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`, `Alice`, `Arnold`, `Bob`, `Carol`
 - Each person has a unique hobby: `cooking`, `knitting`, `painting`, `gardening`, `woodworking`, `photography`
 - Everyone has a favorite smoothie: `lime`, `cherry`, `desert`, `blueberry`, `watermelon`, `dragonfruit`
 - The people are of nationalities: `chinese`, `dane`, `german`, `norwegian`, `swede`, `brit`
 - People have unique favorite music genres: `hip hop`, `country`, `rock`, `jazz`, `classical`, `pop`

## Clues:
1. The person who loves rock music is Bob.
2. The person who enjoys knitting is the German.
3. The woodworking hobbyist is in the sixth house.
4. The person who loves rock music is directly left of the woodworking hobbyist.
5. There is one house between the Watermelon smoothie lover and the person who loves hip-hop music.
6. The Chinese is the Watermelon smoothie lover.
7. The Desert smoothie lover is the Norwegian.
8. The person who drinks Blueberry smoothies is not in the sixth house.
9. The person who loves pop music is somewhere to the left of the person who enjoys gardening.
10. Carol is somewhere to the left of the Swedish person.
11. Peter is somewhere to the right of the person who loves pop music.
12. The Norwegian is somewhere to the right of the Dragonfruit smoothie lover.
13. The German is the person who loves country music.
14. The person who paints as a hobby is directly left of the person who loves hip-hop music.
15. The Dane is Arnold.
16. The person who loves jazz music is the Chinese.
17. The British person is not in the third house.
18. The Swedish person is the person who loves pop music.
19. The person who drinks Lime smoothies is the photography enthusiast.
20. The person who loves hip-hop music is directly left of Alice.
21. The Dane is the woodworking hobbyist.
 What is the value of attribute Hobby for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: knitting


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`, `Eric`, `Alice`, `Bob`, `Carol`
 - People have unique favorite book genres: `biography`, `science fiction`, `fantasy`, `mystery`, `romance`, `historical fiction`
 - People have unique favorite sports: `baseball`, `basketball`, `swimming`, `volleyball`, `tennis`, `soccer`
 - People own unique car models: `honda civic`, `ford f150`, `tesla model 3`, `chevrolet silverado`, `bmw 3 series`, `toyota camry`

## Clues:
1. Eric is the person who loves mystery books.
2. The person who loves tennis is the person who loves fantasy books.
3. The person who loves soccer is directly left of the person who loves science fiction books.
4. There is one house between the person who owns a Honda Civic and the person who loves biography books.
5. Peter is somewhere to the right of Carol.
6. The person who loves tennis is in the first house.
7. The person who owns a Tesla Model 3 is somewhere to the right of the person who loves baseball.
8. Eric is somewhere to the left of the person who loves romance books.
9. The person who owns a Toyota Camry is somewhere to the right of the person who loves romance books.
10. The person who owns a BMW 3 Series is Peter.
11. The person who owns a BMW 3 Series is the person who loves basketball.
12. The person who owns a Tesla Model 3 is directly left of Arnold.
13. Alice and the person who loves volleyball are next to each other.
14. The person who loves historical fiction books is the person who loves soccer.
15. The person who owns a Chevrolet Silverado is not in the first house.
16. The person who loves science fiction books is directly left of the person who loves swimming.
 What is the value of attribute House for the person whose attribute BookGenre is historical fiction? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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

## Clues:
1. Alice is the person who loves swimming.
2. The person's child is named Alice is directly left of the person who loves historical fiction books.
3. The person who loves the stew is the person who loves historical fiction books.
4. The person with a doctorate is the person who loves the soup.
5. The person who loves science fiction books is in the sixth house.
6. The person who attended trade school is directly left of the person who loves historical fiction books.
7. The person who loves baseball and the person's child is named Bella are next to each other.
8. The person with a master's degree is somewhere to the left of the person who loves mystery books.
9. The person who loves soccer is somewhere to the left of the person who loves fantasy books.
10. The person who loves stir fry is the person with an associate's degree.
11. The person who is a pizza lover is Peter.
12. Bob is not in the sixth house.
13. The person's child is named Meredith is directly left of the person who loves fantasy books.
14. The person's child is named Samantha is Eric.
15. There is one house between the person who loves eating grilled cheese and Bob.
16. The person who loves eating grilled cheese is the person's child is named Samantha.
17. The person who loves volleyball is the person's child is named Samantha.
18. The person's child is named Fred is somewhere to the left of the person's child is named Samantha.
19. Bob is the person who loves tennis.
20. The person who loves soccer is directly left of Carol.
21. The person who loves eating grilled cheese is somewhere to the left of the person who loves mystery books.
22. The person's child is named Meredith is the person who loves biography books.
23. The person's child is named Meredith is the person who loves the soup.
24. Carol is the person with a high school diploma.
 What is the value of attribute Name for the person whose attribute Children is Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Eric`, `Bob`, `Alice`, `Peter`, `Arnold`
 - The people keep unique animals: `dog`, `horse`, `rabbit`, `bird`, `fish`, `cat`
 - People have unique hair colors: `brown`, `black`, `blonde`, `auburn`, `red`, `gray`

## Clues:
1. Arnold is not in the fifth house.
2. The person who has blonde hair is not in the second house.
3. The person who has black hair is the dog owner.
4. The bird keeper and Peter are next to each other.
5. The person who has auburn hair is Eric.
6. There are two houses between the cat lover and Eric.
7. The person who has brown hair is Bob.
8. The bird keeper is in the first house.
9. The person who has gray hair is somewhere to the right of the fish enthusiast.
10. The cat lover is directly left of the person who has black hair.
11. Arnold is directly left of Eric.
12. Carol is somewhere to the left of the person who has auburn hair.
13. The rabbit owner is Arnold.
 What is the value of attribute HairColor for the person whose attribute Animal is horse? Please reason step by step, and put your final answer within \boxed{}

Answer: gray


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`
 - People use unique phone models: `iphone 13`, `oneplus 9`, `google pixel 6`, `samsung galaxy s21`
 - Each person prefers a unique type of vacation: `mountain`, `cruise`, `beach`, `city`
 - They all have a unique favorite flower: `carnations`, `daffodils`, `lilies`, `roses`

