person who loves the boquet of iris is not in the second house.
6. The person who loves the rose bouquet is somewhere to the right of Arnold.
7. The person who loves a bouquet of daffodils is somewhere to the right of the person who loves a carnations arrangement.
8. Arnold is somewhere to the left of Eric.
9. Carol and the person who loves a carnations arrangement are next to each other.
10. Arnold is somewhere to the right of the person who loves the boquet of iris.
11. The person who loves a carnations arrangement is directly left of Alice.
 What is the value of attribute Flower for the person whose attribute House is 6? Please reason step by step, and put your final answer within \boxed{}

Answer: tulips


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 person lives in a unique style of house: `victorian`, `ranch`, `colonial`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `lilies`
 - People have unique favorite book genres: `romance`, `mystery`, `science fiction`
 - People own unique car models: `ford f150`, `toyota camry`, `tesla model 3`
 - Each person has a unique level of education: `associate`, `high school`, `bachelor`

## Clues:
1. The person who loves science fiction books is in the second house.
2. The person with a high school diploma is the person residing in a Victorian house.
3. The person who loves a bouquet of daffodils is in the second house.
4. The person with an associate's degree is the person in a ranch-style home.
5. The person who owns a Tesla Model 3 is not in the third house.
6. The person who loves the boquet of lilies is the person residing in a Victorian house.
7. Arnold is the person in a ranch-style home.
8. The person who owns a Tesla Model 3 and Eric are next to each other.
9. The person who owns a Ford F-150 is the person who loves romance books.
10. The person who owns a Tesla Model 3 is the person residing in a Victorian house.
 What is the value of attribute Education for the person whose attribute Flower is lilies? Please reason step by step, and put your final answer within \boxed{}

Answer: high school


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`, `Alice`
 - Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `pizza`, `stew`
 - People use unique phone models: `iphone 13`, `google pixel 6`, `samsung galaxy s21`, `oneplus 9`
 - Each person has a unique hobby: `painting`, `cooking`, `photography`, `gardening`

## Clues:
1. Peter is the person who is a pizza lover.
2. The person who is a pizza lover and the person who loves the spaghetti eater are next to each other.
3. The person who loves eating grilled cheese is directly left of Eric.
4. Eric is the person who loves cooking.
5. The person who uses a Google Pixel 6 is in the fourth house.
6. The photography enthusiast is in the second house.
7. The person who is a pizza lover is the person who uses a OnePlus 9.
8. The person who uses a Samsung Galaxy S21 is in the third house.
9. Arnold is directly left of the person who enjoys gardening.
 What is the value of attribute House for the person whose attribute PhoneModel is iphone 13? Please reason step by step, and put your final answer within \boxed{}

Answer: 2


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

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

Answer: stew


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

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

Answer: pizza


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`, `Carol`, `Eric`, `Alice`, `Bob`, `Arnold`
 - People use unique phone models: `huawei p50`, `google pixel 6`, `xiaomi mi 11`, `iphone 13`, `samsung galaxy s21`, `oneplus 9`
 - Everyone has a unique favorite cigar: `dunhill`, `pall mall`, `blends`, `blue master`, `prince`, `yellow monster`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `roses`, `tulips`, `lilies`, `iris`
 - Each person has a favorite color: `yellow`, `red`, `green`, `blue`, `white`, `purple`
 - People have unique favorite sports: `soccer`, `tennis`, `basketball`, `volleyball`, `swimming`, `baseball`

## Clues:
1. The person who uses a OnePlus 9 is in the second house.
2. The person who uses a Xiaomi Mi 11 is somewhere to the left of the person who uses a Huawei P50.
3. Carol is the person who loves a carnations arrangement.
4. The person who loves purple is directly left of the person partial to Pall Mall.
5. The person whose favorite color is green is the person who smokes Blue Master.
6. The person who loves yellow and the person who loves blue are next to each other.
7. Eric is somewhere to the right of the person who uses a Samsung Galaxy S21.
8. There are two houses between Carol and the person who loves a bouquet of daffodils.
9. The Prince smoker is the person who loves basketball.
10. The Dunhill smoker is the person who loves volleyball.
11. The person who loves swimming is the person who uses a Google Pixel 6.
12. The person who uses a Huawei P50 is directly left of the person who loves white.
13. The person who uses a OnePlus 9 and the person who loves the rose bouquet are next to each other.
14. The person who loves the boquet of iris is somewhere to the left of Eric.
15. The Dunhill smoker is Peter.
16. The person who loves blue is Peter.
17. The person who loves the vase of tulips is Bob.
18. Alice is in the first house.
19. The person who loves baseball is directly left of the person who smokes Blue Master.
20. The person who uses a Google Pixel 6 is somewhere to the right of the person who smokes many unique blends.
21. The person who loves soccer is Carol.
22. The person who loves a carnations arrangement is directly left of the person who smokes many unique blends.
23. Eric is the person who smokes many unique blends.
24. The person who loves volleyball is the person who uses an iPhone 13.
 What is the value of attribute PhoneModel for the person whose attribute Flower is carnations? Please reason step by step, and put your final answer within \boxed{}

Answer: oneplus 9


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`
 - Each person has a unique type of pet: `hamster`, `bird`, `fish`, `cat`, `dog`
 - Each person has an occupation: `doctor`, `engineer`, `lawyer`, `artist`, `teacher`
 - Each person lives in a unique style of house: `colonial`, `modern`, `ranch`, `craftsman`, `victorian`
 - Each person has a unique level of education: `high school`, `bachelor`, `master`, `doctorate`, `associate`

## Clues:
1. There are two houses between the person with a master's degree and the person in a modern-style house.
2. The person with an aquarium of fish is the person who is an artist.
3. The person who has a cat is the person who is an engineer.
4. The person with a bachelor's degree is the person with an aquarium of fish.
5. The person who has a cat is somewhere to the right of the person with an associate's degree.
6. The person with a master's degree is the person who is a lawyer.
7. The person who is a teacher is somewhere to the right of the person who keeps a pet bird.
8. The person with an associate's degree is the person living in a colonial-style house.
9. Peter is the person in a Craftsman-style house.
10. The person residing in a Victorian house is in the second house.
11. The person who is a teacher is Bob.
12. The person with an associate's degree is in the fourth house.
13. The person with a bachelor's degree is somewhere to the right of the person with a high school diploma.
14. There is one house between the person who owns a dog and the person in a ranch-style home.
15. Bob is somewhere to the right of Alice.
16. Eric is the person with a bachelor's degree.
 What is the value of attribute Name for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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

