3. In an isosceles triangle $ABC$, the angle at the base is $\arcsin \frac{2}{3}$. A circle with its center at the midpoint of the base $BC$ intersects the line $AC$ at points $K$ and $L$, and the line $AB$ at points $M$ and $N$, such that segments $KM$ and $LN$ intersect. Find its radius if the radius of the circle passing through points $A, L$, and $N$ is 2.

Answer: \dfrac{4\sqrt{5}}{3}


Problem 6. Piglet and Winnie-the-Pooh decided to eat a $7 \times 7$ square chocolate bar. They take turns eating pieces from it: Piglet eats $1 \times 1$ pieces, Winnie-the-Pooh eats $2 \times 1$ or $1 \times 2$ pieces (pieces can be eaten not necessarily from the edge). Piglet makes the first move. If before Winnie-the-Pooh's turn, there are no $2 \times 1$ or $1 \times 2$ pieces left in the chocolate bar, the entire remaining chocolate goes to Piglet. Who among the friends can eat more than half of the entire chocolate bar regardless of the actions of the second?

Answer: Piglet


18. There are 30 students standing in a row, and from left to right, they are wearing hats in the order of "red, yellow, blue, red, yellow, blue......". The PE teacher asks the students to count off from left to right as "1, 2, 1, 2, 1, 2.....", and those who count off 2 step forward. Among the remaining students, those wearing red hats step back. At this point, the students are divided into 3 rows, and in the middle row, there are $\qquad$ people wearing blue hats.

Answer: 5


## Task 3 - 201223

In a football tournament, $n$ teams participated. Each team played against every other team exactly once.

The winning team received 2 points, the losing team received no points, and in the event of a draw, both teams received one point each.

After the tournament, the teams were ranked 1, 2, .., n in the final table according to their total points in descending order. (In the event of a tie, additional criteria were used to distinguish between teams.)

Determine the largest possible number that can occur as the point difference between two directly adjacent teams in the final table in all (under these rules) possible tournaments.

Answer: n


3. Petya is the owner of a cashback card offering $1 \%$ cashback on all purchases. In addition to this, the bank offers Petya the option to choose categories with increased cashback each month, but no more than three. Which categories would be the most profitable to choose, considering the cashback percentage and the expected expenses?
1) transport: cashback - $5 \%$, expenses - 2000 rubles
2) groceries: cashback - $3 \%$, expenses - 5000 rubles
3) clothing: cashback - $4 \%$, expenses - 3000 rubles
4) entertainment: cashback - $5 \%$, expenses - 3000 rubles
5) sports goods: cashback - $6 \%$, expenses - 1500 rubles

Answer: 2, 3, 4


King Arthur has two equally wise advisors - Merlin and Percival. Each of them finds the right answer to any question with a probability of $p$ or the wrong answer - with a probability of $q=1-p$.

If both advisors say the same thing, the king listens to them. If they say the opposite, the king makes a decision by flipping a coin.

One day, Arthur wondered - would the probability of making correct decisions not decrease if he kept only one advisor and listened to him? So the king summoned the advisors and said:

- It seems to me that the probability of making correct decisions will not decrease if I keep only one advisor and listen to him. If this is true, I will have to dismiss one of you. If this is not true, I will leave everything as it is. Answer me, should I dismiss one of you?
- Who exactly are you planning to dismiss, King Arthur? - the advisors asked.
- If I decide to dismiss one of you, I will make the choice by drawing lots, flipping a coin.

The advisors left to think about the answer. The advisors, I repeat, are equally wise, but not equally honest.

Percival is very honest and will try to give the correct answer, even if it means he will be dismissed. Merlin, honest in all other respects, in this situation decides to give an answer that minimizes the probability of his dismissal. What is the probability that Merlin will be dismissed?

Answer: \dfrac{1}{4}


61. Insert arithmetic operation signs between the digits 12345 so that the result equals 1.

Answer: 1+2-3-4+5


3. (10 points) The first three numbers in a sequence are $1, 7, 8$, and each subsequent number is the remainder when the sum of the three preceding numbers is divided by 4. What is the sum of the first 2011 numbers in this sequence? $\qquad$ .

Answer: 3028


12. Find the number of matrices that satisfy two conditions:
1) the matrix has the form $\left(\begin{array}{lll}1 & * & * \\ * & 1 & * \\ * & * & 1\end{array}\right)$, where each * can take the value 0 or 1
2) the rows of the matrix do not repeat.

Answer: 42


The edge of a regular tetrahedron \(ABCD\) is \(a\). Points \(E\) and \(F\) are taken on the edges \(AB\) and \(CD\) respectively, such that the sphere circumscribed around the tetrahedron intersects the line passing through \(E\) and \(F\) at points \(M\) and \(N\). Find the length of the segment \(EF\), if \(ME: EF: FN = 3: 12: 4\).

Answer: \dfrac{2a\sqrt{7}}{7}


Acute triangle $ABC$ has altitudes $AD$, $BE$, and $CF$.  Point $D$ is projected onto $AB$ and $AC$ to points $D_c$ and $D_b$ respectively.  Likewise, $E$ is projected to $E_a$ on $BC$ and $E_c$ on $AB$, and $F$ is projected to $F_a$ on $BC$ and $F_b$ on $AC$.  Lines $D_bD_c$, $E_cE_a$, $F_aF_b$ bound a triangle of area $T_1$, and lines $E_cF_b$, $D_bE_a$, $F_aD_c$ bound a triangle of area $T_2$.  What is the smallest possible value of the ratio $T_2/T_1$?

Answer: 25


15. Random Vectors. There are $n$ random vectors of the form $\left(y_{1}, y_{2}, y_{3}\right)$, where exactly one random coordinate is equal to 1, and the others are 0. They are added together. The result is a random vector $\vec{a}$ with coordinates $\left(Y_{1}, Y_{2}, Y_{3}\right)$.

a) (from 9th grade. 2 points). Find the expected value of the random variable $\vec{a}^{2}$.

b) (from 9th grade. 2 points). Prove that $|\vec{a}| \geq \frac{n}{\sqrt{3}}$.

Answer: \dfrac{n^2 + 2n}{3}


3. As shown in Figure $1, \angle A O B=30^{\circ}$, within $\angle A O B$ there is a fixed point $P$, and $O P$ $=10$, on $O A$ there is a point $Q$, and on $O B$ there is a fixed point $R$. To make the perimeter of $\_P Q R$ the smallest, the minimum perimeter is

Answer: 10


435 Given a convex polygon $F$, consider all the figures that are positively homothetic to the convex polygon $F$ and smaller than $F$. Let $n(F)$ be the minimum number of such figures (allowing translation but not rotation) needed to cover the convex polygon $F$. Find the value of $n(F)$.

Answer: 3


Suppose that $A B C D E F$ is a regular hexagon with sides of length 6 . Each interior angle of $A B C D E F$ is equal to $120^{\circ}$.

(a) A circular arc with centre $D$ and radius 6 is drawn from $C$ to $E$, as shown. Determine the area of the shaded sector.

(b) A circular arc with centre $D$ and radius 6 is drawn from $C$ to $E$, as shown. A second arc with centre $A$ and radius 6 is drawn from $B$ to $F$, as shown. These arcs are tangent (that is, touch) at the centre of the hexagon. Line segments $B F$ and $C E$ are also drawn. Determine the total area of the shaded regions.

(c) Along each edge of the hexagon, a semi-circle with diameter 6 is drawn. Determine the total area of the shaded regions; that is, determine the total area of the regions that lie inside exactly two of the semi-circles.

![](https://cdn.mathpix.com/cropped/2024_04_30_aeb4d8fddfe5f1048ea8g-4.jpg?height=303&width=336&top_left_y=862&top_left_x=428)

Diagram for (a)

![](https://cdn.mathpix.com/cropped/2024_04_30_aeb4d8fddfe5f1048ea8g-4.jpg?height=301&width=347&top_left_y=863&top_left_x=867)

Diagram for (b)

![](https://cdn.mathpix.com/cropped/2024_04_30_aeb4d8fddfe5f1048ea8g-4.jpg?height=300&width=344&top_left_y=861&top_left_x=1300)

Diagram for $(\mathrm{c})$

Answer: 12\pi


3. As shown in the figure, $A$ and $P$ are a fixed point and a moving point on the unit circle $O$, respectively. The initial side of angle $x$ is the ray $O A$, and the terminal side is the ray $O P$. Draw a perpendicular from point $P$ to the line $O A$, with the foot of the perpendicular being $M$. Express the distance from point $M$ to the line $O P$ as a function $f(x)$ of $x$, then $f(x)=$ $\qquad$ .

Answer: |\sin x \cos x|


Three, (15 points) Can 2010 be written as the sum of squares of $k$ distinct prime numbers? If so, determine all possible values of $k$, and provide an example for each corresponding $k$ value; if not, briefly explain the reason.

---

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

Answer: 7


(11) (15 points) Divide each side of the equilateral $\triangle A B C$ with side length 3 into three equal parts, and draw lines parallel to the other two sides through each division point. The 10 points formed by the intersections of the sides of $\triangle A B C$ and these parallel lines are called grid points. If $n$ grid points are chosen from these 10 grid points, there will definitely be three grid points that can form an isosceles triangle (including equilateral triangles). Find the minimum value of $n$.