## Clues:
1. The person who uses an iPhone 13 is the person who enjoys mountain retreats.
2. Arnold is not in the second house.
3. The person who loves a bouquet of daffodils is directly left of the person who loves a carnations arrangement.
4. The person who uses a OnePlus 9 is not in the first house.
5. The person who uses an iPhone 13 is somewhere to the right of Eric.
6. The person who loves the rose bouquet is the person who uses a Samsung Galaxy S21.
7. The person who enjoys mountain retreats is in the third house.
8. The person who loves a carnations arrangement is directly left of the person who loves the boquet of lilies.
9. The person who prefers city breaks is not in the second house.
10. The person who uses a OnePlus 9 is Arnold.
11. The person who prefers city breaks is somewhere to the left of the person who loves the boquet of lilies.
12. The person who likes going on cruises is Peter.
 What is the value of attribute Name for the person whose attribute Flower is daffodils? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Eric`, `Arnold`, `Peter`, `Alice`
 - People have unique favorite sports: `tennis`, `baseball`, `basketball`, `soccer`, `swimming`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Meredith`, `Timothy`, `Samantha`
 - The mothers' names in different houses are unique: `Kailyn`, `Holly`, `Penny`, `Janelle`, `Aniya`
 - The people keep unique animals: `horse`, `cat`, `dog`, `bird`, `fish`

## Clues:
1. The person whose mother's name is Penny is in the fourth house.
2. Eric is The person whose mother's name is Penny.
3. The person who keeps horses is the person who loves swimming.
4. The person who loves baseball is the person's child is named Meredith.
5. The dog owner is directly left of the person who loves basketball.
6. The person who loves soccer is the bird keeper.
7. The person who loves swimming is directly left of the person's child is named Fred.
8. The person who loves tennis is The person whose mother's name is Kailyn.
9. The person who is the mother of Timothy is The person whose mother's name is Aniya.
10. Eric is somewhere to the right of the person's child is named Samantha.
11. The person who loves basketball is Bob.
12. The person who is the mother of Timothy is the fish enthusiast.
13. The person's child is named Meredith is somewhere to the right of Peter.
14. The person who loves basketball is somewhere to the left of the person who keeps horses.
15. The bird keeper is Alice.
16. The person whose mother's name is Holly is the bird keeper.
17. Bob is not in the third house.
 What is the value of attribute FavoriteSport for the person whose attribute Children is Fred? Please reason step by step, and put your final answer within \boxed{}

Answer: soccer


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `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 Drink for the person whose attribute PhoneModel is google pixel 6? 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: `Carol`, `Alice`, `Eric`, `Bob`, `Peter`, `Arnold`
 - Each person has a unique birthday month: `jan`, `mar`, `feb`, `may`, `april`, `sept`
 - Each person prefers a unique type of vacation: `city`, `camping`, `beach`, `cruise`, `cultural`, `mountain`
 - Each person has a unique favorite drink: `milk`, `water`, `tea`, `root beer`, `coffee`, `boba tea`

## Clues:
1. There is one house between the person who goes on cultural tours and Alice.
2. The person whose birthday is in February is Peter.
3. The person whose birthday is in January is the person who enjoys camping trips.
4. Eric and Arnold are next to each other.
5. Carol is the person who likes going on cruises.
6. The person whose birthday is in January is directly left of Arnold.
7. The root beer lover is somewhere to the right of the person whose birthday is in April.
8. The person whose birthday is in September is the tea drinker.
9. The coffee drinker is Alice.
10. The person whose birthday is in March is Alice.
11. The person who prefers city breaks is the one who only drinks water.
12. The person whose birthday is in September is in the second house.
13. Bob is directly left of the boba tea drinker.
14. There is one house between the coffee drinker and the one who only drinks water.
15. The person who loves beach vacations and the coffee drinker are next to each other.
 What is the value of attribute Birthday for the person whose attribute Drink is water? Please reason step by step, and put your final answer within \boxed{}

Answer: may


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Eric`, `Alice`
 - They all have a unique favorite flower: `daffodils`, `carnations`, `roses`, `lilies`
 - People have unique heights: `very short`, `short`, `tall`, `average`
 - The mothers' names in different houses are unique: `Janelle`, `Kailyn`, `Holly`, `Aniya`
 - Each person has an occupation: `engineer`, `doctor`, `teacher`, `artist`
 - People have unique favorite sports: `swimming`, `basketball`, `tennis`, `soccer`

## Clues:
1. The person who loves swimming is the person who loves the rose bouquet.
2. The person who loves the rose bouquet is Eric.
3. Arnold is the person who is tall.
4. The person who loves a bouquet of daffodils is somewhere to the right of the person who is an engineer.
5. The person who loves soccer is the person who is short.
6. The person who is a teacher is in the first house.
7. The person whose mother's name is Janelle is the person who loves a carnations arrangement.
8. The person who loves basketball is the person who has an average height.
9. Arnold is not in the third house.
10. The person whose mother's name is Holly is somewhere to the right of the person who has an average height.
11. Peter is the person who is a doctor.
12. The person whose mother's name is Aniya is Alice.
13. Arnold is the person who loves the boquet of lilies.
 What is the value of attribute Occupation for the person whose attribute Flower is lilies? Please reason step by step, and put your final answer within \boxed{}

Answer: teacher


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Alice`, `Arnold`, `Peter`, `Eric`
 - Each person has a unique level of education: `doctorate`, `bachelor`, `associate`, `master`, `high school`
 - People use unique phone models: `oneplus 9`, `samsung galaxy s21`, `google pixel 6`, `iphone 13`, `huawei p50`
 - People have unique favorite music genres: `rock`, `classical`, `jazz`, `pop`, `hip hop`
 - The people keep unique animals: `bird`, `dog`, `horse`, `cat`, `fish`
 - Each person has a unique hobby: `painting`, `cooking`, `knitting`, `gardening`, `photography`

