There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Carol`, `Eric`, `Alice`, `Bob`, `Arnold`
 - People use unique phone models: `huawei p50`, `google pixel 6`, `xiaomi mi 11`, `iphone 13`, `samsung galaxy s21`, `oneplus 9`
 - Everyone has a unique favorite cigar: `dunhill`, `pall mall`, `blends`, `blue master`, `prince`, `yellow monster`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `roses`, `tulips`, `lilies`, `iris`
 - Each person has a favorite color: `yellow`, `red`, `green`, `blue`, `white`, `purple`
 - People have unique favorite sports: `soccer`, `tennis`, `basketball`, `volleyball`, `swimming`, `baseball`

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

Answer: google pixel 6


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

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

Answer: google pixel 6


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Carol`, `Peter`, `Alice`, `Eric`, `Arnold`
 - They all have a unique favorite flower: `daffodils`, `iris`, `lilies`, `roses`, `tulips`, `carnations`
 - People have unique hair colors: `gray`, `red`, `blonde`, `auburn`, `brown`, `black`
 - Each person has a favorite color: `white`, `blue`, `green`, `purple`, `red`, `yellow`
 - People own unique car models: `tesla model 3`, `ford f150`, `honda civic`, `toyota camry`, `chevrolet silverado`, `bmw 3 series`
 - The mothers' names in different houses are unique: `Janelle`, `Holly`, `Kailyn`, `Sarah`, `Penny`, `Aniya`

## Clues:
1. There is one house between Arnold and the person who loves blue.
2. The person whose mother's name is Janelle is directly left of the person who has auburn hair.
3. The person who owns a Chevrolet Silverado and the person who owns a BMW 3 Series are next to each other.
4. Carol is the person who loves a carnations arrangement.
5. The person who loves the boquet of iris is the person who has gray hair.
6. The person who loves the rose bouquet is The person whose mother's name is Kailyn.
7. Bob is the person who loves the boquet of lilies.
8. The person who loves a bouquet of daffodils is somewhere to the left of the person who owns a Chevrolet Silverado.
9. Bob is in the third house.
10. The person who owns a Honda Civic is in the sixth house.
11. The person who loves the vase of tulips is somewhere to the left of The person whose mother's name is Penny.
12. The person who has brown hair is in the fourth house.
13. The person who has brown hair is somewhere to the left of the person who has blonde hair.
14. The person whose mother's name is Holly is Bob.
15. The person who owns a Ford F-150 is in the third house.
16. Eric is directly left of the person who has auburn hair.
17. The person who owns a Tesla Model 3 is the person who loves yellow.
18. There are two houses between the person who loves purple and The person whose mother's name is Aniya.
19. The person who loves purple is in the first house.
20. The person whose favorite color is green is not in the fourth house.
21. The person who has gray hair is the person who owns a BMW 3 Series.
22. The person who has gray hair is somewhere to the left of Alice.
23. The person whose mother's name is Holly is somewhere to the left of the person who loves the vase of tulips.
24. The person who has red hair is the person who loves white.
 What is the value of attribute Mother for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: Holly


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`
 - Each mother is accompanied by their child: `Fred`, `Meredith`, `Bella`
 - The people keep unique animals: `cat`, `bird`, `horse`
 - Each person has a unique favorite drink: `tea`, `water`, `milk`

## Clues:
1. Peter is somewhere to the left of the person's child is named Meredith.
2. The person's child is named Fred is directly left of the person who keeps horses.
3. The person's child is named Fred is in the second house.
4. The person who likes milk is the person who keeps horses.
5. The person whose mother's name is Holly is Eric.
6. The tea drinker is the cat lover.
7. The person's child is named Bella is Eric.
8. The tea drinker and Arnold are next to each other.
9. The person whose mother's name is Janelle is in the second house.
 What is the value of attribute Animal for the person whose attribute Drink is milk? Please reason step by step, and put your final answer within \boxed{}

Answer: horse


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

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

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Arnold`, `Bob`, `Eric`, `Carol`
 - Everyone has something unique for lunch: `stir fry`, `grilled cheese`, `spaghetti`, `pizza`, `soup`, `stew`
 - People use unique phone models: `xiaomi mi 11`, `iphone 13`, `oneplus 9`, `google pixel 6`, `samsung galaxy s21`, `huawei p50`
 - People have unique favorite music genres: `pop`, `country`, `classical`, `jazz`, `rock`, `hip hop`
 - Each person has a unique favorite drink: `water`, `boba tea`, `milk`, `root beer`, `tea`, `coffee`
 - Each person has an occupation: `nurse`, `lawyer`, `artist`, `doctor`, `teacher`, `engineer`

## Clues:
1. The tea drinker is somewhere to the right of the person who is a teacher.
2. Eric is the person who uses a Google Pixel 6.
3. The person who loves the spaghetti eater and the person who loves hip-hop music are next to each other.
4. The boba tea drinker is somewhere to the left of the person who uses a Google Pixel 6.
5. The person who uses a Huawei P50 is somewhere to the left of the person who uses a OnePlus 9.
6. The person who is a pizza lover is the person who loves rock music.
7. The person who is a pizza lover is somewhere to the right of the person who loves the soup.
8. The person who likes milk is somewhere to the left of the person who loves hip-hop music.
9. The person who uses a OnePlus 9 is Arnold.
10. The person who is a lawyer is the person who loves stir fry.
11. The person who is an artist is Alice.
12. Bob is the person who loves classical music.
13. The person who loves rock music is directly left of the person who loves classical music.
14. The person who is a doctor is the person who uses a Huawei P50.
15. Bob is the root beer lover.
16. There are two houses between the person who is an engineer and the person who uses a OnePlus 9.
17. Eric is the person who loves jazz music.
18. The person who uses a Xiaomi Mi 11 is the person who is an artist.
19. Carol is directly left of the person who uses a Huawei P50.
20. The person who is a lawyer is the coffee drinker.
21. The person who loves eating grilled cheese is the person who loves pop music.
22. The person who loves hip-hop music is the person who uses a Samsung Galaxy S21.
23. The coffee drinker is somewhere to the left of the person who likes milk.
 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: tea


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Carol`, `Eric`, `Alice`, `Peter`, `Arnold`
 - Each person prefers a unique type of vacation: `camping`, `cruise`, `mountain`, `cultural`, `city`, `beach`
 - Each person has a unique type of pet: `fish`, `hamster`, `bird`, `rabbit`, `dog`, `cat`
 - The people are of nationalities: `brit`, `swede`, `german`, `norwegian`, `dane`, `chinese`
 - People have unique favorite book genres: `biography`, `romance`, `mystery`, `fantasy`, `science fiction`, `historical fiction`
 - People own unique car models: `tesla model 3`, `bmw 3 series`, `honda civic`, `chevrolet silverado`, `toyota camry`, `ford f150`

## Clues:
1. The person who loves fantasy books is Peter.
2. The Chinese is somewhere to the right of the Dane.
3. The person who owns a Tesla Model 3 is the person with a pet hamster.
4. Carol is the person who loves beach vacations.
5. The person who has a cat is in the second house.
6. There is one house between the person who loves mystery books and the person who prefers city breaks.
7. The person who owns a Honda Civic is in the first house.
8. The person who loves science fiction books is directly left of the person who prefers city breaks.
9. The British person is the person who owns a Honda Civic.
10. There is one house between the person who loves fantasy books and the person who owns a Toyota Camry.
11. The person who keeps a pet bird is the person who owns a Toyota Camry.
12. The Dane is not in the third house.
13. Eric is not in the sixth house.
14. The person who loves romance books is the person who enjoys camping trips.
15. Arnold is the person who likes going on cruises.
16. The person who owns a dog is in the fifth house.
17. The person who enjoys camping trips is directly left of the person who owns a rabbit.
18. The person who owns a Ford F-150 is the person who owns a rabbit.
19. The person who loves fantasy books is directly left of Eric.
20. The German is the person who owns a BMW 3 Series.
21. The person who goes on cultural tours is not in the first house.
22. The person who loves mystery books is not in the sixth house.
23. The person who loves historical fiction books is somewhere to the left of the person who enjoys camping trips.
24. The Dane is Bob.
25. There is one house between the Dane and the Chinese.
26. The Swedish person is somewhere to the right of the person who likes going on cruises.
27. Eric is not in the third house.
 What is the value of attribute House for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{}