## Clues:
1. The person who loves cooking is in the second house.
2. The fish enthusiast is not in the first house.
3. Alice is in the second house.
4. The cat lover is the person residing in a Victorian house.
5. The person who enjoys gardening is the person residing in a Victorian house.
6. The person in a ranch-style home is not in the first house.
7. The person who keeps horses is somewhere to the right of the person residing in a Victorian house.
8. Peter is somewhere to the left of the person who paints as a hobby.
9. The person in a Craftsman-style house is Eric.
10. The person residing in a Victorian house is in the third house.
11. Peter is directly left of the person living in a colonial-style house.
 What is the value of attribute House for the person whose attribute Animal is cat? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`, `Bob`
 - Everyone has something unique for lunch: `stir fry`, `spaghetti`, `stew`, `grilled cheese`, `pizza`
 - People own unique car models: `ford f150`, `tesla model 3`, `bmw 3 series`, `toyota camry`, `honda civic`
 - People use unique phone models: `iphone 13`, `google pixel 6`, `samsung galaxy s21`, `oneplus 9`, `huawei p50`
 - Each person has an occupation: `teacher`, `lawyer`, `doctor`, `artist`, `engineer`
 - Each person has a unique favorite drink: `tea`, `milk`, `water`, `root beer`, `coffee`

## Clues:
1. The root beer lover is the person who owns a Honda Civic.
2. The person who likes milk is directly left of the person who loves eating grilled cheese.
3. Alice is the person who uses a Samsung Galaxy S21.
4. Alice is the person who loves stir fry.
5. The tea drinker is not in the fifth house.
6. The person who owns a BMW 3 Series is somewhere to the left of the tea drinker.
7. The person who is a doctor is Arnold.
8. The person who uses an iPhone 13 is the coffee drinker.
9. The person who is an engineer is the person who owns a BMW 3 Series.
10. The person who loves the stew is the person who uses an iPhone 13.
11. The person who is a doctor is directly left of the person who uses a OnePlus 9.
12. The person who owns a Honda Civic is directly left of the person who loves the spaghetti eater.
13. The person who uses a Google Pixel 6 is the tea drinker.
14. Alice is the person who is an artist.
15. There is one house between Alice and the person who owns a Ford F-150.
16. Arnold is the person who owns a Toyota Camry.
17. Eric is in the fourth house.
18. The person who uses a OnePlus 9 is the person who is a lawyer.
19. The person who loves eating grilled cheese is Peter.
 What is the value of attribute Name for the person whose attribute Occupation is teacher? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Carol`, `Eric`, `Peter`, `Bob`, `Arnold`
 - People have unique favorite music genres: `classical`, `hip hop`, `jazz`, `pop`, `rock`, `country`
 - The mothers' names in different houses are unique: `Sarah`, `Penny`, `Aniya`, `Janelle`, `Kailyn`, `Holly`
 - Each mother is accompanied by their child: `Alice`, `Fred`, `Timothy`, `Bella`, `Samantha`, `Meredith`
 - People have unique heights: `very short`, `tall`, `short`, `very tall`, `super tall`, `average`
 - The people keep unique animals: `bird`, `dog`, `horse`, `rabbit`, `cat`, `fish`

## Clues:
1. The person who loves pop music is the cat lover.
2. The rabbit owner is directly left of The person whose mother's name is Aniya.
3. The person whose mother's name is Holly is directly left of Carol.
4. The person whose mother's name is Holly is the person's child is named Alice.
5. The person whose mother's name is Holly is the person who loves classical music.
6. The person who loves jazz music is The person whose mother's name is Sarah.
7. The person's child is named Meredith is somewhere to the right of The person whose mother's name is Aniya.
8. The person who is super tall is The person whose mother's name is Holly.
9. The person who is the mother of Timothy is Bob.
10. The person who is very short is somewhere to the left of The person whose mother's name is Aniya.
11. Eric is the fish enthusiast.
12. The person's child is named Samantha is somewhere to the right of the person who is very tall.
13. The person who loves rock music is The person whose mother's name is Janelle.
14. There is one house between the person who keeps horses and the person's child is named Meredith.
15. The person's child is named Bella is somewhere to the right of Peter.
16. The fish enthusiast is somewhere to the left of the bird keeper.
17. The fish enthusiast is somewhere to the right of the person's child is named Alice.
18. There is one house between the person's child is named Bella and the person who loves rock music.
19. The person who is short is the cat lover.
20. Alice is directly left of the person who loves classical music.
21. The person's child is named Bella is The person whose mother's name is Aniya.
22. There are two houses between The person whose mother's name is Penny and the person who is short.
23. The person who loves hip-hop music is in the first house.
24. Carol is the person who is tall.
 What is the value of attribute Animal for the person whose attribute Height is super tall? Please reason step by step, and put your final answer within \boxed{}

Answer: rabbit


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`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`, `google pixel 6`
 - Each person has an occupation: `doctor`, `teacher`, `engineer`
 - Each person has a unique hobby: `photography`, `cooking`, `gardening`
 - The people keep unique animals: `bird`, `horse`, `cat`

## Clues:
1. The person who uses a Samsung Galaxy S21 is directly left of the person who is a teacher.
2. The person who uses a Samsung Galaxy S21 and Arnold are next to each other.
3. The person who is an engineer is the person who keeps horses.
4. The person who uses an iPhone 13 is the cat lover.
5. The bird keeper is the person who uses a Samsung Galaxy S21.
6. The person who loves cooking is not in the third house.
7. The person who enjoys gardening is directly left of the person who is a teacher.
8. There is one house between Eric and the person who uses an iPhone 13.
 What is the value of attribute PhoneModel for the person whose attribute Hobby is gardening? Please reason step by step, and put your final answer within \boxed{}