## Clues:
1. The person who loves hip-hop music is in the second house.
2. The person who loves classical music is not in the fifth house.
3. The person who loves classical music is the fish enthusiast.
4. The person who uses an iPhone 13 is the person with a doctorate.
5. The person with a master's degree is not in the second house.
6. The person who enjoys knitting is not in the first house.
7. The person with a high school diploma is somewhere to the left of the photography enthusiast.
8. The person who paints as a hobby is somewhere to the right of the person who loves rock music.
9. Arnold is the bird keeper.
10. The person with a bachelor's degree is the person who uses a Google Pixel 6.
11. The person with a bachelor's degree is somewhere to the right of the person who paints as a hobby.
12. Bob is not in the fourth house.
13. The person who loves cooking is the person who loves classical music.
14. The person who loves cooking is the person who uses a Huawei P50.
15. The person who keeps horses is somewhere to the right of Arnold.
16. The person who paints as a hobby is the person who uses a OnePlus 9.
17. The person who uses a OnePlus 9 is somewhere to the left of the person with an associate's degree.
18. The person who uses an iPhone 13 is the dog owner.
19. The person with a high school diploma is Alice.
20. Peter is the person who enjoys gardening.
21. The person who paints as a hobby is the person who loves jazz music.
 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: master


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`, `Peter`, `Arnold`, `Eric`
 - Each person has an occupation: `teacher`, `doctor`, `engineer`, `artist`
 - The people are of nationalities: `swede`, `dane`, `norwegian`, `brit`
 - The people keep unique animals: `horse`, `bird`, `cat`, `fish`
 - Each person has a favorite color: `green`, `white`, `red`, `yellow`
 - People have unique favorite sports: `tennis`, `soccer`, `swimming`, `basketball`

## Clues:
1. The person who is an artist is directly left of the person who loves swimming.
2. Alice is the fish enthusiast.
3. The person who is a teacher is in the second house.
4. The Norwegian is the person who loves white.
5. Arnold is directly left of the Swedish person.
6. The person who loves white and the person who loves tennis are next to each other.
7. The person who keeps horses is Eric.
8. The person whose favorite color is green is the person who loves tennis.
9. The person who keeps horses is directly left of the person who loves tennis.
10. The person who loves yellow is Peter.
11. The Dane is in the first house.
12. Alice is somewhere to the right of Peter.
13. The person who loves white is not in the second house.
14. There is one house between the cat lover and the person who loves soccer.
15. The person who loves tennis is somewhere to the right of the person who is a doctor.
 What is the value of attribute Name for the person whose attribute Nationality is swede? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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

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

Answer: Peter


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Bob`, `Peter`
 - Each person prefers a unique type of vacation: `mountain`, `city`, `cruise`, `beach`, `camping`
 - Each person has a unique level of education: `doctorate`, `high school`, `bachelor`, `associate`, `master`
 - Each person has a favorite color: `blue`, `red`, `white`, `yellow`, `green`
 - People use unique phone models: `google pixel 6`, `iphone 13`, `oneplus 9`, `huawei p50`, `samsung galaxy s21`
 - Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `stew`

## Clues:
1. The person who loves the stew is not in the first house.
2. There are two houses between the person who loves stir fry and the person with an associate's degree.
3. The person who enjoys mountain retreats is the person with a bachelor's degree.
4. The person with a doctorate is somewhere to the right of Bob.
5. The person who uses a Samsung Galaxy S21 is in the third house.
6. Eric is the person with a doctorate.
7. The person with a doctorate is in the third house.
8. The person who loves stir fry is the person with a bachelor's degree.
9. The person with a doctorate is the person who is a pizza lover.
10. The person whose favorite color is green is somewhere to the right of Peter.
11. The person who enjoys camping trips is the person who uses an iPhone 13.
12. The person who likes going on cruises is Alice.
13. There is one house between the person with a high school diploma and the person who uses a Samsung Galaxy S21.
14. The person who uses a Google Pixel 6 is Arnold.
15. The person who uses a OnePlus 9 is somewhere to the right of the person who uses a Huawei P50.
16. Arnold is the person who loves eating grilled cheese.
17. The person who loves eating grilled cheese is not in the fourth house.
18. There are two houses between the person with a bachelor's degree and the person whose favorite color is red.
19. The person who loves beach vacations is somewhere to the right of the person who prefers city breaks.
20. The person whose favorite color is green is not in the second house.
21. The person who loves blue is somewhere to the right of Peter.
22. There is one house between the person who enjoys camping trips and the person who loves yellow.
 What is the value of attribute Food for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: grilled cheese


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Bob`, `Eric`, `Arnold`, `Peter`, `Carol`
 - People have unique heights: `short`, `tall`, `very short`, `average`, `very tall`, `super tall`
 - People have unique favorite music genres: `rock`, `jazz`, `classical`, `country`, `hip hop`, `pop`
 - Each mother is accompanied by their child: `Samantha`, `Alice`, `Fred`, `Bella`, `Meredith`, `Timothy`

## Clues:
1. The person who loves hip-hop music is not in the second house.
2. The person who is very tall is directly left of the person who is very short.
3. The person's child is named Samantha is in the first house.
4. The person who has an average height is directly left of the person who loves hip-hop music.
5. The person's child is named Alice is the person who loves jazz music.
6. The person who is the mother of Timothy is somewhere to the right of the person who loves jazz music.
7. Eric is directly left of the person who is tall.
8. The person who is short is the person who loves hip-hop music.
9. The person who is very short is the person who is the mother of Timothy.
10. Peter is the person who loves rock music.
11. The person's child is named Bella is Bob.
12. The person's child is named Fred is Alice.
13. The person who loves classical music is directly left of the person who loves pop music.
14. The person who loves rock music is somewhere to the right of the person who is very tall.
15. Carol is somewhere to the left of Alice.
16. Carol is somewhere to the right of Arnold.
17. The person who loves classical music is not in the first house.
18. The person who is super tall is Eric.
 What is the value of attribute House for the person whose attribute Children is Fred? 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: `Eric`, `Arnold`, `Peter`
 - Everyone has a favorite smoothie: `desert`, `watermelon`, `cherry`
 - People have unique favorite book genres: `science fiction`, `romance`, `mystery`