Answer: 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: `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 Food for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: spaghetti


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`, `Alice`
 - They all have a unique favorite flower: `lilies`, `roses`, `daffodils`, `carnations`
 - People have unique favorite sports: `swimming`, `tennis`, `soccer`, `basketball`
 - People have unique hair colors: `black`, `brown`, `blonde`, `red`
 - Each person has a unique birthday month: `feb`, `jan`, `april`, `sept`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `mountain`, `beach`

## Clues:
1. The person who enjoys mountain retreats is in the fourth house.
2. The person whose birthday is in April and the person who loves a bouquet of daffodils are next to each other.
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 the person who loves soccer.
5. Arnold is the person who loves a bouquet of daffodils.
6. Alice is in the third house.
7. The person who loves basketball is the person whose birthday is in April.
8. The person whose birthday is in February is the person who has brown hair.
9. The person who has black hair is somewhere to the left of the person who likes going on cruises.
10. The person who prefers city breaks is Eric.
11. The person who has brown hair is Arnold.
12. The person who has blonde hair is the person who loves tennis.
13. The person who loves tennis is the person who likes going on cruises.
14. The person who loves beach vacations is not in the third house.
15. The person who loves the boquet of lilies is in the first house.
 What is the value of attribute Flower for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: lilies


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Eric`, `Peter`, `Alice`
 - Each person has a unique favorite drink: `milk`, `root beer`, `coffee`, `tea`, `water`
 - Everyone has a favorite smoothie: `dragonfruit`, `lime`, `desert`, `cherry`, `watermelon`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `dunhill`, `blends`, `blue master`
 - Each person has a favorite color: `red`, `yellow`, `green`, `blue`, `white`
 - People have unique favorite music genres: `pop`, `rock`, `jazz`, `classical`, `hip hop`

## Clues:
1. The coffee drinker is the person who likes Cherry smoothies.
2. The Watermelon smoothie lover is the person who loves rock music.
3. The person who loves yellow is the person who loves hip-hop music.
4. Eric is somewhere to the right of the person who loves classical music.
5. The one who only drinks water is the Prince smoker.
6. The person who smokes Blue Master is Eric.
7. The Dunhill smoker is Alice.
8. The root beer lover is the person whose favorite color is red.
9. The Dunhill smoker is somewhere to the left of the Prince smoker.
10. The Dragonfruit smoothie lover is directly left of the person who likes Cherry smoothies.
11. Arnold is the person whose favorite color is green.
12. Eric is the tea drinker.
13. The Dunhill smoker is the person who loves white.
14. The person who loves classical music and the person who drinks Lime smoothies are next to each other.
15. The person who drinks Lime smoothies is Eric.
16. The person who loves rock music is directly left of the root beer lover.
17. The person who loves pop music is the root beer lover.
18. The person whose favorite color is green is not in the third house.
19. The one who only drinks water is the person who loves blue.
20. The person who loves rock music is the person who loves white.
21. Peter is not in the third house.
22. The person who likes Cherry smoothies is somewhere to the right of the person partial to Pall Mall.
 What is the value of attribute Smoothie for the person whose attribute Color is yellow? Please reason step by step, and put your final answer within \boxed{}

Answer: lime


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Bob`, `Peter`, `Eric`, `Carol`, `Alice`
 - Each person lives in a unique style of house: `craftsman`, `colonial`, `mediterranean`, `modern`, `victorian`, `ranch`
 - Each person has an occupation: `nurse`, `doctor`, `artist`, `engineer`, `lawyer`, `teacher`
 - People have unique favorite sports: `swimming`, `basketball`, `baseball`, `tennis`, `soccer`, `volleyball`

## Clues:
1. There are two houses between the person who loves baseball and the person in a modern-style house.
2. Arnold and the person who loves baseball are next to each other.
3. The person living in a colonial-style house is somewhere to the right of the person who is a lawyer.
4. The person who is an artist is Peter.
5. The person who is a nurse is not in the sixth house.
6. There is one house between Carol and Bob.
7. The person who is an engineer is directly left of the person who is an artist.
8. There are two houses between the person who loves swimming and the person who is a doctor.
9. Bob is in the sixth house.
10. The person residing in a Victorian house is not in the third house.
11. The person residing in a Victorian house is not in the second house.
12. The person who loves basketball is Eric.
13. The person living in a colonial-style house is in the fourth house.
14. There are two houses between the person in a ranch-style home and the person who loves tennis.
15. The person in a modern-style house is somewhere to the right of the person in a Mediterranean-style villa.
16. The person living in a colonial-style house is somewhere to the left of the person in a Mediterranean-style villa.
17. The person who loves volleyball is the person who is an engineer.
18. The person living in a colonial-style house is somewhere to the left of the person who loves basketball.
 What is the value of attribute House for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Alice`, `Eric`, `Arnold`, `Peter`
 - The mothers' names in different houses are unique: `Aniya`, `Janelle`, `Penny`, `Kailyn`, `Holly`
 - People have unique favorite music genres: `pop`, `jazz`, `rock`, `classical`, `hip hop`
 - Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `stew`, `spaghetti`, `pizza`

## Clues:
1. Eric is somewhere to the left of the person who loves classical music.
2. The person who loves eating grilled cheese is directly left of The person whose mother's name is Janelle.
3. The person whose mother's name is Penny is directly left of Alice.
4. The person who loves stir fry is Peter.
5. The person who loves the spaghetti eater is Alice.
6. Eric is somewhere to the left of the person who loves rock music.
7. The person whose mother's name is Kailyn is directly left of The person whose mother's name is Aniya.
8. The person who loves rock music is not in the third house.
9. The person who loves eating grilled cheese is directly left of the person who loves the stew.
10. The person who loves pop music is The person whose mother's name is Kailyn.
11. The person who loves the spaghetti eater is the person who loves jazz music.
12. The person who loves pop music is Arnold.
 What is the value of attribute House for the person whose attribute MusicGenre is jazz? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Bob`, `Arnold`, `Eric`, `Peter`
 - Each person prefers a unique type of vacation: `cruise`, `city`, `camping`, `beach`, `mountain`
 - Each mother is accompanied by their child: `Bella`, `Samantha`, `Fred`, `Meredith`, `Timothy`
 - The people are of nationalities: `dane`, `norwegian`, `brit`, `german`, `swede`

## Clues:
1. The Norwegian is Peter.
2. The Swedish person is the person's child is named Bella.
3. The person who loves beach vacations is directly left of the person's child is named Samantha.
4. The person's child is named Bella is not in the second house.
5. Alice is the British person.
6. The person who likes going on cruises is in the first house.
7. The person's child is named Meredith is in the fourth house.
8. Eric is not in the fifth house.
9. The Swedish person is somewhere to the right of the Norwegian.
10. There is one house between the person's child is named Fred and the person who prefers city breaks.
11. Bob is the person who enjoys camping trips.
12. The Dane is in the fifth house.
13. The person who enjoys camping trips is not in the fifth house.
 What is the value of attribute Nationality for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: swede


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `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 roses? Please reason step by step, and put your final answer within \boxed{}

Answer: 2


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Bob`, `Eric`, `Arnold`, `Carol`
 - Each person has a unique level of education: `bachelor`, `high school`, `associate`, `doctorate`, `trade school`, `master`
 - Everyone has something unique for lunch: `spaghetti`, `stir fry`, `stew`, `grilled cheese`, `pizza`, `soup`
 - People have unique favorite sports: `baseball`, `swimming`, `tennis`, `volleyball`, `soccer`, `basketball`
 - People have unique heights: `very short`, `average`, `very tall`, `super tall`, `tall`, `short`