Answer: 5


1. Find all values of $x$, for each of which one of the three given numbers $\log _{x}\left(x-\frac{1}{3}\right)$, $\log _{x-\frac{1}{3}}(x-3)$, and $\log _{x-3} x$ is equal to the product of the other two.

Answer: \dfrac{10}{3}


The real-valued function  $f$  is defined for  $0 \le x \le 1, f(0) = 0, f(1) = 1$ , and  $\frac{1}{2} \le \frac{ f(z) - f(y)}{f(y) - f(x)} \le 2$  for all  $0 \le x < y < z \le 1$  with  $z - y = y -x$ . Prove that  $\frac{1}{7} \le  f (\frac{1}{3} ) \le \frac{4}{7}$ .

Answer: \frac{1}{7} \leq f\left(\frac{1}{3}\right) \leq \frac{4}{7}


6. In a tetrahedron $ABCD$ with volume 12, points $E, F, G$ are on edges $AB, BC, AD$ respectively, and $AE = 2EB, BF = FC, AG = 2GD$. A plane through points $E, F, G$ intersects the tetrahedron in a section $EFGH$. The distance from point $C$ to this plane is 1. Then the area of this section is $\qquad$.

Answer: 7


7.3. A natural number is called curious if, after subtracting the sum of its digits from it, the result is a number consisting of identical digits. How many three-digit curious numbers exist?

Answer: 30


1. It is known that there is a prime number between $10^{17}$ and $10^{17}+10$. Try to find this prime number.

Answer: 10^{17} + 3


There are 7 different numbers on the board, their sum is $10$. For each number on the board, Petya wrote the product of this number and the sum of the remaining 6 numbers in his notebook. It turns out that the notebook only has 4 distinct numbers in it. Determine one of the numbers that is written on the board.

Answer: -20


6. (15 points) A metal bar with a temperature of $20{ }^{\circ} \mathrm{C}$ was submerged into water taken at a temperature of $80{ }^{\circ} \mathrm{C}$. After thermal equilibrium was established, the temperature was found to be $60{ }^{\circ} \mathrm{C}$. After this, without removing the first bar from the water, another identical bar with a temperature of 20 ${ }^{\circ} \mathrm{C}$ was submerged into the water. What will the temperature of the water be after thermal equilibrium is established?

Answer: 50


\section*{Task 1 - 191021}

A rectangular picture, whose side lengths are in the ratio \(2: 3\), is to receive a frame of uniform width, whose area is as large as that of the picture.

Determine all values of the ratio of the lengths of the outer edges of the frame that satisfy this requirement!

Answer: \dfrac{3}{4}


3.12 In the first grade, more than 100 students took exams in Chinese, English, and mathematics. Among them, 92 passed the Chinese exam, 75 passed the English exam, and 65 passed the mathematics exam; 65 passed both Chinese and English exams, 54 passed both Chinese and mathematics exams, and 45 passed both English and mathematics exams. Find the number of students who passed all three subjects.

---

The problem can be solved using the principle of inclusion-exclusion. Let's denote:
- \( A \) as the set of students who passed the Chinese exam,
- \( B \) as the set of students who passed the English exam,
- \( C \) as the set of students who passed the mathematics exam.

We are given:
- \( |A| = 92 \)
- \( |B| = 75 \)
- \( |C| = 65 \)
- \( |A \cap B| = 65 \)
- \( |A \cap C| = 54 \)
- \( |B \cap C| = 45 \)

We need to find \( |A \cap B \cap C| \), the number of students who passed all three subjects.

Using the principle of inclusion-exclusion for three sets, we have:
\[
|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|
\]

We know that the total number of students is more than 100, so:
\[
|A \cup B \cup C| > 100
\]

Substituting the given values:
\[
|A \cup B \cup C| = 92 + 75 + 65 - 65 - 54 - 45 + |A \cap B \cap C|
\]
\[
|A \cup B \cup C| = 168 - 164 + |A \cap B \cap C|
\]
\[
|A \cup B \cup C| = 4 + |A \cap B \cap C|
\]

Since \( |A \cup B \cup C| > 100 \):
\[
4 + |A \cap B \cap C| > 100
\]
\[
|A \cap B \cap C| > 96
\]

Since \( |A \cap B \cap C| \) must be an integer, the smallest possible value is 97. Therefore, the number of students who passed all three subjects is:
\[
\boxed{97}
\]

Answer: 97


16. On Sunday, after Little Fat got up, he found that his alarm clock was broken. He estimated the time and set the alarm clock to 7:00, then he walked to the science museum and saw that the electronic clock on the roof pointed to 8:50. He visited the museum for one and a half hours and returned home at the same speed. When he got home, Little Fat saw that the alarm clock pointed to 11:50. Try to answer: At this time, to what time should the alarm clock be set to be accurate?

Answer: 12:00


4. Ana chose the digits $1,2,3,4,5,6,7$ and 9. She decided to form groups of 4 prime numbers and use all the chosen digits for each group of prime numbers. What is the sum of the prime numbers in each group?

Naloge rešuj samostojno. Za reševanje imaš na voljo 210 minut.

Uporaba zapiskov, literature ali žepnega računala ni dovoljena.

48th Mathematical Competition

for high school students of Slovenia

Ljutomer, April 17, 2004

## Tasks for 2nd year students

Answer: 190


## Task B-2.4.

Upon arriving home, Professor Matko realized he had left his umbrella at one of the four places he visited that day: the bank, the post office, the pharmacy, and the store. The pharmacist noticed the umbrella in the pharmacy and, knowing the professor, realized that he would immediately set out to look for his umbrella. He wondered in how many different ways the professor could visit these four places, assuming that he would immediately return home after finding the umbrella. What number of visits is this about?

Answer: 16


Example 2. Solve the equation $\frac{d y}{d x}=\frac{1}{x \cos y+\sin 2 y}$.

Answer: x = C e^{\sin y} - 2 \sin y - 2


An isosceles right triangle $ABC$ ($\angle B-$ right angle), with an area of $4+2\sqrt{2}$, is inscribed in a circle. Point $D$ lies on this circle, and the chord $BD$ equals 2. Find the chords $AD$ and $CD$.

#

Answer: 2


4. For a given positive integer $n$. Try to find the smallest positive integer $d_{n}$ that cannot be expressed in the form $\sum_{i=1}^{n}(-1)^{a_{i}} \times 2^{b_{i}}$, where $a_{i} 、 b_{i}(i=1,2, \cdots, n)$ are all non-negative integers.

Answer: \dfrac{2^{2n + 1} + 1}{3}


Consider the four-digit numbers that do not contain any digits other than 4 and 5. Form the sum of every possible pair of such distinct numbers. How many different sums appear among these pairs?

Answer: 65


3. (10 points) As shown in the figure, on two identical large rectangular pieces of paper, a small square of the same size is cut from a corner and an edge respectively. If the perimeter of the shaded part in figure (2) is 17 cm more than that of the shaded part in figure (1), then the perimeter of the cut-out small square is $\qquad$ cm.

Answer: 34


6. In a rectangle $A B C D$ (including the boundary) with an area of 1, there are 5 points, among which no three points are collinear. Find the minimum number of triangles, with these 5 points as vertices, whose area is not greater than $\frac{1}{4}$.

Answer: 2


Magicman and his helper want to do some magic trick. They have special card desk. Back of all cards is common color and face is one of $2017$ colors.
Magic trick: magicman go away from scene. Then viewers should put on the table $n>1$ cards in the row face up. Helper looks at these cards, then he turn all cards face down, except one, without changing order in row. Then magicman returns on the scene, looks at cards, then show on the one  card, that lays face down and names it face color.
What is minimal $n$ such that magicman and his helper can has strategy to make magic trick successfully?

Answer: 2018


In an isosceles triangle \( ABC \) (\(|AB| = |BC|\)), a perpendicular is drawn from point \( E \) (on the bisector \( AE \)) to \( AE \), extending to intersect the extension of side \( AC \) at point \( F \) (with \( C \) between \( A \) and \( F \)). Given that \(|AC| = 2m\) and \(|FC| = \frac{m}{4}\), find the area of triangle \( ABC \).

Answer: \dfrac{5\sqrt{11}}{7} m^2


Problem 8. In a right triangle $ABC$ with a right angle at $C$, points $P$ and $Q$ are the midpoints of the angle bisectors drawn from vertices $A$ and $B$. The inscribed circle of the triangle touches the hypotenuse at point $H$. Find the angle $PHQ$.

Answer: 90^\circ


10-6. The places of cyclists in the race are determined by the sum of the times on all stages: the first place goes to the rider with the smallest total time,..., the last place goes to the rider with the largest total time. There were 500 cyclists, the race took place over 15 stages, and there were no cyclists with the same times either on the stages or in the total time over all stages. Vasya always finished seventh. What is the lowest place (i.e., the place with the highest number) he could have taken?