## Clues:
1. The person who likes Cherry smoothies is somewhere to the left of the person who loves mystery books.
2. Arnold is the person who loves mystery books.
3. The person who loves science fiction books is not in the first house.
4. The Desert smoothie lover is directly left of the person who loves mystery books.
5. Peter is in the first house.
 What is the value of attribute BookGenre for the person whose attribute Smoothie is desert? Please reason step by step, and put your final answer within \boxed{}

Answer: science fiction


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

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

Answer: high school


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Arnold`, `Peter`, `Alice`, `Eric`
 - Each person has a unique favorite drink: `boba tea`, `coffee`, `root beer`, `water`, `milk`, `tea`
 - Each person lives in a unique style of house: `ranch`, `victorian`, `craftsman`, `mediterranean`, `colonial`, `modern`
 - Everyone has a unique favorite cigar: `dunhill`, `prince`, `yellow monster`, `blue master`, `blends`, `pall mall`

## Clues:
1. Eric is the Dunhill smoker.
2. Peter and the root beer lover are next to each other.
3. The Prince smoker is Bob.
4. The person in a modern-style house is somewhere to the left of Arnold.
5. The one who only drinks water is somewhere to the right of Bob.
6. The person in a modern-style house is the person who smokes Blue Master.
7. The person in a ranch-style home is directly left of the person in a modern-style house.
8. The person who smokes Yellow Monster is somewhere to the right of the coffee drinker.
9. The root beer lover is in the sixth house.
10. The person who likes milk is somewhere to the left of the tea drinker.
11. Arnold is the person living in a colonial-style house.
12. The person in a Craftsman-style house is the coffee drinker.
13. The boba tea drinker is somewhere to the left of the person living in a colonial-style house.
14. The boba tea drinker is the person partial to Pall Mall.
15. The person residing in a Victorian house is not in the fifth house.
16. The person living in a colonial-style house is in the third house.
17. Alice is not in the first house.
 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: 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`, `Eric`, `Arnold`, `Bob`, `Alice`
 - Each person has a unique type of pet: `fish`, `dog`, `cat`, `bird`, `hamster`
 - People have unique hair colors: `black`, `red`, `gray`, `blonde`, `brown`
 - People have unique heights: `tall`, `very tall`, `very short`, `short`, `average`
 - The mothers' names in different houses are unique: `Janelle`, `Penny`, `Holly`, `Aniya`, `Kailyn`

## Clues:
1. The person who has red hair is the person who keeps a pet bird.
2. The person whose mother's name is Kailyn is Eric.
3. There is one house between the person who has gray hair and the person who has a cat.
4. The person whose mother's name is Janelle is Peter.
5. The person who is tall is directly left of The person whose mother's name is Janelle.
6. The person who has an average height is directly left of the person who has brown hair.
7. The person whose mother's name is Kailyn is the person who is very short.
8. The person who is very tall is somewhere to the right of The person whose mother's name is Janelle.
9. The person whose mother's name is Penny is in the first house.
10. The person with a pet hamster is in the first house.
11. The person who is tall is the person with an aquarium of fish.
12. The person whose mother's name is Kailyn is somewhere to the left of The person whose mother's name is Aniya.
13. The person who owns a dog is in the fifth house.
14. The person whose mother's name is Kailyn is directly left of the person who has black hair.
15. Bob is somewhere to the left of the person with an aquarium of fish.
16. The person who keeps a pet bird is directly left of Arnold.
 What is the value of attribute HairColor for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: gray


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Peter`, `Arnold`, `Eric`, `Alice`, `Carol`
 - People have unique hair colors: `red`, `gray`, `auburn`, `blonde`, `brown`, `black`
 - People have unique favorite book genres: `historical fiction`, `biography`, `romance`, `fantasy`, `mystery`, `science fiction`
 - People have unique heights: `very short`, `very tall`, `tall`, `short`, `super tall`, `average`
 - Each person has a unique level of education: `associate`, `doctorate`, `high school`, `trade school`, `bachelor`, `master`
 - Each person has a unique favorite drink: `boba tea`, `milk`, `water`, `root beer`, `coffee`, `tea`

## Clues:
1. The person with a doctorate and Bob are next to each other.
2. There is one house between Carol and the person who has black hair.
3. Peter is the person with a doctorate.
4. The person who loves science fiction books is Eric.
5. The one who only drinks water is the person who has an average height.
6. Alice is the person who loves mystery books.
7. The person who loves romance books is Bob.
8. The person who has brown hair is in the second house.
9. The person who has an average height is in the fourth house.
10. The boba tea drinker is the person who is very tall.
11. The person with a high school diploma is Bob.
12. The person who is short is somewhere to the left of the person who is super tall.
13. The person who loves historical fiction books and the person with a bachelor's degree are next to each other.
14. The person who attended trade school is the person who has red hair.
15. Carol is the person who has auburn hair.
16. The person who is very short is somewhere to the right of the person who has gray hair.
17. There are two houses between Eric and the person who loves fantasy books.
18. There are two houses between the tea drinker and the person who is very short.
19. Eric is somewhere to the left of the person with a bachelor's degree.
20. The root beer lover is Alice.
21. The person with an associate's degree is Arnold.
22. The person who is tall is not in the second house.
23. The person who loves science fiction books is the boba tea drinker.
24. The person who has black hair is not in the fourth house.
25. The person who is short is the coffee drinker.
26. The coffee drinker and the person with a high school diploma are next to each other.
27. The coffee drinker is not in the second house.
 What is the value of attribute HairColor for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: gray


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Alice`
 - People have unique favorite music genres: `jazz`, `rock`, `classical`, `pop`

## Clues:
1. Alice is directly left of Peter.
2. The person who loves classical music is directly left of Peter.
3. Arnold is the person who loves jazz music.
4. The person who loves rock music is not in the second house.
5. The person who loves rock music is directly left of the person who loves pop music.
 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: 1