## Clues:
1. Alice is somewhere to the left of Bob.
2. The person who loves tennis is the person with an associate's degree.
3. The person who is tall is not in the first house.
4. The person who loves the spaghetti eater is in the second house.
5. The person who loves baseball is in the third house.
6. Arnold is somewhere to the left of the person who is very tall.
7. Eric is the person with a bachelor's degree.
8. The person who loves the soup is the person who is very short.
9. The person who loves swimming is the person who loves the stew.
10. Arnold is somewhere to the right of the person who loves soccer.
11. The person with a doctorate is not in the sixth house.
12. The person who loves stir fry is Carol.
13. The person who has an average height is in the sixth house.
14. There is one house between the person who attended trade school and the person who has an average height.
15. The person who is very tall is directly left of the person who is super tall.
16. Alice is somewhere to the right of the person who attended trade school.
17. The person who is a pizza lover is somewhere to the left of Eric.
18. Alice is the person who loves basketball.
19. The person with a high school diploma is Arnold.
 What is the value of attribute Education for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: high school


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `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 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: `Arnold`, `Bob`, `Alice`, `Eric`, `Peter`
 - People use unique phone models: `huawei p50`, `iphone 13`, `samsung galaxy s21`, `google pixel 6`, `oneplus 9`
 - People have unique hair colors: `red`, `brown`, `gray`, `blonde`, `black`
 - Everyone has a favorite smoothie: `dragonfruit`, `watermelon`, `cherry`, `desert`, `lime`
 - Each person has a unique hobby: `knitting`, `photography`, `gardening`, `painting`, `cooking`
 - They all have a unique favorite flower: `daffodils`, `tulips`, `roses`, `carnations`, `lilies`

## Clues:
1. Bob is the person who loves the vase of tulips.
2. The person who has red hair is Bob.
3. The person who loves a bouquet of daffodils is the person who uses a Google Pixel 6.
4. The person who likes Cherry smoothies is the person who enjoys gardening.
5. The person who uses a Google Pixel 6 is somewhere to the right of the person who loves a carnations arrangement.
6. The person who has brown hair and the person who loves a carnations arrangement are next to each other.
7. The person who paints as a hobby is somewhere to the left of the person who loves cooking.
8. The person who uses an iPhone 13 is somewhere to the left of the person who loves a carnations arrangement.
9. The person who has brown hair is somewhere to the right of the person who uses a OnePlus 9.
10. The person who paints as a hobby is Peter.
11. Eric is directly left of the person who uses an iPhone 13.
12. The person who uses a OnePlus 9 is directly left of the person who uses a Samsung Galaxy S21.
13. Arnold is the person who drinks Lime smoothies.
14. The person who has red hair is the person who enjoys gardening.
15. The Dragonfruit smoothie lover and the Desert smoothie lover are next to each other.
16. The person who has brown hair is directly left of the Desert smoothie lover.
17. The person who loves the boquet of lilies is directly left of the person who loves a carnations arrangement.
18. The person who drinks Lime smoothies is the person who has black hair.
19. The person who uses a Huawei P50 is the person who has gray hair.
20. The person who drinks Lime smoothies is the photography enthusiast.
 What is the value of attribute Hobby for the person whose attribute PhoneModel is oneplus 9? Please reason step by step, and put your final answer within \boxed{}

Answer: gardening


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Bob`, `Alice`, `Arnold`
 - People have unique favorite book genres: `mystery`, `fantasy`, `science fiction`, `romance`, `biography`
 - Everyone has a favorite smoothie: `lime`, `watermelon`, `dragonfruit`, `cherry`, `desert`

## Clues:
1. There is one house between Eric and the person who loves science fiction books.
2. The person who loves fantasy books is directly left of Alice.
3. The person who loves fantasy books is the Watermelon smoothie lover.
4. Arnold and the Dragonfruit smoothie lover are next to each other.
5. The person who loves biography books is the person who likes Cherry smoothies.
6. The person who loves biography books is in the second house.
7. Eric is in the third house.
8. The Desert smoothie lover is in the third house.
9. The person who loves mystery books is not in the third house.
10. Arnold is directly left of Bob.
 What is the value of attribute Smoothie for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: watermelon


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`, `Bob`, `Alice`
 - People use unique phone models: `google pixel 6`, `samsung galaxy s21`, `huawei p50`, `oneplus 9`, `iphone 13`
 - People have unique favorite book genres: `science fiction`, `romance`, `biography`, `mystery`, `fantasy`

## Clues:
1. Peter is the person who uses a Huawei P50.
2. The person who loves fantasy books is directly left of Alice.
3. Bob is in the second house.
4. There are two houses between the person who uses a OnePlus 9 and the person who loves biography books.
5. Arnold is the person who loves romance books.
6. The person who loves fantasy books is the person who uses a OnePlus 9.
7. The person who uses a Samsung Galaxy S21 is not in the fifth house.
8. The person who uses an iPhone 13 is the person who loves science fiction books.
9. Peter is directly left of the person who uses a OnePlus 9.
 What is the value of attribute House for the person whose attribute BookGenre is science fiction? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


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

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

Answer: horse


15. As shown in the figure, $O$ is the origin, point $F$ is the focus of the parabola $C_{1}: x^{2}=2 p y$ $(p>0)$, and the tangent line at point $P$ on the parabola $C_{1}$ is tangent to the circle $C_{2}: x^{2}+y^{2}=1$ at point $Q$.
(1) When the equation of line $P Q$ is $x-y-\sqrt{2}=0$, find the equation of the parabola $C_{1}$;
(2) When the positive number $p$ varies, let $S_{1}, S_{2}$ be the areas of $\triangle F P Q$ and $\triangle F O Q$, respectively. Find the minimum value of $\frac{S_{1}}{S_{2}}$.

Answer: x^2 = 4\sqrt{2} y


Let $x_0=1$, and let $\delta$ be some constant satisfying $0<\delta<1$. Iteratively, for $n=0,1,2,\dots$, a point $x_{n+1}$ is chosen uniformly form the interval $[0,x_n]$. Let $Z$ be the smallest value of $n$ for which $x_n<\delta$. Find the expected value of $Z$, as a function of $\delta$.

Answer: 1 - \ln \delta


Let $p$ be a fixed odd prime. A $p$-tuple $(a_1,a_2,a_3,\ldots,a_p)$ of integers is said to be [i]good[/i] if

[list]
[*] [b](i)[/b] $0\le a_i\le p-1$ for all $i$, and
[*] [b](ii)[/b] $a_1+a_2+a_3+\cdots+a_p$ is not divisible by $p$, and
[*] [b](iii)[/b] $a_1a_2+a_2a_3+a_3a_4+\cdots+a_pa_1$ is divisible by $p$.[/list]

Determine the number of good $p$-tuples.

Answer: (p-1)p^{p-2}


12.298. In a right-angled triangle, a plane is drawn through its hypotenuse, forming an angle $\alpha$ with the plane of the triangle, and an angle $\beta$ with one of the legs. Find the angle between this plane and the second leg.

Answer: \arcsin \sqrt{\sin^2 \alpha - \sin^2 \beta}


One. (50 points) Given that point $M$ is a point on the median $A D$ of $\triangle A B C$, the line $B M$ intersects side $A C$ at point $N$, and $A B$ is the tangent to the circumcircle of $\triangle N B C$. Let $\frac{B C}{B N}=\lambda$, try to find $\frac{B M}{M N}$ (expressed in terms of $\lambda$).

Answer: \lambda^2


[Area and volume (extremum problems).]

In a regular quadrilateral pyramid, two identical spheres of radius $r$ are placed, touching the base of the pyramid at points lying on the segment connecting the midpoints of opposite sides of the base. Each sphere touches a lateral face of the pyramid and the other sphere. Find the height of the pyramid for which the volume of the pyramid is the smallest.

Answer: \dfrac{(5 + \sqrt{17})r}{2}


## Task 3 - V10823

In the number .378., the two dots are to be replaced by digits so that the resulting number is divisible by 72.

How did you determine the missing digits?

Answer: 53784


Problem 3. Let $n$ be a non-zero natural number and $A=\{1,2, \ldots, n\}$. Determine the number of increasing functions $f: A \rightarrow A$ with the property that $|f(x)-f(y)| \leq|x-y|$ for any $x, y \in A$.