Answer: 91


4. In the tetrahedron $P-ABC$, it is known that $BC=3$, $CA=4$, $AB=5$. If the dihedral angles between the three lateral faces and the base are all $45^{\circ}$, then the volume of the tetrahedron $P-ABC$ is $\qquad$

Answer: 2


Answer: n \mid m


Three friends, Xenia, Yvett, and Zita, each arrive at an internet café that is open from noon to 8 PM, at independently and randomly chosen times, each staying for one hour. What is the probability that all three of them meet?

Answer: \dfrac{19}{343}


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`, `Eric`, `Carol`, `Arnold`, `Alice`, `Peter`
 - People use unique phone models: `google pixel 6`, `samsung galaxy s21`, `iphone 13`, `huawei p50`, `oneplus 9`, `xiaomi mi 11`
 - Each person has a favorite color: `white`, `yellow`, `blue`, `green`, `red`, `purple`

## Clues:
1. The person whose favorite color is green is the person who uses a Google Pixel 6.
2. The person who uses a Xiaomi Mi 11 is somewhere to the right of the person who uses a Huawei P50.
3. There are two houses between Peter and the person whose favorite color is red.
4. Eric is somewhere to the right of the person whose favorite color is green.
5. Carol is the person who uses an iPhone 13.
6. The person who loves blue is not in the second house.
7. The person who uses a Samsung Galaxy S21 is somewhere to the left of the person who loves yellow.
8. The person who loves blue is somewhere to the left of the person who loves white.
9. Carol and the person whose favorite color is red are next to each other.
10. The person who uses a Google Pixel 6 is Bob.
11. Alice is the person who uses a Xiaomi Mi 11.
12. The person whose favorite color is green is not in the second house.
13. The person who loves purple is directly left of Carol.
14. Alice is the person who loves purple.
 What is the value of attribute PhoneModel for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: xiaomi mi 11


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`
 - Each mother is accompanied by their child: `Bella`, `Meredith`, `Fred`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`, `google pixel 6`
 - People have unique favorite book genres: `romance`, `science fiction`, `mystery`
 - Everyone has a unique favorite cigar: `blue master`, `prince`, `pall mall`
 - People have unique heights: `short`, `very short`, `average`

## Clues:
1. Eric is directly left of the Prince smoker.
2. The person who has an average height is somewhere to the right of Peter.
3. The person who uses a Samsung Galaxy S21 is in the second house.
4. The person who smokes Blue Master is in the third house.
5. The person who uses a Google Pixel 6 is Eric.
6. Arnold is somewhere to the right of the person who loves science fiction books.
7. The person who uses an iPhone 13 is the person's child is named Bella.
8. The person who is short is the Prince smoker.
9. The person who loves mystery books is the person who uses a Google Pixel 6.
10. The person's child is named Meredith and the person who is short are next to each other.
 What is the value of attribute BookGenre for the person whose attribute Height is very short? Please reason step by step, and put your final answer within \boxed{}

Answer: mystery


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Alice`, `Eric`, `Peter`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `lilies`, `roses`
 - Everyone has a unique favorite cigar: `dunhill`, `blue master`, `pall mall`, `prince`
 - Each mother is accompanied by their child: `Meredith`, `Samantha`, `Bella`, `Fred`
 - The mothers' names in different houses are unique: `Janelle`, `Aniya`, `Holly`, `Kailyn`
 - People use unique phone models: `iphone 13`, `google pixel 6`, `oneplus 9`, `samsung galaxy s21`

## Clues:
1. The person whose mother's name is Kailyn is the Prince smoker.
2. The person whose mother's name is Holly is the person who loves a bouquet of daffodils.
3. Arnold is in the fourth house.
4. The person's child is named Bella is somewhere to the left of the person who uses a OnePlus 9.
5. The person's child is named Fred is not in the second house.
6. The person's child is named Meredith is directly left of The person whose mother's name is Janelle.
7. The person who loves a bouquet of daffodils is Eric.
8. The person who loves the boquet of lilies is the person partial to Pall Mall.
9. The person whose mother's name is Janelle is the person who loves a carnations arrangement.
10. Alice is somewhere to the right of the person's child is named Fred.
11. The person who uses an iPhone 13 is directly left of the Dunhill smoker.
12. The person who loves the rose bouquet is somewhere to the right of the Dunhill smoker.
13. The person who loves the rose bouquet is somewhere to the left of the person who uses a Google Pixel 6.
 What is the value of attribute PhoneModel for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: google pixel 6


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`
 - Each mother is accompanied by their child: `Bella`, `Meredith`, `Fred`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`, `google pixel 6`
 - People have unique favorite book genres: `romance`, `science fiction`, `mystery`
 - Everyone has a unique favorite cigar: `blue master`, `prince`, `pall mall`
 - People have unique heights: `short`, `very short`, `average`

## Clues:
1. Eric is directly left of the Prince smoker.
2. The person who has an average height is somewhere to the right of Peter.
3. The person who uses a Samsung Galaxy S21 is in the second house.
4. The person who smokes Blue Master is in the third house.
5. The person who uses a Google Pixel 6 is Eric.
6. Arnold is somewhere to the right of the person who loves science fiction books.
7. The person who uses an iPhone 13 is the person's child is named Bella.
8. The person who is short is the Prince smoker.
9. The person who loves mystery books is the person who uses a Google Pixel 6.
10. The person's child is named Meredith and the person who is short are next to each other.
 What is the value of attribute Children for the person whose attribute Height is short? Please reason step by step, and put your final answer within \boxed{}

Answer: Fred


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Alice`, `Bob`, `Arnold`, `Carol`
 - Everyone has a unique favorite cigar: `yellow monster`, `blends`, `prince`, `dunhill`, `pall mall`, `blue master`
 - People use unique phone models: `xiaomi mi 11`, `iphone 13`, `google pixel 6`, `huawei p50`, `samsung galaxy s21`, `oneplus 9`
 - People own unique car models: `bmw 3 series`, `honda civic`, `tesla model 3`, `ford f150`, `chevrolet silverado`, `toyota camry`
 - The people are of nationalities: `dane`, `brit`, `chinese`, `swede`, `norwegian`, `german`

## Clues:
1. The person who uses a Xiaomi Mi 11 is somewhere to the left of the person who uses a Google Pixel 6.
2. Carol is somewhere to the left of the person who owns a Ford F-150.
3. Peter is not in the second house.
4. There is one house between the Dane and the person who uses a Google Pixel 6.
5. The Chinese is the person who uses a Google Pixel 6.
6. The person who smokes many unique blends is somewhere to the right of the person who owns a Honda Civic.
7. The person who owns a Tesla Model 3 is in the fourth house.
8. The person who uses a Samsung Galaxy S21 is Alice.
9. There is one house between the person who uses a Xiaomi Mi 11 and the person who smokes Blue Master.
10. The person partial to Pall Mall is directly left of the person who uses a Samsung Galaxy S21.
11. The person who smokes many unique blends is the German.
12. The person who owns a Chevrolet Silverado is the Prince smoker.
13. The person who owns a BMW 3 Series is Eric.
14. The person who owns a Ford F-150 is directly left of Bob.
15. The person who smokes Yellow Monster is not in the second house.
16. The Swedish person is somewhere to the right of the person who smokes Yellow Monster.
17. The person who owns a Chevrolet Silverado is directly left of the person who uses a Huawei P50.
18. The person who smokes Blue Master is in the fifth house.
19. The person who smokes Blue Master is directly left of the person who uses a OnePlus 9.
20. The Norwegian is the person who owns a Toyota Camry.
 What is the value of attribute CarModel for the person whose attribute Cigar is pall mall? Please reason step by step, and put your final answer within \boxed{}

Answer: tesla model 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`, `Bob`, `Carol`
 - Everyone has a favorite smoothie: `cherry`, `blueberry`, `desert`, `lime`, `dragonfruit`, `watermelon`
 - People have unique favorite music genres: `rock`, `classical`, `jazz`, `pop`, `country`, `hip hop`
 - People have unique favorite book genres: `science fiction`, `romance`, `historical fiction`, `fantasy`, `mystery`, `biography`
 - Each person has a favorite color: `yellow`, `white`, `green`, `blue`, `red`, `purple`

## Clues:
1. The person who loves purple and the Dragonfruit smoothie lover are next to each other.
2. The person who loves classical music is in the fifth house.
3. Eric is somewhere to the left of the person who loves classical music.
4. The person who loves hip-hop music is directly left of the Desert smoothie lover.
5. The person who loves yellow is the person who loves science fiction books.
6. Arnold is the person who loves rock music.
7. Carol is the person who likes Cherry smoothies.
8. There are two houses between the person who loves jazz music and the Watermelon smoothie lover.
9. The person whose favorite color is green is somewhere to the right of the person who loves jazz music.
10. The person who drinks Blueberry smoothies is directly left of the Watermelon smoothie lover.
11. Arnold is somewhere to the left of the Watermelon smoothie lover.
12. Bob is somewhere to the left of the person who loves yellow.
13. Bob is the person who loves historical fiction books.
14. The person who loves biography books is the person who loves pop music.
15. The person who loves romance books is in the fifth house.
16. There are two houses between Bob and the person who loves mystery books.
17. The person who loves white is the person who loves historical fiction books.
18. Peter is somewhere to the left of the person who loves blue.
19. There is one house between the person who loves biography books and the person who loves yellow.
 What is the value of attribute Name for the person whose attribute BookGenre is romance? 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: `Eric`, `Carol`, `Bob`, `Peter`, `Arnold`, `Alice`
 - Everyone has something unique for lunch: `stew`, `stir fry`, `soup`, `grilled cheese`, `pizza`, `spaghetti`
 - Each person has a unique favorite drink: `root beer`, `milk`, `boba tea`, `water`, `coffee`, `tea`
 - People have unique heights: `super tall`, `short`, `tall`, `very short`, `very tall`, `average`
 - Each person has a unique birthday month: `sept`, `feb`, `may`, `mar`, `jan`, `april`