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

## Clues:
1. There are two houses between the person who loves fantasy books and the person whose birthday is in April.
2. The person whose birthday is in February is directly left of the person who loves a bouquet of daffodils.
3. The person who likes going on cruises is the person who loves a carnations arrangement.
4. The person whose birthday is in September is directly left of the person who loves science fiction books.
5. The person who loves a bouquet of daffodils is the person who prefers city breaks.
6. The person whose birthday is in April is Arnold.
7. The person whose birthday is in February is the person who loves a carnations arrangement.
8. Alice is the person who likes going on cruises.
9. The person who loves the boquet of lilies is the person who enjoys mountain retreats.
10. Eric is not in the third house.
11. The person who loves science fiction books is the person who loves the boquet of lilies.
12. The person who loves mystery books is Eric.
13. Eric and the person whose birthday is in January are next to each other.
 What is the value of attribute Birthday for the person whose attribute Flower is daffodils? 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: `Arnold`, `Peter`, `Eric`
 - Each person has a unique hobby: `gardening`, `photography`, `cooking`
 - Each person prefers a unique type of vacation: `mountain`, `city`, `beach`
 - Everyone has a unique favorite cigar: `pall mall`, `prince`, `blue master`
 - The mothers' names in different houses are unique: `Janelle`, `Holly`, `Aniya`
 - People have unique heights: `short`, `average`, `very short`

## Clues:
1. The person who loves beach vacations is somewhere to the right of the person who is very short.
2. The person whose mother's name is Aniya is somewhere to the right of the person who loves cooking.
3. Eric is not in the second house.
4. The person who is short is in the third house.
5. The person who prefers city breaks is the photography enthusiast.
6. The person who enjoys gardening is the person who enjoys mountain retreats.
7. The person partial to Pall Mall is the photography enthusiast.
8. The person who enjoys mountain retreats is The person whose mother's name is Holly.
9. The person who enjoys gardening is the person who smokes Blue Master.
10. Peter is The person whose mother's name is Aniya.
 What is the value of attribute Cigar for the person whose attribute House is 2? 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`
 - The people are of nationalities: `dane`, `swede`, `german`, `brit`, `norwegian`
 - Each person has a unique hobby: `gardening`, `painting`, `knitting`, `photography`, `cooking`
 - Everyone has a favorite smoothie: `dragonfruit`, `lime`, `watermelon`, `desert`, `cherry`
 - People have unique hair colors: `brown`, `gray`, `black`, `blonde`, `red`
 - People have unique favorite sports: `baseball`, `soccer`, `swimming`, `tennis`, `basketball`

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

Answer: 3


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`
 - Each mother is accompanied by their child: `Meredith`, `Fred`, `Bella`
 - Each person has a unique birthday month: `jan`, `april`, `sept`
 - Everyone has a favorite smoothie: `desert`, `cherry`, `watermelon`
 - Everyone has something unique for lunch: `spaghetti`, `grilled cheese`, `pizza`
 - The mothers' names in different houses are unique: `Janelle`, `Aniya`, `Holly`

## Clues:
1. Arnold is the person who loves eating grilled cheese.
2. The person who loves the spaghetti eater and The person whose mother's name is Holly are next to each other.
3. Peter is directly left of the person whose birthday is in September.
4. The person who loves the spaghetti eater is the person whose birthday is in January.
5. The person who likes Cherry smoothies is not in the first house.
6. The person's child is named Bella is the Desert smoothie lover.
7. The person whose birthday is in September is Eric.
8. The person whose mother's name is Aniya is in the first house.
9. The person's child is named Fred is somewhere to the right of the person who likes Cherry smoothies.
10. The person who likes Cherry smoothies is the person whose birthday is in January.
 What is the value of attribute Children for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{}

Answer: Meredith


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`, `Eric`, `Bob`, `Alice`, `Carol`, `Peter`
 - The people are of nationalities: `german`, `brit`, `dane`, `chinese`, `swede`, `norwegian`
 - People have unique favorite music genres: `pop`, `jazz`, `hip hop`, `classical`, `country`, `rock`
 - Each person has a unique level of education: `doctorate`, `associate`, `master`, `bachelor`, `high school`, `trade school`

## Clues:
1. The Chinese is the person who loves pop music.
2. The person with a bachelor's degree is directly left of Arnold.
3. The person with a master's degree is in the first house.
4. Carol is somewhere to the left of Peter.
5. The Dane is the person with a doctorate.
6. The person who loves classical music is the person with a master's degree.
7. The person with a bachelor's degree is in the fifth house.
8. Eric is somewhere to the right of Bob.
9. Carol is the British person.
10. The person with a doctorate is somewhere to the right of the Norwegian.
11. The person with a doctorate is the person who loves rock music.
12. The Norwegian is somewhere to the right of the German.
13. The person who attended trade school is somewhere to the left of the person with a high school diploma.
14. The person who attended trade school and the Chinese are next to each other.
15. The person who loves jazz music is Arnold.
16. The person who loves hip-hop music is directly left of Alice.
 What is the value of attribute Nationality for the person whose attribute Education is high school? Please reason step by step, and put your final answer within \boxed{}

Answer: swede


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`, `Eric`, `Carol`, `Alice`
 - People own unique car models: `bmw 3 series`, `ford f150`, `tesla model 3`, `toyota camry`, `honda civic`, `chevrolet silverado`
 - Each person has a unique hobby: `woodworking`, `painting`, `knitting`, `photography`, `gardening`, `cooking`

## Clues:
1. The person who loves cooking is not in the first house.
2. The person who owns a Tesla Model 3 is in the fifth house.
3. The person who owns a Honda Civic is in the third house.
4. Alice and the person who owns a Honda Civic are next to each other.
5. There is one house between the person who owns a Chevrolet Silverado and Carol.
6. The photography enthusiast is directly left of the person who paints as a hobby.
7. Peter is somewhere to the right of the person who owns a Tesla Model 3.
8. The person who owns a Honda Civic is directly left of Bob.
9. The person who enjoys knitting is somewhere to the right of the person who owns a Toyota Camry.
10. The person who enjoys knitting is somewhere to the left of Eric.
11. The woodworking hobbyist is directly left of the person who owns a BMW 3 Series.
12. The person who paints as a hobby is in the third house.
 What is the value of attribute CarModel for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: ford f150