Answer: (n+1)2^{n-2}


2. Let $n \in \mathbb{N}^{*}$ be fixed. Solve the equation: $\left\{x+\frac{1}{2 n}\right\}+\left\{x+\frac{3}{2 n}\right\}+\ldots+\left\{x+\frac{2 n-1}{2 n}\right\}=\frac{n(2 x-1)}{2}$.

Supliment G.M.12/2015

Answer: \left[1 - \dfrac{1}{2n}, 1 + \dfrac{1}{2n}\right)


9. Arrange $1,2, \cdots, 7$ in a row such that the sum of the first term, the sum of the first two terms, the sum of the first three terms, ... up to the sum of all seven terms are not divisible by 3. Then there are $\qquad$ different arrangements.
(Thailand)

Answer: 360


9.1. In the triangular pyramid $S A B C$, the edges $S B, A B$ are perpendicular and $\angle A B C=120^{\circ}$. Point $D$ on edge $A C$ is such that segment $S D$ is perpendicular to at least two medians of triangle $A B C$ and $C D=A B=44 \sqrt[3]{4}$. Find $A D$ (if the answer is not an integer, round it to the nearest hundredth).

Answer: 88


Answer: 16\sqrt{3} - 12


Example 5. Calculate the flux P of the vector field $\vec{F}=y z \vec{i}+$ $+x z \vec{j}+x y \vec{k}$ through the portion of the plane $x+y+z=1$, located in the first octant, along the normal vector to this plane.

Answer: \dfrac{1}{8}


B3. A large rectangle is divided into small rectangles that are twice as high as they are wide. The rectangle is 10 such small rectangles wide, as shown in the figure below. In this figure, you can recognize a number of squares of different sizes.

How many small rectangles tall must the figure be to ensure that there are exactly 345 squares to be found?

![](https://cdn.mathpix.com/cropped/2024_04_17_88f9acd303931df7c94dg-1.jpg?height=414&width=528&top_left_y=2283&top_left_x=1324)

Answer: 15


Example 9 $\triangle A B C$ is inscribed in a unit circle, the angle bisectors of the three interior angles $A, B, C$ are extended to intersect this circle at points $A_{1}, B_{1}, C_{1}$, respectively. Find the value of $\frac{A A_{1} \cos \frac{A}{2}+B B_{1} \cos \frac{B}{2}+C C_{1} \cos \frac{C}{2}}{\sin A+\sin B+\sin C}$.

Answer: 2


$4 \cdot 61$ Given that in the subway network, each line has at least 4 stations, of which no more than 3 are transfer stations, and at each transfer station, no more than two lines intersect. If from any station, one can reach any other station with at most two transfers, how many lines can this network have at most?

Answer: 10


Let $a \circ b=a+b-a b$. Find all triples $(x, y, z)$ of integers such that $(x \circ y) \circ z+(y \circ z) \circ x+(z \circ x) \circ y=0$.

Answer: (0, 0, 0)


4. Consider $n^{2}$ unit squares in the $x y$-plane centred at point $(i, j)$ with integer coordinates, $1 \leq i \leq n, 1 \leq j \leq n$. It is required to colour each unit square in such a way that whenever $1 \leq i<j \leq n$ and $1 \leq k<l \leq n$, the three squares with centres at $(i, k),(j, k),(j, l)$ have distinct colours. What is the least possible number of colours needed?

Answer: 2n - 1


Example 1. In a plane, there are $\mathrm{n}$ lines $(\mathrm{n} \in \mathrm{N})$, among which no two are parallel, and no three intersect at the same point. Question: How many regions does these $\mathrm{n}$ lines divide the plane into?

Answer: \dfrac{n(n + 1)}{2} + 1


A man was building a house for himself. Only the roof remains to be completed. The builder wanted the raindrops falling on the roof to roll off as quickly as possible. Determine the angle of inclination of the roof required to achieve this goal. Ignore friction between the raindrops and the roof.

Answer: 45^\circ


7. (3 points) There are 5 different positive integers, and the product of any two of them is a multiple of 12. The minimum value of the sum of these 5 numbers is $\qquad$ .

Answer: 62


3. A flea jumps along the number line, and the length of each jump cannot be less than $n$. It starts its movement from the origin and wants to visit all integer points belonging to the segment $[0,2013]$ (and only them!) exactly once. For what greatest value of $n$ will it be able to do this?

Answer: 1006


II. (50 points) Try to find the smallest positive integer $m$, such that the following conditions are satisfied simultaneously:
(1) $\left[\frac{2}{1977} m^{2}\right] \geqslant m+2006$ ( $[x]$ denotes the greatest integer not exceeding $x$);
(2) $99^{m}$ leaves a remainder of 11 when divided by 190.

Answer: 2004


Alice and Bob are in a hardware store. The store sells coloured sleeves that fit over keys to distinguish them. The following conversation takes place:
[color=#0000FF]Alice:[/color] Are you going to cover your keys?
[color=#FF0000]Bob:[/color] I would like to, but there are only $7$ colours and I have $8$ keys.
[color=#0000FF]Alice:[/color] Yes, but you could always distinguish a key by noticing that the red key next to the green key was different from the red key next to the blue key.
[color=#FF0000]Bob:[/color] You must be careful what you mean by "[i]next to[/i]" or "[i]three keys over from[/i]" since you can turn the key ring over and the keys are arranged in a circle.
[color=#0000FF]Alice:[/color] Even so, you don't need $8$ colours.
[b]Problem:[/b] What is the smallest number of colours needed to distinguish $n$ keys if all the keys are to be covered.

Answer: 2


5.

The Bank of Russia will ensure the conversion of the "digital ruble" into another form of money (rubles) at a one-to-one ratio.

Correct answers: Stablecoins, backed by cash or gold, are an example of a CBDC., The Bank of Russia will ensure the conversion of the "digital ruble" into another form of money (rubles) at a one-to-one ratio.

Question 19

Score: 7.00

Angelika owns a commercial space of 30 sq. m. She wanted to organize a music club there and give piano lessons. But a friend offered Angelika a job as a manager in his company, and she decided to calculate which option would be more economically beneficial for her. If she opens the club, Angelika plans to choose a simplified tax system with a rate of $15 \%$ of the profit received, while her salary, which she spends entirely on monthly expenses, after paying personal income tax, will be 60,900 rubles per month.

Additional information:

rent rate: 12,000 rubles per 1 sq m per year, paid at the beginning of the year.

interest rate on a loan: $12 \%$ per year, with interest accrued at the end of the year interest rate on a deposit: $9 \%$ per year, with interest accrued at the end of the year Determine the minimum annual profit Angelika needs to achieve from the music club (before taxation) for this alternative to be economically beneficial for her.

Answer: 1321412


Let $S(N)$ be the number of 1's in the binary representation of an integer $N$, and let $D(N) = S(N + 1) - S(N)$.  Compute the sum of $D(N)$ over all $N$ such that $1 \le N \le 2017$ and $D(N) < 0$.

Answer: -1002


A natural number is called a palindrome if it does not change when its digits are written in reverse order (for example, the numbers 4, 55, 626 are palindromes, while 20, 201, 2016 are not). Represent the number 2016 as a product of two palindromes (find all possible options and explain why there are no others).

Answer: 252 \times 8


$\left[\begin{array}{ll}[\text { Classical combinatorics (other) })]\end{array}\right]$

On a $11 \times 11$ grid, 22 cells are marked such that exactly two cells are marked in each row and each column. Two arrangements of marked cells are equivalent if, by swapping any number of columns among themselves and any number of rows among themselves, one arrangement can be transformed into the other. How many non-equivalent arrangements of marked cells exist?

Answer: 14


3. How many distinct triangles satisfy all the following properties:
(i) all three side-lengths are a whole number of centimetres in length;
(ii) at least one side is of length $10 \mathrm{~cm}$;
(iii) at least one side-length is the (arithmetic) mean of the other two side-lengths?