## Clues:
1. The person whose birthday is in January is Peter.
2. The person who loves eating grilled cheese is the person whose birthday is in May.
3. The person whose birthday is in April is the person who loves stir fry.
4. The person who loves the stew is the one who only drinks water.
5. The person whose birthday is in September is not in the fourth house.
6. The person who likes milk is somewhere to the left of the person who loves stir fry.
7. The coffee drinker is in the fifth house.
8. The person who loves eating grilled cheese is directly left of the one who only drinks water.
9. The person whose birthday is in May is directly left of Arnold.
10. The root beer lover is somewhere to the left of Alice.
11. There are two houses between Eric and the person who is a pizza lover.
12. The person who loves the spaghetti eater is the person who is very short.
13. The person who is super tall is the tea drinker.
14. The person who is tall is not in the third house.
15. Peter is directly left of the person who is a pizza lover.
16. The person who likes milk is somewhere to the right of the one who only drinks water.
17. The person who is very short is the coffee drinker.
18. The person who is super tall is Bob.
19. The person who is super tall and the person whose birthday is in March are next to each other.
20. Carol is somewhere to the left of the person who has an average height.
21. The person who is very tall is the person who loves the stew.
22. There is one house between the person who loves eating grilled cheese and Peter.
 What is the value of attribute Drink for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: water


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`, `Alice`, `Bob`
 - Each person prefers a unique type of vacation: `beach`, `mountain`, `cruise`, `city`, `camping`
 - Each person lives in a unique style of house: `ranch`, `modern`, `craftsman`, `colonial`, `victorian`
 - Each person has a unique level of education: `bachelor`, `doctorate`, `master`, `associate`, `high school`
 - The mothers' names in different houses are unique: `Aniya`, `Kailyn`, `Janelle`, `Penny`, `Holly`

## Clues:
1. The person whose mother's name is Aniya is the person in a ranch-style home.
2. The person in a Craftsman-style house is Bob.
3. The person with a high school diploma is not in the fourth house.
4. Arnold and the person in a Craftsman-style house are next to each other.
5. Arnold is The person whose mother's name is Penny.
6. The person with an associate's degree is somewhere to the left of the person with a master's degree.
7. Bob and Peter are next to each other.
8. The person living in a colonial-style house is The person whose mother's name is Penny.
9. The person whose mother's name is Holly is the person who enjoys camping trips.
10. The person with a doctorate is the person who prefers city breaks.
11. The person with a bachelor's degree is The person whose mother's name is Aniya.
12. The person with an associate's degree is somewhere to the right of Eric.
13. Arnold is directly left of the person who likes going on cruises.
14. The person who enjoys camping trips is somewhere to the right of the person residing in a Victorian house.
15. The person who enjoys mountain retreats is in the first house.
16. The person whose mother's name is Janelle is the person with an associate's degree.
17. The person with an associate's degree is directly left of Arnold.
 What is the value of attribute House for the person whose attribute Education is high school? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


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

Answer: roses


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Carol`, `Alice`, `Eric`, `Bob`
 - People have unique favorite book genres: `mystery`, `science fiction`, `fantasy`, `romance`, `biography`, `historical fiction`
 - Everyone has a unique favorite cigar: `dunhill`, `blends`, `yellow monster`, `prince`, `blue master`, `pall mall`
 - The people are of nationalities: `brit`, `swede`, `chinese`, `dane`, `german`, `norwegian`
 - Each person has a unique type of pet: `bird`, `rabbit`, `fish`, `cat`, `hamster`, `dog`

## Clues:
1. The person with an aquarium of fish is in the first house.
2. The person who owns a dog is not in the third house.
3. The British person is the person who loves historical fiction books.
4. Bob is the person who owns a dog.
5. The person with a pet hamster is the British person.
6. Eric is in the sixth house.
7. There is one house between the person who smokes Yellow Monster and the person who owns a dog.
8. Alice is directly left of the person who has a cat.
9. The British person is directly left of the person who smokes Blue Master.
10. Carol is in the second house.
11. The person who loves fantasy books is the Swedish person.
12. The person who loves romance books is directly left of the Dunhill smoker.
13. The person partial to Pall Mall is the Swedish person.
14. The Prince smoker is the Chinese.
15. The person who loves biography books is somewhere to the left of the British person.
16. The person who loves science fiction books is in the fourth house.
17. The British person is Alice.
18. The Norwegian is the person who loves biography books.
19. The Dane and the Dunhill smoker are next to each other.
20. Peter is not in the third house.
21. The person who owns a rabbit is the person who loves romance books.
 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 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Carol`, `Bob`, `Peter`, `Eric`, `Arnold`
 - They all have a unique favorite flower: `lilies`, `tulips`, `roses`, `daffodils`, `iris`, `carnations`
 - The people are of nationalities: `norwegian`, `dane`, `swede`, `german`, `brit`, `chinese`
 - Everyone has a favorite smoothie: `cherry`, `watermelon`, `desert`, `dragonfruit`, `blueberry`, `lime`
 - Each person has a unique hobby: `photography`, `cooking`, `knitting`, `woodworking`, `painting`, `gardening`
 - Each person has a unique type of pet: `rabbit`, `hamster`, `fish`, `cat`, `bird`, `dog`

## Clues:
1. The Swedish person is the person who loves cooking.
2. The person who drinks Blueberry smoothies is Alice.
3. The person who loves the rose bouquet is not in the sixth house.
4. The photography enthusiast is somewhere to the right of the Dragonfruit smoothie lover.
5. The person who loves cooking is the person who loves a bouquet of daffodils.
6. The person who loves the boquet of lilies and the person who loves the boquet of iris are next to each other.
7. The person who paints as a hobby is Alice.
8. Arnold is somewhere to the right of the Watermelon smoothie lover.
9. The woodworking hobbyist is somewhere to the right of the German.
10. The woodworking hobbyist is somewhere to the left of the person who loves a bouquet of daffodils.
11. The Dane is the Watermelon smoothie lover.
12. The Dragonfruit smoothie lover is Peter.
13. The person who drinks Lime smoothies is the woodworking hobbyist.
14. There is one house between the Watermelon smoothie lover and the person who likes Cherry smoothies.
15. The person who keeps a pet bird is the person who drinks Blueberry smoothies.
16. The Desert smoothie lover is the person who enjoys gardening.
17. The person with a pet hamster is in the fifth house.
18. The person who owns a dog is the Norwegian.
19. The person who has a cat is somewhere to the right of Bob.
20. The British person is directly left of Carol.
21. The person who loves the boquet of iris is Arnold.
22. The German is somewhere to the right of the person who loves a carnations arrangement.
23. Bob is the photography enthusiast.
24. The person with an aquarium of fish is Arnold.
 What is the value of attribute Pet for the person whose attribute Smoothie is lime? Please reason step by step, and put your final answer within \boxed{}

Answer: fish


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

## Clues:
1. Alice is the person who loves cooking.
2. Bob is not in the second house.
3. The person who enjoys gardening is the person who smokes Blue Master.
4. The person partial to Pall Mall is the person who enjoys knitting.
5. The person who enjoys gardening is directly left of the Dunhill smoker.
6. The person who smokes many unique blends is directly left of Carol.
7. The person partial to Pall Mall is directly left of Bob.
8. The Dunhill smoker is the person who paints as a hobby.
9. The person who smokes Yellow Monster is in the second house.
10. The woodworking hobbyist is somewhere to the right of the Dunhill smoker.
11. Eric is somewhere to the left of the person who enjoys gardening.
12. There are two houses between the photography enthusiast and Peter.
 What is the value of attribute Hobby for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: painting


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Peter`
 - People have unique favorite music genres: `pop`, `rock`, `jazz`, `classical`
 - Everyone has something unique for lunch: `pizza`, `stew`, `grilled cheese`, `spaghetti`
 - Each person has a unique level of education: `master`, `associate`, `bachelor`, `high school`
 - Each mother is accompanied by their child: `Samantha`, `Bella`, `Meredith`, `Fred`