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Alice`, `Peter`, `Eric`
 - Everyone has something unique for lunch: `grilled cheese`, `stew`, `pizza`, `spaghetti`
 - People have unique hair colors: `blonde`, `black`, `red`, `brown`
 - Each person has a favorite color: `red`, `white`, `yellow`, `green`
 - The mothers' names in different houses are unique: `Holly`, `Aniya`, `Janelle`, `Kailyn`

## Clues:
1. Alice is the person whose favorite color is red.
2. The person who has black hair is the person who loves the stew.
3. The person who loves white is Arnold.
4. The person whose favorite color is red and The person whose mother's name is Kailyn are next to each other.
5. The person who loves yellow and the person who has black hair are next to each other.
6. The person who is a pizza lover is somewhere to the left of the person whose favorite color is green.
7. Peter is The person whose mother's name is Janelle.
8. The person who has blonde hair is the person who loves white.
9. The person who has red hair is Alice.
10. The person who loves white is somewhere to the right of the person who loves eating grilled cheese.
11. The person who loves white is not in the second house.
12. The person whose mother's name is Kailyn is the person who is a pizza lover.
13. The person whose mother's name is Holly is the person who has red hair.
 What is the value of attribute Color for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: yellow


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`
 - People own unique car models: `ford f150`, `tesla model 3`, `toyota camry`
 - Each person prefers a unique type of vacation: `beach`, `mountain`, `city`
 - The people are of nationalities: `dane`, `swede`, `brit`
 - People have unique hair colors: `blonde`, `black`, `brown`
 - Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`

## Clues:
1. The Swedish person is the person who owns a Ford F-150.
2. The person who has blonde hair is not in the second house.
3. The person who owns a Toyota Camry and Arnold are next to each other.
4. The person who has black hair is somewhere to the right of the person in a ranch-style home.
5. The person who has black hair is the Dane.
6. The person residing in a Victorian house is not in the second house.
7. Peter is directly left of the person who loves beach vacations.
8. The person living in a colonial-style house is the person who has blonde hair.
9. The person who has black hair is Arnold.
10. The Dane is the person who loves beach vacations.
11. Peter is the person who prefers city breaks.
 What is the value of attribute House for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`, `Bob`
 - Each person has a favorite color: `red`, `green`, `white`, `blue`, `yellow`
 - Each mother is accompanied by their child: `Bella`, `Timothy`, `Samantha`, `Meredith`, `Fred`
 - They all have a unique favorite flower: `tulips`, `daffodils`, `carnations`, `lilies`, `roses`

## Clues:
1. Alice is not in the fifth house.
2. Eric is the person who is the mother of Timothy.
3. Alice and Bob are next to each other.
4. The person who loves blue is not in the fourth house.
5. The person's child is named Samantha is the person who loves the vase of tulips.
6. The person who loves the vase of tulips is Alice.
7. The person's child is named Fred is the person whose favorite color is red.
8. The person's child is named Bella is in the first house.
9. There is one house between the person who loves blue and the person who loves yellow.
10. The person who loves yellow is the person who loves the rose bouquet.
11. The person's child is named Meredith is somewhere to the left of Bob.
12. The person who loves white is not in the second house.
13. The person who loves a carnations arrangement is not in the second house.
14. The person who loves white is Arnold.
15. The person who loves the boquet of lilies is in the first house.
 What is the value of attribute House for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


Fill the numbers from 1 to 9 in the spaces of the given diagram (with 2 and 3 already filled), so that the number on the left is greater than the number on the right, and the number above is greater than the number below. How many different ways are there to fill the diagram?

Answer: 16


A farmer bought two sheep in 1996. That year, he didn't have any offspring. The first sheep gave birth to one lamb every three years, and the second sheep gave birth to one lamb every two years. All the sheep born each year also gave birth to one lamb annually. How many sheep will the farmer have in the year 2000?

Answer: 9


In the figure below, $ABCD$ is a trapezoid and its diagonals $AC$ and $BD$ are perpendicular. Additionally, $BC=10$ and $AD=30$.

a) Determine the ratio between the segments $BE$ and $ED$.

b) Find the length of the segments $EC$, $AE$, and $ED$ in terms of the length of $BE=x$.

c) If $AE \cdot EC=108$, determine the value of $BE \cdot ED$.

Answer: 192


Every day, Ivan Ivanovich is driven to work by a company car. One day, Ivan Ivanovich decided to walk and left his house an hour earlier than usual. On the way, he met the company car, and he completed the remaining distance in the car. As a result, he arrived to work 10 minutes earlier than usual. How long did Ivan Ivanovich walk?

Answer: 55 \text{ minutes}


\(D\) is the point of tangency of the incircle with side \(BC\). \(N\) is an arbitrary point on segment \(ID\). The perpendicular to \(ID\) at point \(N\) intersects the circumcircle. \(O_1\) is the center of the circumcircle of \(\triangle XIY\). Find the product \(OO_1 \cdot IN\).

Answer: Rr


Let \( x, y, z \) be distinct positive integers such that \( xyz \mid (xy-1)(yz-1)(zx-1) \). Find all possible values of \( x, y, z \).

Answer: (2,3,5)


Let \(\alpha\) and \(\beta\) be real numbers. If for any real numbers \(x, y, z\), the inequality \(a(xy + yz + zx) \leq M \leq \beta (x^2 + y^2 + z^2)\) always holds, where \(M = \sqrt{x^2 + xy + y^2} \cdot \sqrt{y^2 + yz + z^2} + \sqrt{y^2 + yz + z^2} \cdot \sqrt{z^2 + zx + x^2} + \sqrt{z^2 + zx + x^2} \cdot \sqrt{x^2 + xy + y^2}\), find the maximum value of \(\alpha\) and the minimum value of \(\beta\).

Answer: 3


Mrs. Lígia has a square-shaped plot. She decides to divide it into five regions: four rectangles and one square, as illustrated in the figure below:

In the figure above:

- The central square has an area of \(64 \, \text{m}^2\);
- The longer sides of the four rectangles have the same length;
- The five regions have the same perimeter.

Determine the area of Mrs. Lígia's plot.

Answer: 256 \text{ m}^2


Consider each permutation of the nine digits \(1, 2, \ldots, 9\) as a nine-digit number. How many of these nine-digit numbers are divisible by 11?