Answer: 17


The base of the pyramid SABCD is a parallelogram ABCD. What figure is obtained by the section of this pyramid by the plane $ABM$, where $M$ is a point on the edge SC?

Answer: Trapezoid


Problem 11.8. In a $28 \times 35$ table, some $k$ cells are painted red, another $r-$ in pink, and the remaining $s-$ in blue. It is known that

- $k \geqslant r \geqslant s$
- each boundary cell has at least 2 neighbors of the same color;
- each non-boundary cell has at least 3 neighbors of the same color.

What is the smallest value that the quantity $k-s$ can take?

(A cell is called boundary if it is adjacent to the edge of the table. Neighbors are cells that share a common side.)

Answer: 28


2. The ten positive integers from $1 \sim 10$ are written in a row in some order, denoted as $a_{1}, a_{2}, \cdots, a_{10}, S_{1}=a_{1}, S_{2}=a_{1}+a_{2}$, $\cdots, S_{10}=a_{1}+a_{2}+\cdots+a_{10}$. Then, among $S_{1}, S_{2}, \cdots, S_{10}$, the maximum number of primes that can occur is .

Answer: 7


11. (12 points) In the figure, the area of rectangle $A B C D$ is 2013 square centimeters. $\triangle A O D$, $\triangle B O C$, $\triangle A B E$, $\triangle B C F$, $\triangle C D G$, $\triangle A D H$ are all equilateral triangles, and $M$, $N$, $P$, $Q$ are the centers of $\triangle A B E$, $\triangle B C F$, $\triangle C D G$, $\triangle A D H$ respectively. The area of the shaded part is $\qquad$ square centimeters.

Answer: 2684


4. (10 points) In a deck of cards, $J, Q, K$ are considered as $11,12,13$ points respectively. From 13 cards numbered from 1 to 13, what is the maximum number of cards you can pick so that there are no 2 pairs of cards, where the sum of the points of one pair equals the sum of the points of the other pair?

Answer: 6


10. In the Cartesian coordinate system $x O y$, it is known that the vertices of the equilateral $\triangle A B C$ (vertices in counterclockwise order) are $A(-2,2)$, vertex $B$ is on the $y$-axis, and $C B \parallel x$-axis; point $D(2,6)$, $E(2,2)$, and the radius of $\odot O$ is 2. Find the radius of the circle that is externally tangent to $\odot O$ and tangent to line segments $A B$ and $D E$ (accurate to $10^{-4}$).

Answer: 1.4726


The venusian prophet Zabruberson sent to his pupils a $ 10000$-letter word, each letter being $ A$ or $ E$: the [i]Zabrubic word[/i]. Their pupils consider then that for $ 1 \leq k \leq 10000$, each word comprised of $ k$ consecutive letters of the Zabrubic word is a [i]prophetic word[/i] of length $ k$. It is known that there are at most $ 7$ prophetic words of lenght $ 3$. Find the maximum number of prophetic words of length $ 10$.

Answer: 504


11. As shown in the figure, 12 congruent disks are placed on the circumference of a circle $C$ with radius 1, such that they cover $C$. No two disks overlap, and adjacent disks are tangent to each other. The sum of the areas of these disks can be written as
$$
\pi(a-b \sqrt{c}) \text {, where }
$$
$a, b, c$ are positive integers, and $c$ is not divisible by the square of any prime. Find $a+b+c$.

Answer: 135


11. (3 points) There are 20 points below, with each adjacent pair of points being equidistant. By connecting four points with straight lines, you can form a square. Using this method, you can form $\qquad$ squares.

The text above has been translated into English, preserving the original text's line breaks and format.

Answer: 20


In a convex quadrilateral $A B C D$, diagonals $A C$ and $B D$ are drawn. It is known that $A D=2, \angle A B D=\angle A C D=$ $90^{\circ}$, and the distance between the centers of the circles inscribed in triangles $A B D$ and $A C D$ is $\sqrt{2}$. Find

$B C$.

Answer: \sqrt{3}


Ostrovsky $M$.

A number from 1 to 144 is guessed. You are allowed to select one subset of the set of numbers from 1 to 144 and ask whether the guessed number belongs to it. You have to pay 2 rubles for a "yes" answer and 1 ruble for a "no" answer. What is the minimum amount of money needed to surely guess the number?

Answer: 11


An equilateral triangle \(ABC\) with side length 3 is inscribed in a circle. Point \(D\) lies on the circle such that the chord \(AD\) has a length of \(\sqrt{3}\). Find the lengths of the chords \(BD\) and \(CD\).

Answer: \sqrt{3}


15. Given the set $A=\{1,2,3,4\}$, every second, Andre will randomly pick a number from $A$ (repetition is allowed), and he will stop picking when the sum of the last two numbers picked is a prime number. What is the probability that the last number picked is “1”?

Answer: \dfrac{15}{44}


The rectangular spiral shown in the diagram is constructed as follows. Starting at \((0,0)\), line segments of lengths \(1,1,2,2,3,3,4,4, \ldots\) are drawn in a clockwise manner. The integers from 1 to 1000 are placed, in increasing order, wherever the spiral passes through a point with integer coordinates (that is, 1 at \((0,0)\), 2 at \((1,0)\), 3 at \((1,-1)\), and so on). What is the sum of all of the positive integers from 1 to 1000 which are written at points on the line \(y=-x\)?

Answer: 10944


3. Znayka knows that any triangle can be cut into 4 equal triangles. But does there exist a quadrilateral that can be cut into 7 equal triangles?

Answer: Yes


4.1. On a grid sheet, a $1 \times 5$ rectangle was painted. Each minute, all those uncolored cells that have at least one side-adjacent cell already colored are colored. For example, after one minute, 17 cells will be colored. How many cells will be colored after 5 minutes?

Answer: 105


12. Given that $P$ is a moving point on the hyperbola $\frac{x^{2}}{8}-\frac{y^{2}}{4}=1$, $F_{1}$ and $F_{2}$ are its left and right foci, and $O$ is the origin. Then the range of $\frac{\left|P F_{1}\right|+\left|P F_{2}\right|}{|O P|}$ is $\qquad$.

Answer: (2, \sqrt{6}]


Let $n$ be a positive integer with the following property: $2^n-1$ divides a number of the form $m^2+81$, where $m$ is a positive integer. Find all possible $n$.

Answer: 2^k


A grasshopper is sitting on the number line at the number 0. Each second, it jumps one unit to the left or to the right, with equal probability. The directions of the jumps are chosen independently of each other. Let \( p \) denote the probability that, after 2022 jumps, the grasshopper is sitting at a number divisible by 5. Determine whether \( p < \frac{1}{5} \), \( p = \frac{1}{5} \), or \( p > \frac{1}{5} \).

Answer: p > \frac{1}{5}


Divide an equilateral triangle into \( n^2 \) smaller equilateral triangles of the same size. Label a portion of these smaller triangles with the numbers \( 1, 2, \ldots, m \) such that triangles with consecutive numbers share a common edge. Prove that \( m \leq n^2 - n + 1 \).

Answer: m \leq n^2 - n + 1


5. Given in the Cartesian coordinate system $x O y$, the vertices of square $A B C D$ are $A(-1,1)$, vertex $C(1,1+2 \sqrt{3})$. Then, the coordinates of vertices $B$ and $D$ are $\qquad$
$\qquad$

Answer: (\sqrt{3}, \sqrt{3})


6. Given a pyramid $S-ABCD$ with a height of $\frac{\sqrt{2}}{4}$, the base is a square with side length 1, and points $S, A, B, C, D$ are all on the same sphere with a radius of 1. Then the maximum length of the lateral edge $SA$ is $\qquad$

Answer: \sqrt{\dfrac{3 + \sqrt{7}}{2}}


In one container, there is one liter of wine, in another, one liter of water. From the first container, we pour one deciliter into the second, mix it, then pour one deciliter of the mixture back into the first container. Calculate the limit of the amount of wine in the first container if the above procedure is repeated infinitely. (We assume perfect mixing during each transfer, and there is no fluid loss during the process.)