## Clues:
1. The person's child is named Samantha is in the second house.
2. Arnold is the person's child is named Samantha.
3. The person who loves the spaghetti eater is directly left of the person with a master's degree.
4. The person who loves eating grilled cheese is the person who loves classical music.
5. The person who loves the stew is the person's child is named Bella.
6. The person who loves pop music is Alice.
7. The person who loves jazz music is directly left of the person's child is named Samantha.
8. The person with a high school diploma is Arnold.
9. The person with a bachelor's degree is Peter.
10. The person who loves the spaghetti eater is the person with an associate's degree.
11. The person who loves classical music is the person's child is named Fred.
 What is the value of attribute House for the person whose attribute Education is master? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Arnold`, `Eric`
 - The people keep unique animals: `cat`, `fish`, `bird`, `horse`
 - People have unique favorite sports: `soccer`, `swimming`, `tennis`, `basketball`
 - People have unique hair colors: `blonde`, `brown`, `black`, `red`
 - Each person has a unique type of pet: `bird`, `fish`, `dog`, `cat`

## Clues:
1. The person who loves tennis is in the second house.
2. The person who has brown hair and the person who loves basketball are next to each other.
3. Alice is the person who keeps a pet bird.
4. Arnold is the person who loves soccer.
5. The person who has blonde hair is the person with an aquarium of fish.
6. The person who keeps a pet bird is in the second house.
7. Arnold is in the third house.
8. The person who loves swimming is in the first house.
9. The person who has red hair is not in the first house.
10. The person who keeps horses is in the fourth house.
11. Eric is somewhere to the left of the fish enthusiast.
12. The person who has a cat is directly left of the bird keeper.
 What is the value of attribute FavoriteSport for the person whose attribute HairColor is red? Please reason step by step, and put your final answer within \boxed{}

Answer: tennis


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Eric`, `Arnold`, `Peter`, `Alice`
 - Everyone has a unique favorite cigar: `blends`, `prince`, `pall mall`, `blue master`, `dunhill`
 - Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `stew`, `pizza`, `stir fry`
 - The people are of nationalities: `norwegian`, `swede`, `brit`, `dane`, `german`
 - Each person has an occupation: `teacher`, `lawyer`, `doctor`, `artist`, `engineer`
 - People have unique heights: `average`, `very tall`, `short`, `very short`, `tall`

## Clues:
1. The person who smokes Blue Master is the person who is a lawyer.
2. Alice is the person partial to Pall Mall.
3. The person partial to Pall Mall is somewhere to the left of the Dunhill smoker.
4. The German is the person who loves stir fry.
5. The person who is tall is the person who smokes many unique blends.
6. The person who is an artist is the person who loves the spaghetti eater.
7. Peter is the person who is short.
8. The Dunhill smoker is not in the fourth house.
9. The person who is very short is the person who smokes Blue Master.
10. There are two houses between the person who loves the spaghetti eater and the person who loves stir fry.
11. The person who has an average height is in the second house.
12. The Prince smoker is the person who is a doctor.
13. The Swedish person is the person who is an engineer.
14. Eric is the person who loves stir fry.
15. There is one house between the British person and the person who loves the stew.
16. The person who is very tall is the Norwegian.
17. The Dane is the person who is short.
18. The person who is very tall is Arnold.
19. There are two houses between the person who is a pizza lover and the person who is very tall.
20. The person who is a teacher is not in the third house.
 What is the value of attribute Nationality for the person whose attribute Food is grilled cheese? Please reason step by step, and put your final answer within \boxed{}

Answer: norwegian


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`
 - Each person has a unique level of education: `bachelor`, `associate`, `high school`, `master`

## Clues:
1. There is one house between Eric and the person with a high school diploma.
2. There is one house between the person with an associate's degree and the person with a master's degree.
3. The person with an associate's degree is not in the fourth house.
4. The person with a high school diploma is directly left of Arnold.
5. Peter is in the third house.
 What is the value of attribute Education for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: high school


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`, `Peter`, `Bob`, `Arnold`
 - People have unique favorite sports: `soccer`, `baseball`, `swimming`, `tennis`, `basketball`
 - Each person lives in a unique style of house: `modern`, `victorian`, `colonial`, `craftsman`, `ranch`
 - Each person prefers a unique type of vacation: `beach`, `city`, `cruise`, `mountain`, `camping`
 - Each person has an occupation: `artist`, `engineer`, `lawyer`, `doctor`, `teacher`
 - The mothers' names in different houses are unique: `Penny`, `Aniya`, `Janelle`, `Holly`, `Kailyn`

## Clues:
1. There is one house between The person whose mother's name is Janelle and Eric.
2. Arnold is not in the fifth house.
3. The person whose mother's name is Janelle is Peter.
4. The person who enjoys mountain retreats is The person whose mother's name is Holly.
5. The person whose mother's name is Aniya is the person in a modern-style house.
6. The person who likes going on cruises is The person whose mother's name is Kailyn.
7. The person who prefers city breaks is the person living in a colonial-style house.
8. The person who loves soccer is The person whose mother's name is Holly.
9. The person who is an artist is Eric.
10. The person who is a doctor is in the second house.
11. The person who is a teacher is somewhere to the left of the person in a modern-style house.
12. The person whose mother's name is Penny is not in the second house.
13. The person in a ranch-style home is in the third house.
14. The person who loves swimming is The person whose mother's name is Kailyn.
15. Arnold is not in the third house.
16. The person who loves swimming is in the fourth house.
17. The person who loves baseball and the person who prefers city breaks are next to each other.
18. The person who loves basketball is somewhere to the left of the person who loves soccer.
19. Bob is somewhere to the left of the person in a modern-style house.
20. The person who enjoys camping trips is in the fifth house.
21. The person in a Craftsman-style house is the person who is an engineer.
22. There are two houses between the person living in a colonial-style house and the person in a modern-style house.
 What is the value of attribute FavoriteSport for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: swimming


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

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

Answer: victorian


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`, `Arnold`, `Peter`
 - Each person has a unique favorite drink: `milk`, `tea`, `coffee`, `water`
 - The people keep unique animals: `horse`, `bird`, `fish`, `cat`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`

## Clues:
1. Peter is the cat lover.
2. The fish enthusiast is not in the third house.
3. The person who loves beach vacations is the person who keeps horses.
4. The fish enthusiast is not in the fourth house.
5. The coffee drinker is directly left of the bird keeper.
6. The one who only drinks water is Eric.
7. The tea drinker is somewhere to the right of Peter.
8. Eric is not in the second house.
9. The person who loves beach vacations is somewhere to the right of Peter.
10. The person who loves beach vacations is Alice.
11. The cat lover is somewhere to the left of the person who likes going on cruises.
12. The person who keeps horses is directly left of the person who enjoys mountain retreats.
 What is the value of attribute House for the person whose attribute Animal is bird? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Eric`, `Arnold`
 - The people keep unique animals: `horse`, `cat`, `fish`, `bird`
 - People use unique phone models: `oneplus 9`, `google pixel 6`, `iphone 13`, `samsung galaxy s21`
 - Each person has a favorite color: `red`, `white`, `yellow`, `green`
 - Each person lives in a unique style of house: `colonial`, `victorian`, `ranch`, `craftsman`

## Clues:
1. The fish enthusiast is the person who uses an iPhone 13.
2. Alice is in the fourth house.
3. Peter is in the first house.
4. The person residing in a Victorian house is the person whose favorite color is red.
5. The person who loves white is the person in a Craftsman-style house.
6. The person whose favorite color is green is in the fourth house.
7. The person living in a colonial-style house is Eric.
8. The bird keeper is Peter.
9. The person who uses a Google Pixel 6 is in the fourth house.
10. The person who loves white is the person who uses a Samsung Galaxy S21.
11. The person living in a colonial-style house is the cat lover.
12. Eric is not in the third house.
 What is the value of attribute 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: `Peter`, `Eric`, `Arnold`, `Alice`
 - Each person has a unique birthday month: `april`, `sept`, `jan`, `feb`
 - Everyone has a unique favorite cigar: `dunhill`, `prince`, `pall mall`, `blue master`
 - People use unique phone models: `google pixel 6`, `samsung galaxy s21`, `oneplus 9`, `iphone 13`
 - They all have a unique favorite flower: `lilies`, `roses`, `carnations`, `daffodils`
 - People have unique heights: `average`, `short`, `tall`, `very short`

## Clues:
1. The person who loves a bouquet of daffodils is Arnold.
2. The person whose birthday is in April is directly left of the person who smokes Blue Master.
3. The person who is short is the person who uses an iPhone 13.
4. The person who uses a Samsung Galaxy S21 is the person who is tall.
5. Eric is the person who uses a OnePlus 9.
6. The person who uses a Samsung Galaxy S21 is directly left of the person who uses a Google Pixel 6.
7. The person whose birthday is in February is Alice.
8. The Prince smoker is somewhere to the right of the person who is short.
9. The Prince smoker is the person whose birthday is in February.
10. The person who uses a OnePlus 9 is directly left of the person who loves the rose bouquet.
11. The person partial to Pall Mall is somewhere to the left of the person who loves the boquet of lilies.
12. The person who has an average height and the person whose birthday is in September are next to each other.
13. The person who loves a bouquet of daffodils is in the fourth house.
 What is the value of attribute House for the person whose attribute Flower is daffodils? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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