Answer: samsung galaxy s21


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Bob`, `Alice`, `Arnold`
 - People have unique heights: `very short`, `average`, `tall`, `short`, `very tall`
 - People own unique car models: `toyota camry`, `bmw 3 series`, `honda civic`, `ford f150`, `tesla model 3`
 - People use unique phone models: `iphone 13`, `oneplus 9`, `samsung galaxy s21`, `google pixel 6`, `huawei p50`

## Clues:
1. Arnold is in the fifth house.
2. The person who is short is the person who owns a Tesla Model 3.
3. The person who has an average height is somewhere to the right of Alice.
4. The person who owns a Honda Civic is not in the third house.
5. The person who owns a BMW 3 Series is directly left of Arnold.
6. The person who uses a OnePlus 9 is directly left of the person who owns a Ford F-150.
7. Alice is directly left of the person who is very short.
8. The person who uses an iPhone 13 is not in the second house.
9. The person who uses a Google Pixel 6 is Arnold.
10. The person who uses a Google Pixel 6 is the person who is tall.
11. Peter is the person who uses a Huawei P50.
12. Peter is directly left of the person who uses a OnePlus 9.
13. Bob is the person who owns a Tesla Model 3.
 What is the value of attribute Height for the person whose attribute CarModel is ford f150? Please reason step by step, and put your final answer within \boxed{}

Answer: tall


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Eric`, `Bob`, `Peter`, `Arnold`
 - People have unique favorite book genres: `fantasy`, `romance`, `mystery`, `science fiction`, `biography`
 - Each person has a unique level of education: `bachelor`, `master`, `high school`, `doctorate`, `associate`

## Clues:
1. The person who loves fantasy books is Alice.
2. Bob is directly left of the person with a bachelor's degree.
3. The person with a high school diploma is the person who loves science fiction books.
4. The person with an associate's degree is Bob.
5. The person who loves fantasy books is somewhere to the right of the person with a master's degree.
6. Arnold is the person with a high school diploma.
7. Eric is not in the second house.
8. The person who loves biography books is the person with a doctorate.
9. The person who loves science fiction books is in the third house.
10. The person who loves mystery books is not in the first house.
11. The person with a master's degree is somewhere to the left of the person with a doctorate.
 What is the value of attribute BookGenre for the person whose attribute Education is associate? Please reason step by step, and put your final answer within \boxed{}

Answer: mystery


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Bob`, `Carol`, `Peter`, `Eric`, `Alice`
 - People have unique favorite music genres: `classical`, `hip hop`, `jazz`, `pop`, `rock`, `country`
 - Everyone has something unique for lunch: `soup`, `stir fry`, `grilled cheese`, `spaghetti`, `stew`, `pizza`
 - Each person lives in a unique style of house: `craftsman`, `ranch`, `mediterranean`, `modern`, `colonial`, `victorian`
 - Each person has a unique birthday month: `feb`, `sept`, `april`, `may`, `jan`, `mar`
 - People have unique hair colors: `red`, `black`, `blonde`, `brown`, `gray`, `auburn`

## Clues:
1. The person whose birthday is in April is Bob.
2. The person residing in a Victorian house is the person who loves stir fry.
3. There are two houses between the person who loves jazz music and the person who has auburn hair.
4. The person who loves the stew is in the second house.
5. The person who loves stir fry is the person whose birthday is in February.
6. The person who loves classical music is in the fifth house.
7. The person who loves jazz music is Alice.
8. The person living in a colonial-style house is in the fifth house.
9. The person who has gray hair is the person who loves the stew.
10. The person whose birthday is in March is the person who has red hair.
11. The person who loves country music is directly left of the person whose birthday is in September.
12. The person whose birthday is in May is somewhere to the left of the person who loves country music.
13. The person in a ranch-style home is the person who loves the soup.
14. The person whose birthday is in January is the person who loves the stew.
15. The person who has blonde hair is the person in a Mediterranean-style villa.
16. Arnold is somewhere to the right of the person whose birthday is in April.
17. The person whose birthday is in February is the person who loves hip-hop music.
18. The person who has blonde hair is somewhere to the left of Eric.
19. The person residing in a Victorian house is Carol.
20. The person who has black hair is the person in a ranch-style home.
21. The person in a modern-style house is not in the second house.
22. The person who loves the spaghetti eater is somewhere to the left of the person who loves country music.
23. The person who is a pizza lover is Bob.
24. The person who loves pop music is somewhere to the left of the person whose birthday is in September.
 What is the value of attribute Food for the person whose attribute HairColor is black? Please reason step by step, and put your final answer within \boxed{}

Answer: soup


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

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

Answer: white


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Peter`, `Eric`, `Alice`
 - Each person has a unique birthday month: `sept`, `mar`, `april`, `feb`, `jan`
 - People have unique favorite sports: `baseball`, `basketball`, `soccer`, `tennis`, `swimming`
 - Each person has a favorite color: `white`, `red`, `yellow`, `blue`, `green`
 - Each person has an occupation: `doctor`, `teacher`, `lawyer`, `artist`, `engineer`
 - The mothers' names in different houses are unique: `Kailyn`, `Holly`, `Aniya`, `Penny`, `Janelle`

## Clues:
1. There is one house between the person who is a doctor and the person whose birthday is in March.
2. The person whose mother's name is Penny is not in the fourth house.
3. The person who loves baseball is somewhere to the right of the person who is a doctor.
4. The person who loves soccer is Peter.
5. There is one house between Bob and The person whose mother's name is Kailyn.
6. The person who loves yellow is in the third house.
7. The person who loves yellow is The person whose mother's name is Kailyn.
8. The person who loves swimming is the person who loves white.
9. Alice is in the fourth house.
10. The person whose birthday is in February is The person whose mother's name is Holly.
11. The person who loves baseball is the person whose birthday is in January.
12. The person who loves white is the person whose birthday is in April.
13. The person whose mother's name is Aniya is the person who loves swimming.
14. Alice is the person who loves baseball.
15. The person who is a doctor and the person who is a lawyer are next to each other.
16. The person whose birthday is in April is somewhere to the left of the person whose favorite color is red.
17. The person who loves tennis is somewhere to the right of the person who is a teacher.
18. The person whose favorite color is green is in the second house.
19. Arnold is the person whose birthday is in February.
20. The person whose birthday is in February is the person who is an artist.
21. The person who loves blue is not in the fifth house.
22. The person who loves tennis is not in the fifth house.
23. The person whose mother's name is Holly is the person who loves basketball.
 What is the value of attribute Birthday for the person whose attribute Occupation is lawyer? Please reason step by step, and put your final answer within \boxed{}