Answer: 31680


As shown in the diagram, in the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, $M$ and $N$ are the midpoints of edges $A_{1} B_{1}$ and $B B_{1}$, respectively. A cross-section of the cube passes through points $D, M,$ and $N$, and the cross-section forms a polygon $\Gamma$. Find the cosine of the interior angle of $\Gamma$ at vertex $D$.

Answer: \frac{4}{13}


The sets \( A \) and \( B \) form a partition of positive integers if \( A \cap B = \emptyset \) and \( A \cup B = \mathbb{N} \). The set \( S \) is called prohibited for the partition if \( k + l \neq s \) for any \( k, l \in A, s \in S \) and any \( k, l \in B, s \in S \).

a) Define Fibonacci numbers \( f_{i} \) by letting \( f_{1} = 1, f_{2} = 2 \) and \( f_{i+1} = f_{i} + f_{i-1} \), so that \( f_{3} = 3, f_{4} = 5 \), etc. How many partitions for which the set \( F \) of all Fibonacci numbers is prohibited are there? (We count \( A, B \) and \( B, A \) as the same partition.)

b) How many partitions for which the set \( P \) of all powers of 2 is prohibited are there? What if we require in addition that \( P \subseteq A \)?

Answer: 1


For every polynomial
$$
f(x) = a_{0} + a_{1} x + \cdots + a_{n} x^{n},
$$
let $\Gamma(f(x)) = a_{0}^{2} + a_{1}^{2} + \cdots + a_{n}^{2}$. Given the polynomial
$$
P(x) = (x + 1)(x + 2) \cdots (x + 2020),
$$
prove that there exist at least $2^{2019}$ polynomials with positive coefficients $Q_{k}(x)$ $(1 \leqslant k \leqslant 2^{2019})$ that satisfy the following two conditions:
1. $\operatorname{deg} Q_{k}(x) = 2020$ $(1 \leqslant k \leqslant 2^{2019})$;
2. For every positive integer $n$,
$$
\Gamma\left(Q_{k}^{n}(x)\right) = \Gamma\left(P^{n}(x)\right).
$$

Answer: 2^{2019}


Identical gases are in two thermally insulated vessels with volumes \( V_{1}=2 \) L and \( V_{2}=3 \) L. The pressures of the gases are \( p_{1}=3 \) atm and \( p_{2}=4 \) atm, and their temperatures are \( T_{1}=400 \) K and \( T_{2}=500 \) K respectively. The gases are mixed. Determine the temperature that will be established in the vessels.

Answer: 462\,


Assume the quartic \( x^{4} - a x^{3} + b x^{2} - a x + d = 0 \) has four real roots \( \frac{1}{2} \leq x_{1}, x_{2}, x_{3}, x_{4} \leq 2 \). Find the maximum possible value of \( \frac{\left(x_{1} + x_{2}\right) \left(x_{1} + x_{3}\right) x_{4}}{\left(x_{4} + x_{2}\right) \left(x_{4} + x_{3}\right) x_{1}} \) (over all valid choices of \( a, b, d \)).

Answer: \frac{5}{4}


Let \( N \) be the number of functions \( f \) from \(\{1,2, \ldots, 101\}\) to \(\{1,2, \ldots, 101\}\) such that \( f^{101}(1) = 2 \). Find the remainder when \( N \) is divided by 103.

Answer: 43


As shown in the figure, a truck travels from $A$ to $C$ at a speed of 50 km/h, while at the same time, delivery person A and delivery person B set out from $B$ to travel to $A$ and $C$ respectively, with both traveling at the same speed. If A travels 3 km before meeting the truck, and 12 minutes later, the truck and B arrive at $C$ simultaneously, then what is the distance between cities $A$ and $C$ in kilometers?

Answer: 17.5


In the ring bounded by concentric circles with radii $R$ and $r$ centered at point $O$, two points $A$ and $B$ are taken; the distance $AB$ is equal to 1. What is the smallest possible value of the angle $AOB$?

Answer: 0


\( AB \) is the diameter of a circle; \( C, D, E \) are points on one semicircle \( ACDEB \). Points \( F \) and \( G \) are taken on the diameter \( AB \) such that \(\angle CFA = \angle DFB\) and \(\angle DGA = \angle EGB \). Find \(\angle FDG\), if the arc \( AC \) equals \( 60^\circ \) and the arc \( BE \) equals \( 20^\circ \).

Answer: 50


Petya's bank account contains 500 dollars. The bank allows only two types of transactions: withdrawing 300 dollars or adding 198 dollars. What is the maximum amount Petya can withdraw from the account if he has no other money?

Answer: 498


Given that \(b\) and \(c\) are both integers and \(c < 2000\). If the quadratic equation \(x^{2} - bx + c = 0\) has roots whose real parts are both greater than 1, how many pairs \((b, c)\) satisfy this condition?

Answer: 1995003


A Hare and a Wolf are running in the same direction along a circular track with a length of 200 meters, at speeds of \( 5 \, \mathrm{m/s} \) and \( 3 \, \mathrm{m/s} \), respectively. It turns out that the distance between them is exactly the same as it was 40 seconds ago (distance is measured along the shortest of the two arcs). What could this distance be?

Choose one answer from the following options: \( 40, 50, 60, 70, 80, 90 \) meters.

Answer: 60


From the vertex of an acute angle of a rhombus, perpendiculars are drawn to the lines containing the sides of the rhombus, which do not include this vertex. The length of each perpendicular is 3 cm, and the distance between their bases is $3 \sqrt{3}$ cm. Calculate the lengths of the diagonals of the rhombus.

Answer: 2\sqrt{3}


A porter needs to transport 200 steamed buns from the kitchen to the construction site (he is currently in the kitchen). He can carry 40 buns each time. However, because he is very greedy, he will eat 1 bun each time he travels from the kitchen to the construction site or from the construction site to the kitchen. What is the maximum number of buns he can transport to the construction site?