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

Answer: toyota camry


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`, `Alice`, `Bob`, `Carol`
 - Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `lime`, `desert`, `blueberry`, `watermelon`
 - Each person has a unique type of pet: `rabbit`, `fish`, `bird`, `hamster`, `cat`, `dog`
 - Each person has a unique level of education: `master`, `bachelor`, `high school`, `trade school`, `associate`, `doctorate`
 - People have unique heights: `short`, `very tall`, `very short`, `tall`, `average`, `super tall`

## Clues:
1. The person with an aquarium of fish is in the first house.
2. The person with a doctorate is somewhere to the left of the person who owns a dog.
3. Peter and the person with a high school diploma are next to each other.
4. There is one house between the person with a pet hamster and the person who owns a rabbit.
5. The person who has a cat is Eric.
6. Bob and the person who owns a dog are next to each other.
7. The person who is tall is Carol.
8. The person with a master's degree is the person with a pet hamster.
9. Peter is the person who is very tall.
10. The person who likes Cherry smoothies is the person who is very tall.
11. The person who is super tall is somewhere to the right of Arnold.
12. The Watermelon smoothie lover is in the sixth house.
13. The person who is super tall is the Desert smoothie lover.
14. The person who is very short is the person with an associate's degree.
15. The person with an associate's degree and the Watermelon smoothie lover are next to each other.
16. The person who drinks Lime smoothies is the person with a pet hamster.
17. The person who is short is in the second house.
18. The person who drinks Blueberry smoothies is the person who attended trade school.
19. The person who is very short is somewhere to the right of Bob.
 What is the value of attribute Height for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: short


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`, `Peter`, `Alice`, `Carol`, `Arnold`, `Eric`
 - Each person has a unique favorite drink: `milk`, `coffee`, `tea`, `root beer`, `boba tea`, `water`
 - They all have a unique favorite flower: `iris`, `roses`, `carnations`, `daffodils`, `lilies`, `tulips`
 - Each person has a unique birthday month: `sept`, `jan`, `feb`, `april`, `may`, `mar`
 - Each person has a unique hobby: `photography`, `cooking`, `woodworking`, `gardening`, `knitting`, `painting`

## Clues:
1. The root beer lover is in the fifth house.
2. The person whose birthday is in February is Peter.
3. The boba tea drinker is not in the fourth house.
4. The person who loves the boquet of iris is somewhere to the right of the person whose birthday is in April.
5. The coffee drinker is Arnold.
6. Eric is the photography enthusiast.
7. The person who paints as a hobby is the person who loves the vase of tulips.
8. The person whose birthday is in April is in the third house.
9. The tea drinker is the person who loves a bouquet of daffodils.
10. There are two houses between the person who loves the boquet of lilies and the person who likes milk.
11. The person whose birthday is in March is somewhere to the left of the person who enjoys gardening.
12. There are two houses between the person who loves a bouquet of daffodils and the person who paints as a hobby.
13. The person whose birthday is in February is in the fourth house.
14. The person who loves cooking is not in the fourth house.
15. The person who enjoys gardening is somewhere to the left of the person who loves a carnations arrangement.
16. The person whose birthday is in January is Bob.
17. Carol is the person whose birthday is in April.
18. The woodworking hobbyist is in the second house.
19. The person who likes milk is in the sixth house.
20. Peter is the person who loves a carnations arrangement.
21. The person whose birthday is in May is the woodworking hobbyist.
 What is the value of attribute Hobby for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: gardening


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`
 - Everyone has a unique favorite cigar: `pall mall`, `dunhill`, `blue master`, `prince`
 - Each person has a unique birthday month: `sept`, `april`, `feb`, `jan`
 - Each person has a unique hobby: `gardening`, `cooking`, `photography`, `painting`
 - People have unique favorite music genres: `pop`, `classical`, `jazz`, `rock`

## Clues:
1. The person who loves jazz music is the person whose birthday is in April.
2. Alice is the person whose birthday is in April.
3. Peter is directly left of the person who loves cooking.
4. The person whose birthday is in February is Arnold.
5. The Dunhill smoker is not in the third house.
6. The Prince smoker is Arnold.
7. The person who loves jazz music is the person partial to Pall Mall.
8. The person whose birthday is in January is not in the third house.
9. The person who loves rock music is Peter.
10. The person who enjoys gardening is directly left of the photography enthusiast.
11. The person who loves classical music is in the first house.
12. The person who loves pop music is somewhere to the left of the person partial to Pall Mall.
13. The person who smokes Blue Master is the person who loves pop music.
 What is the value of attribute MusicGenre for the person whose attribute Birthday is jan? Please reason step by step, and put your final answer within \boxed{}

Answer: rock


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 favorite color: `red`, `white`, `yellow`, `green`
 - Each person has a unique birthday month: `feb`, `sept`, `jan`, `april`
 - The mothers' names in different houses are unique: `Aniya`, `Janelle`, `Kailyn`, `Holly`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`, `blue master`, `dunhill`
 - They all have a unique favorite flower: `lilies`, `daffodils`, `carnations`, `roses`

## Clues:
1. The person who loves yellow is directly left of The person whose mother's name is Kailyn.
2. The person whose birthday is in September and Peter are next to each other.
3. The person whose favorite color is red is not in the fourth house.
4. The person who smokes Blue Master and Arnold are next to each other.
5. The person whose mother's name is Holly is the Dunhill smoker.
6. The person whose birthday is in January is the person who loves a bouquet of daffodils.
7. There are two houses between the person who loves the boquet of lilies and the person whose birthday is in January.
8. The person whose mother's name is Janelle is the person who loves a carnations arrangement.
9. The person whose birthday is in September and the person whose favorite color is red are next to each other.
10. The person whose birthday is in February is the person whose favorite color is green.
11. The person whose favorite color is green is directly left of The person whose mother's name is Janelle.
12. There is one house between the person whose birthday is in February and the person partial to Pall Mall.
13. The person who smokes Blue Master is The person whose mother's name is Aniya.
14. Eric is the person whose birthday is in February.
 What is the value of attribute Mother for the person whose attribute Cigar is prince? Please reason step by step, and put your final answer within \boxed{}

Answer: Janelle


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Arnold`, `Bob`, `Alice`, `Eric`, `Peter`
 - People use unique phone models: `xiaomi mi 11`, `iphone 13`, `huawei p50`, `google pixel 6`, `oneplus 9`, `samsung galaxy s21`
 - People have unique favorite book genres: `science fiction`, `fantasy`, `mystery`, `historical fiction`, `romance`, `biography`

## Clues:
1. Bob is somewhere to the left of the person who uses a Samsung Galaxy S21.
2. The person who uses a OnePlus 9 is Alice.
3. The person who loves romance books is Alice.
4. The person who loves biography books is Bob.
5. The person who loves science fiction books is Arnold.
6. Eric is somewhere to the left of the person who uses a Google Pixel 6.
7. There is one house between Eric and Peter.
8. The person who loves fantasy books is Carol.
9. The person who loves science fiction books and the person who uses a Huawei P50 are next to each other.
10. The person who uses a Huawei P50 and the person who loves fantasy books are next to each other.
11. The person who loves romance books is directly left of the person who loves science fiction books.
12. The person who uses a Xiaomi Mi 11 is in the sixth house.
13. The person who loves historical fiction books is not in the fourth house.
 What is the value of attribute BookGenre for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: historical fiction


As shown in the figure, in the right triangle $ABC$, point $F$ is on $AB$ such that $AF = 2FB$. The quadrilateral $EBCD$ is a parallelogram. What is the ratio $FD: EF$?

Answer: 2:1


A pot contains $3 \pi$ liters of water taken at a temperature of $t=0{ }^{\circ} C$ and brought to a boil in 12 minutes. After this, without removing the pot from the stove, ice at a temperature of $t=0{ }^{\circ} C$ is added. The next time the water begins to boil is after 15 minutes. Determine the mass of the added ice. The specific heat capacity of water is $c_{B}=4200 \, \text{J} / \text{kg} \cdot { }^{\circ} \mathrm{C}$, the specific heat of fusion of ice is $\lambda=3.3 \times 10^{5} \, \text{J} / \text{kg}$, the density of water is $\rho = 1000 \, \text{kg} / \text{m}^{3}$.

Answer: 2.1 kg

Answer: 2.1 \, \text{kg}


A $72 \mathrm{db}$ $4,5 \mathrm{~V}$ $2 \Omega$ internal resistance batteries are connected together. How should we connect them so that the current through an external resistance of $R=36 \Omega$ is

a) maximum,

b) minimum?

What are the values of these currents? (Only consider configurations consisting of series-connected groups of equal numbers of batteries connected in parallel.)

Answer: 0.125 \text{ A}


Let \( f:[0,1] \rightarrow \mathbb{R} \) be continuous and satisfy:

\[
\begin{aligned}
b f(2 x) & = f(x), & & 0 \leq x \leq 1/2 ; \\
f(x) & = b + (1-b) f(2 x - 1), & & 1/2 \leq x \leq 1,
\end{aligned}
\]

where \( b=\frac{1+c}{2+c}, \, c>0 \). Show that \( 0 < f(x) - x < c \) for every \( x \), \( 0 < x < 1 \).