Answer: jan


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`
 - Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `desert`, `watermelon`
 - People have unique favorite sports: `soccer`, `tennis`, `basketball`, `swimming`
 - People own unique car models: `tesla model 3`, `toyota camry`, `honda civic`, `ford f150`
 - They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `carnations`

## Clues:
1. The person who owns a Tesla Model 3 is the person who loves the rose bouquet.
2. Peter is the Dragonfruit smoothie lover.
3. The Desert smoothie lover is the person who owns a Toyota Camry.
4. The person who loves tennis is in the first house.
5. The person who owns a Toyota Camry and the person who loves basketball are next to each other.
6. Arnold is the person who loves basketball.
7. The person who owns a Honda Civic is the person who loves a bouquet of daffodils.
8. Eric is the person who loves the rose bouquet.
9. The Watermelon smoothie lover is not in the first house.
10. The person who owns a Honda Civic is somewhere to the right of the Desert smoothie lover.
11. The person who loves basketball is the person who loves the boquet of lilies.
12. The person who loves tennis and the person who loves soccer are next to each other.
 What is the value of attribute Name for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Carol`, `Bob`, `Eric`, `Peter`
 - People use unique phone models: `iphone 13`, `samsung galaxy s21`, `xiaomi mi 11`, `oneplus 9`, `google pixel 6`, `huawei p50`
 - Each person has a unique birthday month: `april`, `mar`, `feb`, `may`, `jan`, `sept`
 - Each person has an occupation: `nurse`, `doctor`, `engineer`, `teacher`, `artist`, `lawyer`

## Clues:
1. The person who uses a Google Pixel 6 is directly left of the person whose birthday is in March.
2. The person who is a nurse is Eric.
3. Arnold is directly left of the person whose birthday is in April.
4. Alice and the person whose birthday is in January are next to each other.
5. The person who is an artist is the person whose birthday is in May.
6. The person whose birthday is in September is not in the sixth house.
7. There is one house between the person whose birthday is in March and the person who is a nurse.
8. The person whose birthday is in March is the person who is a lawyer.
9. The person who uses a Xiaomi Mi 11 is directly left of the person who is a nurse.
10. The person who is a teacher is not in the sixth house.
11. Eric is the person who uses an iPhone 13.
12. The person who is an engineer and Peter are next to each other.
13. The person whose birthday is in January is in the third house.
14. The person who uses a Samsung Galaxy S21 is Bob.
15. The person who is a lawyer and the person whose birthday is in April are next to each other.
16. The person who uses a OnePlus 9 is somewhere to the right of the person who is a doctor.
 What is the value of attribute House for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

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: `Alice`, `Arnold`, `Peter`, `Eric`
 - People have unique favorite sports: `tennis`, `swimming`, `basketball`, `soccer`
 - Each person lives in a unique style of house: `victorian`, `colonial`, `craftsman`, `ranch`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `desert`, `dragonfruit`
 - Each person has an occupation: `teacher`, `artist`, `engineer`, `doctor`

## Clues:
1. Alice and the person in a Craftsman-style house are next to each other.
2. The Desert smoothie lover is in the first house.
3. The Dragonfruit smoothie lover is Eric.
4. The person in a ranch-style home is somewhere to the right of the person living in a colonial-style house.
5. The person who is a doctor is not in the second house.
6. Peter is the person who likes Cherry smoothies.
7. The person who is an artist is the Dragonfruit smoothie lover.
8. Alice is in the third house.
9. The person who is an engineer is somewhere to the right of the person who loves swimming.
10. The person who loves basketball is the person who is an artist.
11. The Dragonfruit smoothie lover is not in the second house.
12. The person residing in a Victorian house is directly left of the person who loves soccer.
13. The person who loves tennis is somewhere to the left of the person who loves swimming.
 What is the value of attribute Occupation for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: teacher


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Carol`, `Peter`, `Bob`, `Arnold`, `Alice`
 - They all have a unique favorite flower: `tulips`, `lilies`, `iris`, `roses`, `carnations`, `daffodils`

## Clues:
1. The person who loves the vase of tulips is directly left of the person who loves a bouquet of daffodils.
2. Alice is somewhere to the right of Peter.
3. There are two houses between Carol and Peter.
4. The person who loves the boquet of lilies is Bob.
5. The person who loves the boquet of iris is not in the second house.
6. The person who loves the boquet of iris and the person who loves a carnations arrangement are next to each other.
7. Arnold is not in the second house.
8. The person who loves a bouquet of daffodils is Peter.
9. Bob is in the fifth house.
 What is the value of attribute Flower for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: tulips


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

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

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`, `Peter`, `Arnold`, `Alice`
 - Each person lives in a unique style of house: `victorian`, `ranch`, `colonial`, `craftsman`
 - Each person has an occupation: `teacher`, `engineer`, `doctor`, `artist`
 - Everyone has a unique favorite cigar: `prince`, `dunhill`, `pall mall`, `blue master`
 - People have unique favorite music genres: `pop`, `rock`, `classical`, `jazz`
 - People have unique heights: `very short`, `tall`, `average`, `short`