Answer: \dfrac{1}{2}


From 49 balls numbered 1 to 49, select some balls and arrange them in a circle so that the product of the numbers on any two adjacent balls is less than 100. What is the maximum number of balls that can be selected?

Answer: 18


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Alice`, `Carol`, `Bob`, `Eric`
 - Each person has an occupation: `artist`, `nurse`, `engineer`, `lawyer`, `teacher`, `doctor`
 - The mothers' names in different houses are unique: `Holly`, `Penny`, `Aniya`, `Janelle`, `Sarah`, `Kailyn`
 - People have unique favorite music genres: `pop`, `rock`, `classical`, `jazz`, `hip hop`, `country`

## Clues:
1. The person who is an engineer is directly left of the person who is an artist.
2. The person whose mother's name is Janelle is the person who is an artist.
3. The person who loves classical music is directly left of Peter.
4. The person whose mother's name is Janelle and the person who loves pop music are next to each other.
5. The person whose mother's name is Sarah is somewhere to the left of Arnold.
6. The person who loves country music is The person whose mother's name is Aniya.
7. The person whose mother's name is Penny is not in the second house.
8. Bob is the person who loves jazz music.
9. Carol is not in the sixth house.
10. The person who is an engineer is the person who loves classical music.
11. The person who is a nurse is somewhere to the right of the person who loves rock music.
12. There are two houses between Bob and The person whose mother's name is Penny.
13. The person who is a lawyer is directly left of the person who is a doctor.
14. The person whose mother's name is Penny is not in the third house.
15. The person who is an engineer is not in the fourth house.
16. The person who is a doctor is The person whose mother's name is Kailyn.
17. Carol is somewhere to the right of the person who loves country music.
18. The person who loves classical music is Alice.
19. The person who is a nurse is The person whose mother's name is Holly.
 What is the value of attribute Mother for the person whose attribute House is 5? Please reason step by step, and put your final answer within \boxed{}

Answer: Penny


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Alice`, `Eric`, `Bob`, `Peter`
 - Each person lives in a unique style of house: `victorian`, `colonial`, `ranch`, `modern`, `craftsman`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `oneplus 9`, `samsung galaxy s21`, `huawei p50`
 - Everyone has a unique favorite cigar: `blue master`, `dunhill`, `pall mall`, `blends`, `prince`
 - People have unique favorite book genres: `mystery`, `science fiction`, `biography`, `romance`, `fantasy`

## Clues:
1. There is one house between the person residing in a Victorian house and the person who uses a Samsung Galaxy S21.
2. The person who smokes many unique blends is Eric.
3. The person who smokes many unique blends is the person who loves fantasy books.
4. Alice is somewhere to the right of the person who uses a Samsung Galaxy S21.
5. Bob is directly left of Eric.
6. The person who loves mystery books is directly left of the person who loves fantasy books.
7. Bob is somewhere to the left of the person who uses an iPhone 13.
8. The person who uses a Google Pixel 6 is somewhere to the right of Peter.
9. The person who loves romance books is directly left of the person in a ranch-style home.
10. The person living in a colonial-style house is in the fourth house.
11. The person who loves fantasy books is in the fourth house.
12. The person partial to Pall Mall is Peter.
13. The person in a modern-style house and the person who smokes Blue Master are next to each other.
14. The person who loves science fiction books is the Dunhill smoker.
15. Eric is the person who uses a Samsung Galaxy S21.
16. The person who uses a Huawei P50 and the person who loves fantasy books are next to each other.
 What is the value of attribute HouseStyle for the person whose attribute PhoneModel is oneplus 9? Please reason step by step, and put your final answer within \boxed{}

Answer: modern


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`
 - Each person has a unique level of education: `bachelor`, `high school`, `associate`, `master`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`, `Kailyn`
 - The people keep unique animals: `fish`, `horse`, `cat`, `bird`
 - Each person has a unique birthday month: `jan`, `feb`, `sept`, `april`
 - People have unique favorite music genres: `rock`, `pop`, `jazz`, `classical`

## Clues:
1. The person with an associate's degree is The person whose mother's name is Aniya.
2. Peter is the person whose birthday is in September.
3. The person with a bachelor's degree is directly left of the person who loves pop music.
4. Arnold is The person whose mother's name is Janelle.
5. The person with a master's degree is Arnold.
6. The person whose mother's name is Janelle is the person who loves classical music.
7. The person whose birthday is in April is somewhere to the right of the person who loves rock music.
8. The cat lover is in the second house.
9. The fish enthusiast is in the third house.
10. Eric is the person whose birthday is in April.
11. The person who loves pop music is the person whose birthday is in January.
12. The person whose mother's name is Holly is the person with a bachelor's degree.
13. The person who keeps horses is the person with a master's degree.
14. The person whose mother's name is Aniya is the fish enthusiast.
15. Arnold is somewhere to the left of the fish enthusiast.
 What is the value of attribute Mother for the person whose attribute Animal is bird? 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: `Arnold`, `Peter`, `Carol`, `Alice`, `Bob`, `Eric`
 - Each mother is accompanied by their child: `Alice`, `Timothy`, `Bella`, `Meredith`, `Fred`, `Samantha`
 - Everyone has a favorite smoothie: `desert`, `cherry`, `watermelon`, `blueberry`, `lime`, `dragonfruit`

## Clues:
1. The person's child is named Fred and the Desert smoothie lover are next to each other.
2. The person who drinks Blueberry smoothies is somewhere to the left of the person's child is named Fred.
3. Alice is not in the fifth house.
4. The person's child is named Samantha is not in the second house.
5. The Watermelon smoothie lover is somewhere to the right of the person who likes Cherry smoothies.
6. Alice is the person's child is named Alice.
7. Alice is the Watermelon smoothie lover.
8. Peter is somewhere to the right of the person's child is named Samantha.
9. Arnold is not in the second house.
10. Bob is the person who is the mother of Timothy.
11. Arnold is directly left of Carol.
12. The person who likes Cherry smoothies is directly left of the person's child is named Samantha.
13. The person's child is named Meredith is in the sixth house.
14. The Dragonfruit smoothie lover is the person's child is named Meredith.
 What is the value of attribute Children for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: Samantha


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

## Clues:
1. Alice is the person who uses a Huawei P50.
2. The person who uses a Xiaomi Mi 11 is somewhere to the left of the one who only drinks water.
3. The one who only drinks water is somewhere to the left of Bob.
4. Carol is the person who has gray hair.
5. Eric is the tea drinker.
6. The person who has black hair is not in the sixth house.
7. The person who uses a Samsung Galaxy S21 is directly left of the person who loves classical music.
8. The person who uses a OnePlus 9 is not in the third house.
9. Alice is somewhere to the right of Carol.
10. The person who loves jazz music is Alice.
11. The person who loves jazz music is the boba tea drinker.
12. There is one house between the person who uses a OnePlus 9 and Eric.
13. The person who has brown hair is the person who loves hip-hop music.
14. The person who loves pop music is not in the first house.
15. The root beer lover is in the second house.
16. Eric is the person who uses an iPhone 13.
17. The person who has red hair is the person who uses an iPhone 13.
18. The person who has red hair and the coffee drinker are next to each other.
19. Peter is in the first house.
20. Arnold is somewhere to the right of the person who has auburn hair.
21. The person who has gray hair is not in the second house.
22. The person who loves country music is in the fifth house.
 What is the value of attribute Drink for the person whose attribute PhoneModel is samsung galaxy s21? 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: `Eric`, `Alice`, `Arnold`, `Carol`, `Peter`, `Bob`
 - Each person has a unique level of education: `high school`, `trade school`, `bachelor`, `doctorate`, `master`, `associate`
 - Each person has a favorite color: `purple`, `blue`, `white`, `red`, `green`, `yellow`
 - Each person prefers a unique type of vacation: `cultural`, `cruise`, `beach`, `mountain`, `camping`, `city`
 - People have unique favorite book genres: `science fiction`, `biography`, `historical fiction`, `fantasy`, `romance`, `mystery`