Answer: 0 < f(x) - x <c


The numbers 0 and 1 are placed in the cells of the table as shown in the figure.

| 0 | 1 | 0 | 0 |
| - | - | - | - |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 |

Permissible actions:

- Add one to all numbers in a row;
- Add one to all numbers in a column;
- Add one to all numbers along a line parallel to any diagonal (in particular, you can add one to the number in any corner cell).

Is it possible, as a result of several such actions, to obtain a table in which all numbers are equal?

Answer: \text{No}


A tourist travels from point \(A\) to point \(B\) in 1 hour and 56 minutes. The route from \(A\) to \(B\) first goes uphill, then on flat terrain, and finally downhill. What is the length of the flat terrain if the tourist's speed downhill is 6 km/h, uphill is 4 km/h, and on flat terrain is 5 km/h, and the total distance between \(A\) and \(B\) is \(x\) km? The distances uphill and on flat terrain are both whole numbers of kilometers.

Answer: 3


The cube $ABCDEFGH$ standing on a table has its three vertical edges divided by points $K, L$, and $M$ in the ratios $1:2$, $1:3$, and $1:4$, respectively, as shown in the figure. The plane $KLM$ cuts the cube into two parts. What is the ratio of the volumes of the two parts?

Answer: \frac{4}{11}


Masha's school lessons usually end at 13:00, and her mother picks her up by car to go home. One day, lessons ended at 12:00, and Masha decided to walk home. On her way, she met her mother, who as usual was on her way to pick Masha up at 13:00. They then continued their journey home by car and arrived 12 minutes earlier than usual. At what time did Masha meet her mother on the road? (Assume that both Masha and her mother travel at constant speeds and that no time is spent for Masha to get into the car.)

Answer: 12:54


The given quadratic polynomial \( f(x) \) has two distinct roots. Can it be the case that the equation \( f(f(x)) = 0 \) has three distinct roots, while the equation \( f(f(f(x))) = 0 \) has seven distinct roots?

Answer: \text{No}


A sphere of radius 4 with center at point $Q$ touches three parallel lines at points $F$, $G$, and $H$. It is known that the area of triangle $QGH$ is $4 \sqrt{2}$, and the area of triangle $FGH$ is greater than 16. Find the angle $GFH$.

Answer: 67.5^\circ


A 99-sided polygon has its sides painted in sequence with the colors red, blue, red, blue, $\cdots$, red, blue, yellow. Each side is painted in one color. Then, the following operation is allowed: ensuring that any two adjacent sides have different colors, one can change the color of one side each time. Can the coloring of the 99 sides be changed to red, blue, red, blue, $\cdots$, red, yellow, blue after a number of operations?

Answer: \text{No}


Let \(R\) be the rectangle in the Cartesian plane with vertices at \((0,0), (2,0), (2,1)\), and \((0,1)\). The resulting figure has 7 segments of unit length, connecting neighboring lattice points (those lying on or inside \(R\)). Compute the number of paths from \((0,1)\) (the upper left corner) to \((2,0)\) (the lower right corner) along these 7 segments, where each segment can be used at most once.

Answer: 4


Fold a rectangular piece of paper which is 16 cm long and 12 cm wide as shown in the figure. Find the length of the crease \( GF \) in cm.

Answer: 15


$n$ trains travel in the same direction along a circular track at equal intervals. Stations $A$, $B$, and $C$ are located at the vertices of an equilateral triangle along this track (in the direction of travel). Ira boards at station $A$ and Alex boards at station $B$ to catch the nearest trains. It is known that if they arrive at the stations just as the engineer Roma is passing through the forest, then Ira will board a train before Alex; otherwise, Alex boards before Ira or at the same time. What portion of the track passes through the forest?

Answer: \frac{1}{3}


Given a rectangular prism with a base $A B C D$ and a top face parallel midpoint line $E F$ where the midpoint of this segment is $G$. The reflection of point $X$ on segment $E G$ across point $G$ is $Y$. For which position of point $X$ will the sum $A X + D X + X Y + Y B + Y C$ be minimized?

Answer: x = G


A triangle \( EGF \) is inscribed in a circle with center \( O \), and the angle \( \angle EFG \) is obtuse. There exists a point \( L \) outside the circle such that \( \angle LEF = \angle FEG \) and \( \angle LGF = \angle FGE \). Find the radius of the circumcircle of triangle \( ELG \), given that the area of triangle \( EGO \) is \( 81 \sqrt{3} \) and \( \angle OEG = 60^\circ \).

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

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

Answer: 3


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`, `Alice`
 - The mothers' names in different houses are unique: `Holly`, `Kailyn`, `Aniya`, `Janelle`
 - People have unique favorite book genres: `science fiction`, `mystery`, `fantasy`, `romance`
 - Each person has a favorite color: `green`, `red`, `white`, `yellow`
 - Each person prefers a unique type of vacation: `mountain`, `cruise`, `beach`, `city`

## Clues:
1. The person who loves romance books and the person who likes going on cruises are next to each other.
2. Arnold is The person whose mother's name is Janelle.
3. The person who prefers city breaks is the person who loves yellow.
4. The person who loves science fiction books is directly left of Peter.
5. The person who loves science fiction books is somewhere to the left of The person whose mother's name is Kailyn.
6. The person who loves beach vacations is not in the first house.
7. There is one house between Alice and the person who likes going on cruises.
8. The person who loves mystery books is the person who loves white.
9. Peter is the person who prefers city breaks.
10. The person whose favorite color is green is in the third house.
11. The person whose mother's name is Aniya is Peter.
12. The person whose favorite color is green is The person whose mother's name is Janelle.
 What is the value of attribute Mother for the person whose attribute BookGenre is mystery? Please reason step by step, and put your final answer within \boxed{}

Answer: Kailyn


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`, `Peter`, `Alice`, `Arnold`
 - Everyone has something unique for lunch: `spaghetti`, `stew`, `grilled cheese`, `soup`, `stir fry`, `pizza`

## Clues:
1. The person who loves stir fry is somewhere to the left of the person who is a pizza lover.
2. There is one house between Bob and the person who loves the soup.
3. The person who loves stir fry is Carol.
4. Arnold is in the fourth house.
5. Bob is in the first house.
6. The person who loves the spaghetti eater is in the fifth house.
7. Alice is in the third house.
8. Peter is the person who loves eating grilled cheese.
 What is the value of attribute Food for the person whose attribute House is 6? Please reason step by step, and put your final answer within \boxed{}

Answer: grilled cheese


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`, `Arnold`, `Peter`
 - Each person has a unique favorite drink: `milk`, `tea`, `coffee`, `water`
 - The people keep unique animals: `horse`, `bird`, `fish`, `cat`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`

## Clues:
1. Peter is the cat lover.
2. The fish enthusiast is not in the third house.
3. The person who loves beach vacations is the person who keeps horses.
4. The fish enthusiast is not in the fourth house.
5. The coffee drinker is directly left of the bird keeper.
6. The one who only drinks water is Eric.
7. The tea drinker is somewhere to the right of Peter.
8. Eric is not in the second house.
9. The person who loves beach vacations is somewhere to the right of Peter.
10. The person who loves beach vacations is Alice.
11. The cat lover is somewhere to the left of the person who likes going on cruises.
12. The person who keeps horses is directly left of the person who enjoys mountain retreats.
 What is the value of attribute Name for the person whose attribute Drink is milk? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Alice`, `Arnold`, `Eric`, `Peter`
 - People use unique phone models: `samsung galaxy s21`, `google pixel 6`, `iphone 13`, `huawei p50`, `oneplus 9`, `xiaomi mi 11`
 - The people are of nationalities: `swede`, `chinese`, `norwegian`, `dane`, `german`, `brit`
 - Each person has a favorite color: `blue`, `red`, `yellow`, `green`, `white`, `purple`

## Clues:
1. Carol is not in the third house.
2. There is one house between the Dane and the British person.
3. Carol is the person whose favorite color is green.
4. Arnold is directly left of Alice.
5. Alice is the German.
6. The person who uses a OnePlus 9 is the person who loves purple.
7. The person who uses a Huawei P50 is not in the third house.
8. The person who uses a Samsung Galaxy S21 is in the fifth house.
9. The person who loves white is somewhere to the right of the person whose favorite color is red.
10. The person who uses a Samsung Galaxy S21 is Bob.
11. The Dane is the person who loves yellow.
12. The person who uses a Samsung Galaxy S21 is somewhere to the left of Peter.
13. The person who loves blue is Peter.
14. Peter is the British person.
15. The person who uses a Samsung Galaxy S21 is directly left of the person who uses an iPhone 13.
16. The Norwegian is the person who loves purple.
17. The person who uses a Xiaomi Mi 11 is the Chinese.
 What is the value of attribute Name for the person whose attribute PhoneModel is iphone 13? 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: `Peter`, `Arnold`, `Carol`, `Alice`, `Eric`, `Bob`
 - People have unique favorite book genres: `mystery`, `science fiction`, `fantasy`, `romance`, `biography`, `historical fiction`
 - Everyone has a unique favorite cigar: `dunhill`, `blends`, `yellow monster`, `prince`, `blue master`, `pall mall`
 - The people are of nationalities: `brit`, `swede`, `chinese`, `dane`, `german`, `norwegian`
 - Each person has a unique type of pet: `bird`, `rabbit`, `fish`, `cat`, `hamster`, `dog`