## Clues:
1. The person who loves classical music is the person living in a colonial-style house.
2. The person who smokes Blue Master is the person in a ranch-style home.
3. The person who loves rock music is the person who smokes Blue Master.
4. The Dunhill smoker is directly left of Peter.
5. Eric is in the first house.
6. The person residing in a Victorian house is in the third house.
7. The person who loves rock music and the person who loves classical music are next to each other.
8. The person who is a teacher is the person who is short.
9. The person who loves classical music is the Prince smoker.
10. The person who is a doctor is somewhere to the left of the person who is very short.
11. Arnold is the person who is an artist.
12. The person who smokes Blue Master is in the first house.
13. The person who is tall is directly left of the person who loves pop music.
14. The person residing in a Victorian house is the person who is a teacher.
 What is the value of attribute Cigar for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: prince


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Carol`, `Eric`, `Bob`, `Alice`
 - Everyone has something unique for lunch: `stir fry`, `stew`, `grilled cheese`, `soup`, `pizza`, `spaghetti`

## Clues:
1. The person who loves the soup is somewhere to the left of Carol.
2. The person who loves stir fry is in the fifth house.
3. Peter is not in the sixth house.
4. The person who loves the stew is somewhere to the left of Peter.
5. Bob is the person who loves the soup.
6. The person who loves eating grilled cheese is somewhere to the right of the person who loves the spaghetti eater.
7. The person who loves the spaghetti eater is directly left of the person who loves the soup.
8. Arnold is in the second house.
9. The person who loves the stew is directly left of Arnold.
10. Alice is directly left of the person who loves the soup.
 What is the value of attribute Food for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


## Task B-4.4.

How many passwords consisting of 4 characters from the set $\{a, b, c, 1,2,3,4,5,+,!\}$ are there such that all characters in the password are different or the password contains exactly two, not necessarily different letters and two, not necessarily different digits?

Answer: 5670


On a blackboard, Kiara wrote 20 integers, all of them different from zero. Then, for each pair of numbers written by Kiara, Yndira wrote on the same blackboard the respective product between them (including, if the result of some product was already written, Yndira repeated it).

For example, if the numbers 2, 3, 4, and 6 were among those written by Kiara, then Yndira would have written the numbers $6, 8, 12, 12, 18$, and 24, because we have $6=2 \times 3$, $8=2 \times 4$, $12=2 \times 6=3 \times 4$, $18=3 \times 6$, and $24=4 \times 6$. Note that the number 6 would have been written again even though it was already written by Kiara, while the number 12 would have been written twice by Yndira.

a) In total, how many numbers were written by Kiara and Yndira on the blackboard?

b) Suppose that, of the total numbers written on the blackboard, exactly 120 are positive. If Kiara wrote more positive numbers than negative ones, how many of the numbers written by Kiara were positive?

Answer: 210


7. (10 points) As shown in the figure, the length $AB$ of rectangle $ABCD$ is 20 cm, and the width $BC$ is 16 cm. Inside the rectangle, there are two overlapping squares $DEFG$ and $BHIJ$. It is known that the perimeters of the three shaded rectangles are equal. Therefore, the area of rectangle INFM is $\qquad$ square centimeters.

Answer: 32


4. In a rectangular flower bed, install two identical sprinklers so that the entire flower bed can be watered. It is known that the watering area of each sprinkler is a circle with a radius of $10 \mathrm{~m}$. How should it be designed (find the distance between the two sprinklers and the length and width of the rectangle) to maximize the area of the rectangular flower bed?

Answer: 10\sqrt{2}


Answer: 1000


A regular triangle's sides (in the same direction) were divided in the ratio $p: q$. By connecting the division points, a triangle is formed whose area is $\frac{19}{64}$ of the area of the original triangle. What is the ratio $p: q$? () Suggested by: Koncz Levente, Budapest

Answer: \dfrac{5}{3}


Let  $ABC$  and  $A_{1}B_{1}C_{1}$  be two triangles. Prove that

 $\frac{a}{a_{1}}+\frac{b}{b_{1}}+\frac{c}{c_{1}}\leq\frac{3R}{2r_{1}}$ ,

where  $a = BC$ ,  $b = CA$ ,  $c = AB$  are the sidelengths of triangle  $ABC$ , where  $a_{1}=B_{1}C_{1}$ ,  $b_{1}=C_{1}A_{1}$ ,  $c_{1}=A_{1}B_{1}$  are the sidelengths of triangle  $A_{1}B_{1}C_{1}$ , where  $R$  is the circumradius of triangle  $ABC$  and  $r_{1}$  is the inradius of triangle  $A_{1}B_{1}C_{1}$ .

Answer: \frac{a}{a_{1}}+\frac{b}{b_{1}}+\frac{c}{c_{1}}\leq\frac{3R}{2r_{1}}


Problem 55. Find the best constant $k$ (smallest) for the inequality
$$a^{k}+b^{k}+c^{k} \geq a b+b c+c a$$
to hold for $a, b, c$ are three non-negative real numbers with $a+b+c=3$.

Answer: \log_{\frac{3}{2}} \frac{9}{8}


Given \( N \geq 3 \) points, numbered \( 1, 2, \ldots, N \). Each pair of points is connected by an arrow from the smaller number to the larger number. A coloring of all the arrows in red and blue is called monotone if there are no two points \( A \) and \( B \) such that one can travel from \( A \) to \( B \) using both red and blue arrows. Find the number of monotone colorings.

Answer: N!


8.8. (Austria - PDR, 79). For each value of $n \in \mathbf{N}$, find the greatest value of $k \in \mathbf{Z}^{+}$, for which the number $\left[(3+\sqrt{11})^{2 n-1}\right]$ is divisible by $2^{k}$.

Answer: n


9. Given that the increasing function $f(x)$ is defined on $(0,+\infty)$, and for any positive number $x$ it satisfies $f(x)$ $f\left[f(x)+\frac{1}{x}\right]=1$, find the value of $f(1)$.

Answer: \dfrac{1 - \sqrt{5}}{2}


Let $BCB'C'$ be a rectangle, let $M$ be the midpoint of $B'C'$, and let $A$ be a point on the circumcircle of the rectangle. Let triangle $ABC$ have orthocenter $H$, and let $T$ be the foot of the perpendicular from $H$ to line $AM$. Suppose that $AM=2$, $[ABC]=2020$, and $BC=10$. Then $AT=\frac{m}{n}$, where $m$ and $n$ are positive integers with $\gcd(m,n)=1$. Compute $100m+n$.