## Clues:
1. Alice is the person with a master's degree.
2. There is one house between the person with an associate's degree and Peter.
3. The person who loves historical fiction books is somewhere to the left of the person who loves biography books.
4. The person who loves historical fiction books is the person with a high school diploma.
5. Bob is the person with a bachelor's degree.
6. Carol is somewhere to the right of Eric.
7. The person with a master's degree is somewhere to the right of the person who enjoys camping trips.
8. The person who loves science fiction books is somewhere to the left of the person who loves yellow.
9. The person who loves historical fiction books is somewhere to the left of the person whose favorite color is green.
10. The person with a high school diploma is not in the second house.
11. The person who loves beach vacations is the person with a doctorate.
12. The person who loves mystery books is somewhere to the left of the person with a bachelor's degree.
13. The person with a doctorate is in the first house.
14. The person with a high school diploma is directly left of the person who enjoys camping trips.
15. The person who loves romance books is not in the third house.
16. There is one house between the person who loves purple and the person with a bachelor's degree.
17. The person who loves biography books is the person whose favorite color is red.
18. There is one house between the person who loves fantasy books and the person who loves blue.
19. The person who goes on cultural tours is the person who loves blue.
20. Carol is not in the fifth house.
21. The person who loves purple is the person with a doctorate.
22. The person who enjoys mountain retreats is somewhere to the right of the person who loves science fiction books.
23. The person who prefers city breaks is the person whose favorite color is green.
 What is the value of attribute House for the person whose attribute Color is blue? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Eric`, `Arnold`
 - Each person has a unique hobby: `cooking`, `painting`, `gardening`, `photography`
 - The people keep unique animals: `horse`, `fish`, `cat`, `bird`
 - People have unique favorite book genres: `fantasy`, `mystery`, `romance`, `science fiction`
 - Each person has a unique birthday month: `april`, `jan`, `sept`, `feb`
 - People have unique favorite music genres: `pop`, `rock`, `classical`, `jazz`

## Clues:
1. The person who loves cooking is the person who loves romance books.
2. The person whose birthday is in February is the person who loves pop music.
3. Eric is not in the second house.
4. The person who loves romance books is not in the fourth house.
5. The person whose birthday is in February is the fish enthusiast.
6. Alice is somewhere to the right of the person who loves fantasy books.
7. The person who keeps horses is the person who loves rock music.
8. The person who enjoys gardening is the person whose birthday is in April.
9. The person who loves jazz music is the person who loves cooking.
10. The person who loves rock music is the person who loves mystery books.
11. The person who paints as a hobby is directly left of the person who loves romance books.
12. Peter is the person who loves pop music.
13. The person who enjoys gardening is Arnold.
14. The person who loves rock music is directly left of the person whose birthday is in January.
15. The person who loves cooking is not in the third house.
16. The cat lover is somewhere to the right of the person who keeps horses.
 What is the value of attribute Name for the person whose attribute Birthday is feb? 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`, `Bob`, `Carol`, `Alice`, `Eric`
 - People have unique heights: `very tall`, `very short`, `super tall`, `average`, `tall`, `short`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `blueberry`, `desert`, `dragonfruit`, `lime`
 - Everyone has a unique favorite cigar: `prince`, `blue master`, `yellow monster`, `dunhill`, `blends`, `pall mall`
 - Each person prefers a unique type of vacation: `camping`, `city`, `beach`, `cultural`, `mountain`, `cruise`

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

Answer: short


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

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

Answer: iphone 13


There are 2 houses, numbered 1 to 2 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`
 - The people keep unique animals: `cat`, `horse`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`
 - Each person has a unique type of pet: `cat`, `dog`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`

## Clues:
1. Arnold and the person who uses a Samsung Galaxy S21 are next to each other.
2. The person partial to Pall Mall and Eric are next to each other.
3. The person who owns a dog is directly left of Eric.
4. The cat lover and the person who uses a Samsung Galaxy S21 are next to each other.
 What is the value of attribute PhoneModel for the person whose attribute Animal is cat? Please reason step by step, and put your final answer within \boxed{}

Answer: iphone 13


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Eric`, `Arnold`, `Peter`
 - People have unique favorite sports: `basketball`, `soccer`, `tennis`, `swimming`
 - Each person lives in a unique style of house: `craftsman`, `victorian`, `ranch`, `colonial`
 - People have unique favorite book genres: `mystery`, `science fiction`, `romance`, `fantasy`

## Clues:
1. The person in a Craftsman-style house is somewhere to the left of the person who loves science fiction books.
2. The person residing in a Victorian house is somewhere to the right of the person living in a colonial-style house.
3. Eric is somewhere to the left of Arnold.
4. The person who loves basketball is the person who loves romance books.
5. The person who loves soccer is somewhere to the right of Arnold.
6. Alice is the person who loves tennis.
7. The person who loves science fiction books is the person in a ranch-style home.
8. The person who loves tennis is somewhere to the left of the person in a Craftsman-style house.
9. Arnold is directly left of the person who loves mystery books.
 What is the value of attribute House for the person whose attribute BookGenre is fantasy? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Bob`, `Alice`, `Arnold`, `Peter`
 - Each person has an occupation: `engineer`, `doctor`, `artist`, `lawyer`, `teacher`
 - Everyone has a favorite smoothie: `desert`, `dragonfruit`, `lime`, `cherry`, `watermelon`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Meredith`, `Samantha`, `Timothy`

## Clues:
1. Arnold is somewhere to the right of the person who is a teacher.
2. The person's child is named Bella is in the third house.
3. The person who is the mother of Timothy is the person who is an artist.
4. Alice is in the third house.
5. The person who is a doctor is directly left of the person who is an engineer.
6. The Desert smoothie lover is the person who is an engineer.
7. The person's child is named Fred is the person who is a teacher.
8. The person who is an engineer is not in the third house.
9. Bob is the Dragonfruit smoothie lover.
10. Peter is somewhere to the right of the person who is an engineer.
11. The person's child is named Meredith is the person who drinks Lime smoothies.
12. The person's child is named Meredith is in the first house.
13. The person who likes Cherry smoothies is somewhere to the right of the Desert smoothie lover.
 What is the value of attribute House for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: 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`, `Arnold`, `Alice`, `Peter`
 - They all have a unique favorite flower: `lilies`, `roses`, `carnations`, `daffodils`
 - People have unique favorite book genres: `fantasy`, `mystery`, `science fiction`, `romance`
 - Each person prefers a unique type of vacation: `city`, `beach`, `cruise`, `mountain`
 - People have unique hair colors: `black`, `red`, `brown`, `blonde`
 - Everyone has something unique for lunch: `grilled cheese`, `pizza`, `stew`, `spaghetti`

## Clues:
1. The person who likes going on cruises is the person who has brown hair.
2. The person who loves the stew is the person who loves beach vacations.
3. Peter is the person who loves romance books.
4. There is one house between the person who has brown hair and the person who loves the spaghetti eater.
5. The person who is a pizza lover is Arnold.
6. The person who prefers city breaks is somewhere to the right of the person who loves the boquet of lilies.
7. The person who loves the stew is directly left of the person who loves mystery books.
8. The person who has black hair is directly left of the person who loves fantasy books.
9. The person who loves a carnations arrangement is directly left of the person who is a pizza lover.
10. The person who has blonde hair is not in the fourth house.
11. The person who prefers city breaks is directly left of Eric.
12. The person who loves the boquet of lilies is somewhere to the right of Alice.
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 Food is grilled cheese? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Bob`, `Alice`, `Peter`, `Arnold`, `Carol`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `roses`, `tulips`, `iris`, `lilies`
 - People have unique heights: `very tall`, `super tall`, `average`, `short`, `very short`, `tall`
 - Each person has a favorite color: `blue`, `yellow`, `purple`, `red`, `green`, `white`
 - Everyone has a unique favorite cigar: `yellow monster`, `pall mall`, `prince`, `blue master`, `blends`, `dunhill`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `xiaomi mi 11`, `samsung galaxy s21`, `huawei p50`, `oneplus 9`