## Clues:
1. The person with an aquarium of fish is in the first house.
2. The person who owns a dog is not in the third house.
3. The British person is the person who loves historical fiction books.
4. Bob is the person who owns a dog.
5. The person with a pet hamster is the British person.
6. Eric is in the sixth house.
7. There is one house between the person who smokes Yellow Monster and the person who owns a dog.
8. Alice is directly left of the person who has a cat.
9. The British person is directly left of the person who smokes Blue Master.
10. Carol is in the second house.
11. The person who loves fantasy books is the Swedish person.
12. The person who loves romance books is directly left of the Dunhill smoker.
13. The person partial to Pall Mall is the Swedish person.
14. The Prince smoker is the Chinese.
15. The person who loves biography books is somewhere to the left of the British person.
16. The person who loves science fiction books is in the fourth house.
17. The British person is Alice.
18. The Norwegian is the person who loves biography books.
19. The Dane and the Dunhill smoker are next to each other.
20. Peter is not in the third house.
21. The person who owns a rabbit is the person who loves romance books.
 What is the value of attribute Nationality for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: german


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`, `Bob`, `Carol`, `Alice`
 - Each person prefers a unique type of vacation: `cruise`, `beach`, `cultural`, `mountain`, `city`, `camping`
 - People have unique hair colors: `gray`, `black`, `brown`, `blonde`, `auburn`, `red`
 - People use unique phone models: `oneplus 9`, `huawei p50`, `xiaomi mi 11`, `iphone 13`, `google pixel 6`, `samsung galaxy s21`
 - Each person has a unique favorite drink: `root beer`, `boba tea`, `milk`, `coffee`, `tea`, `water`

## Clues:
1. There is one house between the boba tea drinker and Bob.
2. There are two houses between the person who uses a Google Pixel 6 and the person who enjoys camping trips.
3. The person who goes on cultural tours is Carol.
4. The person who enjoys camping trips is Eric.
5. The person who uses a Google Pixel 6 is not in the fifth house.
6. The person who uses a OnePlus 9 and the person who goes on cultural tours are next to each other.
7. The person who has gray hair and the person who goes on cultural tours are next to each other.
8. The person who uses a Samsung Galaxy S21 is somewhere to the right of the person who has red hair.
9. The person who enjoys mountain retreats is somewhere to the right of the person who uses a Xiaomi Mi 11.
10. The person who uses a OnePlus 9 is Peter.
11. The person who likes going on cruises is the person who has brown hair.
12. The coffee drinker is the person who goes on cultural tours.
13. The person who likes milk is directly left of the person who has black hair.
14. The person who uses a Xiaomi Mi 11 is directly left of the person who uses a Samsung Galaxy S21.
15. The person who prefers city breaks is not in the sixth house.
16. The person who has blonde hair is Arnold.
17. The person who goes on cultural tours is not in the sixth house.
18. The one who only drinks water and the person who goes on cultural tours are next to each other.
19. The tea drinker is somewhere to the left of the person who enjoys mountain retreats.
20. The person who likes milk is the person who uses a Huawei P50.
21. The person who has blonde hair is directly left of the person who has gray hair.
22. Bob is not in the third house.
23. Peter is the person who prefers city breaks.
 What is the value of attribute Drink for the person whose attribute PhoneModel is oneplus 9? 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: `Peter`, `Bob`, `Arnold`, `Carol`, `Eric`, `Alice`
 - Everyone has something unique for lunch: `spaghetti`, `stir fry`, `stew`, `soup`, `grilled cheese`, `pizza`
 - Everyone has a unique favorite cigar: `blends`, `pall mall`, `dunhill`, `yellow monster`, `prince`, `blue master`
 - Each person has a unique favorite drink: `boba tea`, `water`, `coffee`, `root beer`, `milk`, `tea`
 - Each person has a unique level of education: `associate`, `bachelor`, `trade school`, `doctorate`, `high school`, `master`

## Clues:
1. Bob is not in the second house.
2. The person who smokes many unique blends is somewhere to the left of the person who is a pizza lover.
3. The person partial to Pall Mall is somewhere to the right of the Dunhill smoker.
4. The person who loves the soup is not in the first house.
5. The person who likes milk is directly left of the person who loves the stew.
6. The person who loves the soup is the person with a doctorate.
7. The coffee drinker is the person with a high school diploma.
8. There are two houses between the person who loves the spaghetti eater and the person with an associate's degree.
9. The Prince smoker is not in the third house.
10. The Dunhill smoker and Bob are next to each other.
11. There are two houses between Alice and the boba tea drinker.
12. The person with a high school diploma is Eric.
13. The person who attended trade school is the Prince smoker.
14. There is one house between the Dunhill smoker and the person who loves stir fry.
15. The Dunhill smoker is directly left of the person who is a pizza lover.
16. There is one house between the person partial to Pall Mall and the person who smokes Blue Master.
17. The person who smokes Blue Master is the coffee drinker.
18. The person with a bachelor's degree is the Dunhill smoker.
19. Alice is the tea drinker.
20. Arnold is directly left of the root beer lover.
21. The person with a master's degree is Peter.
22. Arnold is somewhere to the left of the person who likes milk.
 What is the value of attribute House for the person whose attribute Food is pizza? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`, `Alice`
 - The people keep unique animals: `fish`, `cat`, `horse`, `bird`
 - Everyone has a unique favorite cigar: `pall mall`, `blue master`, `dunhill`, `prince`
 - They all have a unique favorite flower: `lilies`, `roses`, `daffodils`, `carnations`
 - People have unique favorite music genres: `classical`, `jazz`, `rock`, `pop`

## Clues:
1. The Dunhill smoker is Eric.
2. Eric is the cat lover.
3. The person who loves the boquet of lilies is the person who loves pop music.
4. The person partial to Pall Mall is the fish enthusiast.
5. The person who smokes Blue Master is the person who keeps horses.
6. Arnold is not in the third house.
7. The person who loves rock music is somewhere to the left of the person who loves a carnations arrangement.
8. The person who loves classical music is somewhere to the left of the fish enthusiast.
9. The person who loves rock music is Peter.
10. The person who loves jazz music is the person who smokes Blue Master.
11. The person who loves a bouquet of daffodils is in the fourth house.
 What is the value of attribute Cigar for the person whose attribute Animal is bird? Please reason step by step, and put your final answer within \boxed{}

Answer: prince


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`, `Arnold`, `Eric`, `Alice`
 - Everyone has something unique for lunch: `stew`, `stir fry`, `spaghetti`, `grilled cheese`, `pizza`
 - Everyone has a favorite smoothie: `watermelon`, `lime`, `desert`, `dragonfruit`, `cherry`
 - People have unique favorite book genres: `fantasy`, `biography`, `mystery`, `science fiction`, `romance`
 - Each person has a unique hobby: `photography`, `knitting`, `cooking`, `gardening`, `painting`

## Clues:
1. The person who loves stir fry is the Desert smoothie lover.
2. The person who loves the spaghetti eater is the person who enjoys gardening.
3. Bob is somewhere to the left of the person who loves mystery books.
4. The person who paints as a hobby is directly left of Alice.
5. The Desert smoothie lover is the person who loves romance books.
6. The photography enthusiast and the person who loves eating grilled cheese are next to each other.
7. The person who loves cooking is somewhere to the left of the Desert smoothie lover.
8. The person who likes Cherry smoothies is Alice.
9. There is one house between the person who drinks Lime smoothies and the person who enjoys gardening.
10. The Watermelon smoothie lover is Eric.
11. The person who loves eating grilled cheese is directly left of the Dragonfruit smoothie lover.
12. The person who is a pizza lover is Alice.
13. The person who loves romance books is Peter.
14. The person who loves fantasy books is the Watermelon smoothie lover.
15. Alice is the person who loves biography books.
16. Eric is not in the third house.
 What is the value of attribute House for the person whose attribute Hobby is painting? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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

## Clues:
1. The fish enthusiast is somewhere to the right of Eric.
2. The person who is an engineer is Arnold.
3. The person who loves a carnations arrangement is the person in a ranch-style home.
4. Alice is the person in a Craftsman-style house.
5. The person partial to Pall Mall is the person who loves a bouquet of daffodils.
6. The cat lover is Arnold.
7. The Dunhill smoker is Peter.
8. The person living in a colonial-style house is not in the fourth house.
9. The person who is a teacher is the bird keeper.
10. The person residing in a Victorian house is Peter.
11. The person who loves the boquet of lilies is the person who smokes Blue Master.
12. Peter is somewhere to the right of the person who is an artist.
13. The person who is an engineer and the person who is a teacher are next to each other.
14. The person who is a doctor is the person who loves a carnations arrangement.
15. The person partial to Pall Mall is the person living in a colonial-style house.
 What is the value of attribute Cigar for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: prince


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

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

Answer: teacher