[i]Proposed by Ankit Bisain[/i]

Answer: 2102


In triangle $K L M$, the ratio of the radii of the circumscribed and inscribed circles is 3. The inscribed circle touches the sides of triangle $K L M$ at points $A, B$, and $C$. Find the ratio of the area of triangle $K L M$ to the area of triangle $A B C$.

#

Answer: 6


$\textbf{Anna's Vintage Postcards}$

Anna organizes the postcards in her collection by country and by the decade in which they were issued. The prices she paid for them at a collectibles shop were: Italy and Germany, $7$ cents each; Japan $5$ cents each; and India $6$ cents each. (Italy and Germany are European countries, and Japan and India are Asian countries.) In that collection:

- 60s: Italy (5), Germany (7), Japan (6), India (8)
- 70s: Italy (9), Germany (6), Japan (10), India (12)
- 80s: Italy (10), Germany (12), Japan (15), India (11)

In dollars and cents, how much did her Asian postcards issued in the 80s cost her?

Answer: \$1.41


In triangle $PQR$, the angle bisectors are $PL$, $QM$, and $RN$, which intersect at the incenter $I$. If $\angle PRQ = 52^\circ$, then find the measure of $\angle PIM$, in degrees.

Answer: 64^\circ


The formula for converting a Fahrenheit temperature $F$ to the corresponding Celsius temperature $C$ is $C = \frac{5}{9}(F-32)$. An integer Fahrenheit temperature is converted to Celsius using truncation (floor function), converted back to Fahrenheit using truncation, and again converted to Celsius using truncation.
For how many integer Fahrenheit temperatures between 30 and 1200 inclusive does the original temperature equal the final Fahrenheit temperature after two conversions?

Answer: 130


A rectangle with integer dimensions has an area that is numerically five times the number of units in its perimeter. What is the number of units in the perimeter of this rectangle if one of its sides is greater than 10 units?

Answer: 90


Maria wants to save money for a down payment on a house and decides to invest in a savings account that compounds semiannually with an annual interest rate of \(8\%\). She needs a total of $\$100,\!000$ at the end of \(10\) years. To the nearest dollar, how much should she initially invest?

Answer: \$45,639


A rectangle and an isosceles triangle share a common side, which lies along the $x$-axis, with the right vertex of the rectangle and the left vertex of the triangle located at $(15, 0)$. The dimensions of the rectangle are $15$ units wide (along the $x$-axis) and $10$ units high, while the base and height of the triangle are both $10$ units. A segment is drawn from the top left vertex of the rectangle to the top vertex of the triangle. Calculate the area of the triangle formed by this segment and part of the $x$-axis.

Answer: 75 \text{ sq. units}


In a similar race setup, all runners start at point $A$, must touch any part of a 1500-meter wall, and stop at point $B$. Given that the distances from $A$ to the closest point on the wall is 400 meters and from $B$ to the closest point on the wall is 600 meters, what is the minimum distance a participant must run? Round your answer to the nearest meter.

Answer: 1803


A geometric sequence of positive integers is formed where the first term is 6 and the fourth term is 768. What is the second term of this sequence?

Answer: 24


In the diagram, \( O \) is the center of a circle with radii \( OP=OQ=7 \). Determine the perimeter of the shaded region if \( \widehat{PQ} \) subtends an angle of \( 270^\circ \).

Answer: 14 + \frac{21\pi}{2}


Margo walks to her friend's house in 15 minutes and takes 30 minutes using the same, but slippery, route to get back home. Her average walking rate for the outbound trip is 5 miles per hour and 3 miles per hour on the return trip. What are the total miles Margo walked, if her average speed for the entire trip was 3.6 miles per hour?

Answer: 2.75 \text{ miles}


Determine the total number of pieces required to create a ten-row triangle using unit rods and connectors. Each n-row triangle uses rods in the pattern of the arithmetic sequence $3n$ and connectors forming an $(n+1)$-row triangle.

Answer: 231


Cara is sitting with her seven friends in a line at a table. How many different combinations of friends can sit immediately next to her on the right?

Answer: 7


There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`
 - The people keep unique animals: `cat`, `horse`
 - People have unique heights: `short`, `very short`
 - People have unique favorite book genres: `science fiction`, `mystery`
 - Each person prefers a unique type of vacation: `mountain`, `beach`

## Clues:
1. The person who loves beach vacations is directly left of Eric.
2. The person who loves beach vacations and the person who is very short are next to each other.
3. The cat lover is the person who is short.
4. The person who is short is the person who loves mystery books.
 What is the value of attribute Animal for the person whose attribute Vacation is mountain? Please reason step by step, and put your final answer within \boxed{}

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`, `Peter`, `Eric`, `Arnold`, `Bob`
 - Each person has a unique birthday month: `sept`, `mar`, `april`, `feb`, `jan`
 - The people keep unique animals: `horse`, `bird`, `dog`, `fish`, `cat`

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

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: `Arnold`, `Peter`, `Eric`, `Alice`
 - Each person lives in a unique style of house: `craftsman`, `colonial`, `victorian`, `ranch`
 - People have unique hair colors: `red`, `blonde`, `black`, `brown`
 - Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`, `Samantha`
 - People have unique favorite book genres: `mystery`, `fantasy`, `romance`, `science fiction`

## Clues:
1. The person in a Craftsman-style house is in the third house.
2. Alice is the person who loves romance books.
3. The person who has brown hair is in the fourth house.
4. The person's child is named Samantha is in the fourth house.
5. The person in a ranch-style home is somewhere to the right of the person who has red hair.
6. Peter is the person's child is named Bella.
7. Arnold is the person who has red hair.
8. Alice is the person living in a colonial-style house.
9. The person who has black hair is in the second house.
10. The person who loves fantasy books is Peter.
11. Arnold is the person's child is named Meredith.
12. The person who has black hair is Eric.
13. The person who loves science fiction books is Arnold.
 What is the value of attribute House for the person whose attribute BookGenre is mystery? Please reason step by step, and put your final answer within \boxed{}