## Clues:
1. The person who uses an iPhone 13 is the person who loves white.
2. Peter is the person whose favorite color is red.
3. The Prince smoker is directly left of the person partial to Pall Mall.
4. The person who smokes Blue Master and the Dunhill smoker are next to each other.
5. The person who loves blue is the person who uses a Xiaomi Mi 11.
6. The person who loves white is Alice.
7. The person who uses a OnePlus 9 is somewhere to the left of Arnold.
8. The person who is tall is the person who smokes Blue Master.
9. The person who uses a Samsung Galaxy S21 is the Dunhill smoker.
10. Bob is directly left of the person who is very short.
11. The person who loves a bouquet of daffodils is Eric.
12. The person who loves the boquet of iris is the person who uses a OnePlus 9.
13. The person who uses a Huawei P50 is the person who is very short.
14. The person who smokes many unique blends is directly left of Peter.
15. The Prince smoker is not in the first house.
16. The person who is very tall is the person who loves a bouquet of daffodils.
17. The person who uses a Google Pixel 6 is not in the fifth house.
18. The person who is tall is not in the third house.
19. The person who uses a Huawei P50 is somewhere to the left of the person who uses a Samsung Galaxy S21.
20. Arnold is somewhere to the left of the person who is short.
21. The person who loves the vase of tulips is not in the first house.
22. The person who loves the boquet of lilies is directly left of the person who loves yellow.
23. Arnold is the person who loves purple.
24. The person who uses a OnePlus 9 and the person who uses a Samsung Galaxy S21 are next to each other.
25. The person who has an average height is not in the first house.
26. The person who loves the rose bouquet is Alice.
 What is the value of attribute House for the person whose attribute Cigar is pall mall? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Bob`, `Peter`, `Alice`, `Carol`
 - People have unique heights: `very tall`, `tall`, `average`, `short`, `super tall`, `very short`
 - Each person has a unique birthday month: `sept`, `may`, `jan`, `april`, `feb`, `mar`
 - People have unique hair colors: `blonde`, `red`, `black`, `auburn`, `gray`, `brown`
 - People have unique favorite book genres: `science fiction`, `romance`, `biography`, `mystery`, `fantasy`, `historical fiction`
 - Each person has a unique type of pet: `bird`, `hamster`, `fish`, `dog`, `cat`, `rabbit`

## Clues:
1. The person with an aquarium of fish is the person who loves mystery books.
2. The person who has black hair is the person who owns a dog.
3. The person who has gray hair is the person who loves science fiction books.
4. The person who loves historical fiction books is somewhere to the left of the person who has black hair.
5. The person who loves historical fiction books is directly left of the person who owns a rabbit.
6. The person whose birthday is in February is the person who owns a dog.
7. Bob is the person who keeps a pet bird.
8. The person who keeps a pet bird is the person who loves romance books.
9. Alice is directly left of the person who loves fantasy books.
10. The person who owns a rabbit is directly left of the person who is very short.
11. The person who is short is somewhere to the left of the person who is super tall.
12. The person who has an average height is in the sixth house.
13. The person who has red hair is not in the first house.
14. The person who is very tall is somewhere to the right of the person who is super tall.
15. There are two houses between the person who loves romance books and Eric.
16. The person with an aquarium of fish is in the sixth house.
17. The person who has blonde hair is the person who loves historical fiction books.
18. The person who is tall is somewhere to the right of the person whose birthday is in February.
19. The person who has auburn hair is Carol.
20. The person with an aquarium of fish is the person whose birthday is in March.
21. The person who loves science fiction books is directly left of the person with an aquarium of fish.
22. The person whose birthday is in September is not in the first house.
23. The person who loves biography books is directly left of the person who has a cat.
24. The person whose birthday is in January is the person who loves science fiction books.
25. Arnold is the person whose birthday is in May.
 What is the value of attribute House for the person whose attribute HairColor is brown? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


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

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

Answer: 1


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

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

Answer: sept


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`
 - Each person lives in a unique style of house: `victorian`, `ranch`, `colonial`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `lilies`
 - People have unique favorite book genres: `romance`, `mystery`, `science fiction`
 - People own unique car models: `ford f150`, `toyota camry`, `tesla model 3`
 - Each person has a unique level of education: `associate`, `high school`, `bachelor`

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

Answer: 1


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Bob`, `Eric`, `Arnold`
 - They all have a unique favorite flower: `lilies`, `carnations`, `daffodils`, `roses`, `tulips`
 - People have unique favorite sports: `swimming`, `soccer`, `tennis`, `basketball`, `baseball`
 - The mothers' names in different houses are unique: `Aniya`, `Kailyn`, `Janelle`, `Penny`, `Holly`

## Clues:
1. The person whose mother's name is Kailyn is the person who loves basketball.
2. Arnold is somewhere to the left of the person who loves baseball.
3. The person who loves basketball is the person who loves a carnations arrangement.
4. The person who loves the rose bouquet is Bob.
5. The person who loves baseball is The person whose mother's name is Holly.
6. The person whose mother's name is Aniya is directly left of Peter.
7. The person who loves tennis is The person whose mother's name is Janelle.
8. The person who loves the rose bouquet is somewhere to the left of the person who loves swimming.
9. The person who loves a bouquet of daffodils is in the fifth house.
10. The person who loves tennis and the person who loves the boquet of lilies are next to each other.
11. The person who loves the rose bouquet is directly left of Alice.
12. The person who loves basketball is in the second house.
13. There are two houses between Eric and the person who loves baseball.
 What is the value of attribute House for the person whose attribute FavoriteSport is swimming? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Alice`, `Peter`, `Eric`
 - People use unique phone models: `oneplus 9`, `google pixel 6`, `iphone 13`, `huawei p50`, `samsung galaxy s21`
 - Each person has a favorite color: `blue`, `red`, `yellow`, `green`, `white`
 - The mothers' names in different houses are unique: `Janelle`, `Penny`, `Holly`, `Aniya`, `Kailyn`
 - The people are of nationalities: `german`, `norwegian`, `swede`, `dane`, `brit`
 - Everyone has something unique for lunch: `spaghetti`, `grilled cheese`, `stew`, `pizza`, `stir fry`

## Clues:
1. The person who uses a OnePlus 9 and Arnold are next to each other.
2. There are two houses between the person who uses a OnePlus 9 and The person whose mother's name is Kailyn.
3. The person whose mother's name is Penny is somewhere to the left of the Swedish person.
4. The person who loves yellow is the person who uses a Google Pixel 6.
5. The person who loves eating grilled cheese is The person whose mother's name is Holly.
6. Arnold is the person who loves the spaghetti eater.
7. Bob is the person who uses a Huawei P50.
8. The German is the person who is a pizza lover.
9. Eric is directly left of the person who loves blue.
10. Alice is The person whose mother's name is Holly.
11. The person who loves stir fry is the British person.
12. The person whose mother's name is Penny is not in the third house.
13. Arnold is directly left of the person who uses a Huawei P50.
14. The British person is somewhere to the left of the Dane.
15. The person who uses a Google Pixel 6 is Arnold.
16. The person whose mother's name is Aniya is the person who uses a Samsung Galaxy S21.
17. The person who loves blue is the Norwegian.
18. The person who loves white is the person who uses a Huawei P50.
19. The person whose favorite color is red is directly left of the person who loves blue.
 What is the value of attribute Mother for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: Holly


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`
 - People have unique favorite music genres: `classical`, `pop`, `rock`
 - They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`
 - People have unique heights: `average`, `very short`, `short`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`

## Clues:
1. Peter is the person who has an average height.
2. The person who smokes Blue Master is the person who is short.
3. The person who loves a bouquet of daffodils is directly left of the person partial to Pall Mall.
4. The person who loves pop music is the person who loves a bouquet of daffodils.
5. The person whose mother's name is Janelle is the person who loves the boquet of lilies.
6. The person whose mother's name is Aniya is in the first house.
7. The person who has an average height is in the second house.
8. The person who loves pop music and the person who loves classical music are next to each other.
9. Eric is in the third house.
10. The person whose mother's name is Holly is the person who is very short.
 What is the value of attribute Cigar for the person whose attribute Flower is carnations? Please reason step by step, and put your final answer within \boxed{}

Answer: prince