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`, `Alice`, `Eric`
 - Each person has an occupation: `lawyer`, `teacher`, `artist`, `engineer`, `doctor`
 - Each person lives in a unique style of house: `victorian`, `craftsman`, `modern`, `ranch`, `colonial`
 - People have unique hair colors: `blonde`, `gray`, `red`, `brown`, `black`
 - People have unique favorite book genres: `romance`, `biography`, `science fiction`, `mystery`, `fantasy`

## Clues:
1. Alice is not in the fifth house.
2. Peter is not in the second house.
3. Peter is directly left of Eric.
4. The person living in a colonial-style house is somewhere to the left of the person who loves fantasy books.
5. Arnold is the person who is a doctor.
6. The person who has gray hair is the person who loves fantasy books.
7. The person who loves science fiction books is not in the fifth house.
8. Peter is the person who has red hair.
9. The person who loves romance books is the person who has black hair.
10. Eric is the person who has black hair.
11. The person who is a doctor is somewhere to the right of Peter.
12. The person who has blonde hair is the person who is a teacher.
13. Peter is the person who loves mystery books.
14. The person who is a lawyer is Eric.
15. The person living in a colonial-style house is the person who is an engineer.
16. The person residing in a Victorian house is the person who loves mystery books.
17. The person who is a teacher is not in the fourth house.
18. The person who is an artist is somewhere to the left of the person in a modern-style house.
19. The person who is a teacher is not in the third house.
20. The person in a ranch-style home is directly left of the person in a Craftsman-style house.
 What is the value of attribute BookGenre for the person whose attribute HouseStyle is ranch? Please reason step by step, and put your final answer within \boxed{}

Answer: fantasy


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Alice`, `Arnold`
 - People have unique favorite sports: `swimming`, `tennis`, `basketball`, `soccer`
 - Each person prefers a unique type of vacation: `cruise`, `beach`, `mountain`, `city`
 - Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `stew`, `pizza`

## Clues:
1. The person who loves the spaghetti eater is somewhere to the left of the person who likes going on cruises.
2. The person who loves the stew is directly left of the person who loves eating grilled cheese.
3. The person who is a pizza lover is in the fourth house.
4. Peter is somewhere to the left of the person who enjoys mountain retreats.
5. The person who likes going on cruises is in the third house.
6. Arnold is the person who loves soccer.
7. The person who loves basketball is not in the first house.
8. There are two houses between the person who prefers city breaks and Eric.
9. The person who loves tennis is the person who likes going on cruises.
10. Alice is in the first house.
 What is the value of attribute Name for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
 - The mothers' names in different houses are unique: `Penny`, `Kailyn`, `Aniya`, `Janelle`, `Holly`
 - Everyone has a unique favorite cigar: `blue master`, `pall mall`, `prince`, `dunhill`, `blends`
 - The people keep unique animals: `bird`, `cat`, `horse`, `fish`, `dog`
 - Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `stew`

## Clues:
1. The person who loves the stew is somewhere to the left of the fish enthusiast.
2. The person who is a pizza lover is somewhere to the right of the Dunhill smoker.
3. Peter is the cat lover.
4. The dog owner is directly left of the person who loves the spaghetti eater.
5. The person who loves stir fry is The person whose mother's name is Aniya.
6. There are two houses between the fish enthusiast and Eric.
7. The person who smokes many unique blends is The person whose mother's name is Kailyn.
8. The fish enthusiast is the person who loves the spaghetti eater.
9. The fish enthusiast is in the second house.
10. The person whose mother's name is Kailyn is the person who loves the stew.
11. The person whose mother's name is Janelle is not in the fifth house.
12. The person whose mother's name is Holly is the person who smokes Blue Master.
13. Arnold is The person whose mother's name is Aniya.
14. The person who loves the spaghetti eater and the person partial to Pall Mall are next to each other.
15. Peter is not in the third house.
16. Arnold is the person who keeps horses.
17. The person whose mother's name is Holly is Bob.
 What is the value of attribute Food for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: stir fry


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Eric`, `Alice`, `Peter`, `Arnold`
 - People have unique heights: `super tall`, `tall`, `very short`, `average`, `very tall`, `short`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `samsung galaxy s21`, `xiaomi mi 11`, `oneplus 9`, `huawei p50`
 - Each mother is accompanied by their child: `Fred`, `Timothy`, `Alice`, `Bella`, `Meredith`, `Samantha`

## Clues:
1. The person who uses a Xiaomi Mi 11 is the person who is short.
2. Alice is somewhere to the right of Bob.
3. The person who uses a OnePlus 9 is Carol.
4. The person who uses a Xiaomi Mi 11 is the person's child is named Alice.
5. The person who has an average height is not in the fourth house.
6. The person who uses a Samsung Galaxy S21 is in the second house.
7. Alice is directly left of the person's child is named Fred.
8. The person's child is named Meredith and Arnold are next to each other.
9. The person's child is named Samantha is the person who is super tall.
10. The person who is short is somewhere to the right of the person who uses a Samsung Galaxy S21.
11. The person who is very tall is the person who is the mother of Timothy.
12. Bob is not in the fourth house.
13. The person who is very short is the person who uses a Huawei P50.
14. The person who uses a Samsung Galaxy S21 is directly left of the person who is super tall.
15. Peter is somewhere to the right of the person who is tall.
16. Arnold is somewhere to the left of the person's child is named Bella.
17. The person who uses a Google Pixel 6 is directly left of the person who uses an iPhone 13.
18. Eric is in the first house.
 What is the value of attribute Height for the person whose attribute PhoneModel is google pixel 6? Please reason step by step, and put your final answer within \boxed{}

Answer: super tall


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Arnold`, `Peter`, `Bob`
 - People have unique heights: `average`, `tall`, `short`, `very short`, `very tall`
 - Each person has a unique hobby: `cooking`, `knitting`, `photography`, `gardening`, `painting`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`, `camping`
 - People own unique car models: `ford f150`, `toyota camry`, `tesla model 3`, `honda civic`, `bmw 3 series`
 - Each person has a unique level of education: `bachelor`, `doctorate`, `master`, `high school`, `associate`

## Clues:
1. The person who is short is directly left of the person with a high school diploma.
2. The person who enjoys mountain retreats is the person who paints as a hobby.
3. The person who loves cooking is the person with a doctorate.
4. The person who owns a Honda Civic is in the third house.
5. The person who owns a Honda Civic is the person who has an average height.
6. Bob is the person who paints as a hobby.
7. The person with a master's degree is Eric.
8. The person who enjoys knitting is directly left of the person with a high school diploma.
9. The person who owns a Toyota Camry and the person who enjoys camping trips are next to each other.
10. Peter is not in the fifth house.
11. The person who prefers city breaks is the person who owns a BMW 3 Series.
12. The person who owns a Honda Civic is Eric.
13. The person who paints as a hobby is the person with a bachelor's degree.
14. Arnold is not in the second house.
15. The person who owns a Ford F-150 is not in the second house.
16. The person who enjoys gardening is the person who likes going on cruises.
17. The person who loves beach vacations is the person who is very short.
18. The person who owns a BMW 3 Series is not in the first house.
19. The person who owns a Toyota Camry is directly left of the person who is tall.
20. Arnold is not in the fifth house.
 What is the value of attribute CarModel for the person whose attribute Hobby is photography? Please reason step by step, and put your final answer within \boxed{}

Answer: ford f150


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Eric`, `Arnold`, `Carol`, `Bob`
 - People have unique heights: `very short`, `very tall`, `short`, `super tall`, `tall`, `average`
 - Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `soup`, `stew`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Penny`, `Aniya`, `Kailyn`, `Sarah`
 - Each person has a unique favorite drink: `tea`, `water`, `milk`, `coffee`, `boba tea`, `root beer`
 - Each person has a unique type of pet: `rabbit`, `fish`, `bird`, `hamster`, `cat`, `dog`

## Clues:
1. Arnold is the person who loves the stew.
2. The person who owns a dog is directly left of the person who has a cat.
3. The person whose mother's name is Holly is in the sixth house.
4. The tea drinker is somewhere to the left of the boba tea drinker.
5. The tea drinker is in the second house.
6. The person who is very tall is Bob.
7. The person who has a cat is The person whose mother's name is Penny.
8. The person who is very short is directly left of Alice.
9. Carol is the person who is a pizza lover.
10. The person who has an average height is not in the sixth house.
11. The person who loves stir fry is Bob.
12. The person with a pet hamster is not in the third house.
13. The person whose mother's name is Janelle is somewhere to the left of the person with a pet hamster.
14. Eric is the person who loves the soup.
15. The person whose mother's name is Kailyn is directly left of the person who keeps a pet bird.
16. The one who only drinks water is somewhere to the right of the person who likes milk.
17. The person who owns a rabbit is the person who loves the stew.
18. The person who is tall is The person whose mother's name is Aniya.
19. The person who is very short is somewhere to the left of the person who likes milk.
20. The person who is tall is not in the fifth house.
21. The person who is very short is in the second house.
22. The person who loves the stew is the root beer lover.
23. The person whose mother's name is Kailyn is the boba tea drinker.
24. The person who is tall is not in the fourth house.
25. The person who is super tall is directly left of the person who loves eating grilled cheese.
26. Carol is directly left of the root beer lover.
 What is the value of attribute Drink for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: milk


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Alice`, `Arnold`
 - Each person has a unique birthday month: `sept`, `feb`, `april`, `jan`
 - People have unique favorite book genres: `romance`, `fantasy`, `mystery`, `science fiction`
 - They all have a unique favorite flower: `roses`, `daffodils`, `lilies`, `carnations`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`

## Clues:
1. There are two houses between the person who loves fantasy books and the person whose birthday is in April.
2. The person whose birthday is in February is directly left of the person who loves a bouquet of daffodils.
3. The person who likes going on cruises is the person who loves a carnations arrangement.
4. The person whose birthday is in September is directly left of the person who loves science fiction books.
5. The person who loves a bouquet of daffodils is the person who prefers city breaks.
6. The person whose birthday is in April is Arnold.
7. The person whose birthday is in February is the person who loves a carnations arrangement.
8. Alice is the person who likes going on cruises.
9. The person who loves the boquet of lilies is the person who enjoys mountain retreats.
10. Eric is not in the third house.
11. The person who loves science fiction books is the person who loves the boquet of lilies.
12. The person who loves mystery books is Eric.
13. Eric and the person whose birthday is in January are next to each other.
 What is the value of attribute BookGenre for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: mystery


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Bob`, `Arnold`, `Eric`, `Alice`
 - Each person has a favorite color: `red`, `white`, `green`, `blue`, `yellow`
 - Each person has a unique hobby: `gardening`, `cooking`, `painting`, `photography`, `knitting`
 - People have unique heights: `very tall`, `tall`, `average`, `short`, `very short`
 - People have unique hair colors: `black`, `blonde`, `brown`, `gray`, `red`

## Clues:
1. The person whose favorite color is green is somewhere to the right of the person who has black hair.
2. The person who has an average height is somewhere to the right of the person who loves blue.
3. The person who has red hair is Alice.
4. The person who loves cooking is not in the first house.
5. The person who loves yellow is the person who has gray hair.
6. The person who is short is somewhere to the left of the person who loves yellow.
7. The person who enjoys gardening is the person who loves white.
8. Arnold is somewhere to the left of the person who has black hair.
9. The person who is short is somewhere to the right of the person who has blonde hair.
10. Eric and the person who loves cooking are next to each other.
11. The person who has black hair is directly left of the person who loves blue.
12. The person who is very short is the person who has black hair.
13. Bob is the person who loves blue.
14. The person who is tall is directly left of the photography enthusiast.
15. The person who loves white is not in the first house.
16. The person who loves yellow is the person who enjoys knitting.
17. The person who loves blue is the person who has blonde hair.
 What is the value of attribute Hobby for the person whose attribute Color is white? Please reason step by step, and put your final answer within \boxed{}

Answer: gardening