Answer: 191


7. As shown in the figure, in rectangle $A B C D$ with an area of 2, point $E$ is the midpoint of side $A D$. If $\triangle A B E$ and $\triangle D E C$ are folded along $B E$ and $C E$ respectively, such that points $A$ and $D$ coincide at point $P$, then the maximum volume of the tetrahedron $P-E B C$ is . $\qquad$

Answer: \dfrac{\sqrt{2} \cdot \sqrt[4]{3}}{9}


5. Select some numbers without repetition from $1,2, \ldots 15$, such that the sum of any two numbers is not a perfect square of a natural number, then the maximum number of numbers that can be selected is ( ).

Answer: 8


Given a polynomial \( P(x) \) of degree \( n \) with the leading coefficient equal to 1, it is known that if \( x \) is an integer, then \( P(x) \) is an integer multiple of \( p \) (where \( p \) is a natural number). Prove that \( n! \) is divisible by \( p \).

Answer: p \mid n!


In a warehouse, the inventory is stored in packages weighing no more than 1 ton each. We have a 1-ton and a 4-ton truck. What is the maximum load that we can definitely deliver in one trip?

Answer: 4


4. A magician and his assistant have a deck of cards, all of which have the same back, and the front is one of 2017 colors (each color has 1000000 cards). The magic trick is: the magician first leaves the room, the audience arranges $n$ face-up cards in a row on the table, the magician's assistant then flips $n-1$ of these cards over in their original positions, leaving only one card face-up, and then the magician enters the room, observes the cards on the table, and selects a face-down card, guessing its color. Find the minimum value of $n$, such that the magician and his assistant can complete this trick according to a predetermined strategy.

Answer: 2018


From the conversation of the sailors, we noted the following detail this year:

Cook: When I was as old as the sailor is now, I was twice as old as he is.

Engineer: I am only 4 years older than the sailor.

Sailor: Only the cook's age is an odd number, and the least common multiple of our three ages is the captain's birth year.

How old is the captain?

Answer: 1938


Suppose you have $27$ identical unit cubes colored such that $3$ faces adjacent to a vertex are red and the other $3$ are colored blue. Suppose further that you assemble these $27$ cubes randomly into a larger cube with $3$ cubes to an edge (in particular, the orientation of each cube is random). The probability that the entire cube is one solid color can be written as $\frac{1}{2^n}$ for some positive integer $n$. Find $n$.

Answer: 53


Let $\alpha_{1}, \beta_{1}, \gamma_{1}, \alpha_{2}, \beta_{2}$ and $\gamma_{2}$ be real numbers such that $\alpha_{1}+\beta_{1}+\gamma_{1} \neq 0$ and $\alpha_{2}+\beta_{2}+\gamma_{2} \neq 0$. Show that $\left\langle\alpha_{1}, \beta_{1}, \gamma_{1}\right\rangle=\left\langle\alpha_{2}, \beta_{2}, \gamma_{2}\right\rangle$ if and only if the triplets $\left(\alpha_{1}, \beta_{1}, \gamma_{1}\right)$ and $\left(\alpha_{2}, \beta_{2}, \gamma_{2}\right)$ are multiples of each other.

Answer: \left\langle\alpha_{1}, \beta_{1}, \gamma_{1}\right\rangle=\left\langle\alpha_{2}, \beta_{2}, \gamma_{2}\right\rangle \text{ if and only if } (\alpha_{1}, \beta_{1}, \gamma_{1}) \text{ and } (\alpha_{2}, \beta_{2}, \gamma_{2}) \text{ are scalar multiples of each other.}


Example 3 㷵 On a board, there is a convex 2011-gon, and Betya draws its diagonals one by one. It is known that each diagonal drawn intersects at most one of the previously drawn diagonals at an interior point. Question: What is the maximum number of diagonals Betya can draw? [3]

Answer: 4016


## Zadatak B-4.6.

Zadane su elipsa s jednadžbom $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ i hiperbola kojoj su žarišta u tjemenima elipse na velikoj osi, a tjemena u žarištima elipse. Kolika je površina šesterokuta kojemu su vrhovi tjemena elipse na maloj osi i sjecišta zadanih krivulja?

Answer: \dfrac{12}{7} \left( \sqrt{35} + \sqrt{10} \right)


A farmer sold his house geese. By the end of the market, he sold exactly one-tenth as many pieces as the price per piece he set. He divided the revenue between his two sons. Starting with the elder, the boys alternately received one hundred forints each, until finally, only a few ten-forint coins were left for the younger one. Then the father gave him his pocket knife and said that this way both of them received the same value. How much was the knife worth?

Answer: 40


6. A line cuts off triangle $A K N$ from a regular hexagon $A B C D E F$ such that $A K+A N=A B$. Find the sum of the angles under which segment $K N$ is seen from the vertices of the hexagon ( $\angle K A N+\angle K B N+\angle K C N+\angle K D N+\angle K E N+$ $+\angle K F N$).

## 9 t h  g r a d e

Answer: 240


Problem 4. Sashka had 3 baskets of apples. The baskets contained 12, 14, and 22 apples. Sashka is allowed to choose two of the three baskets and transfer apples from one to the other. In doing so, she must transfer as many apples as there are in the basket to which she is adding (transferring) the apples. Sashka made three such transfers, and in the end, all the baskets had the same number of apples. How did Sashka do this?

Answer: 16


3. A circle is inscribed in an isosceles trapezoid $A B C D$ and touches the base $C D$ at point $L$, and the legs $B C$ and $A D$ at points $K$ and $M$, respectively. In what ratio does the line $A L$ divide the segment $M K$?

Answer: \dfrac{1}{3}


In an obtuse triangle, the largest side is 4, and the smallest side is 2. Can the area of the triangle be greater than $2 \sqrt{3}$?

Answer: No


Task 10.

Find all natural numbers $n$ such that the sum $S(n)$ of the digits in the decimal representation of the number $2^{n}$ is 5.

Answer: 5


12.149. An isosceles trapezoid is circumscribed around a circle of radius $r$. The lateral side of the trapezoid forms an angle $\alpha$ with the smaller base. Find the radius of the circle circumscribed around the trapezoid.

Answer: \dfrac{r \sqrt{1 + \sin^2 \alpha}}{\sin^2 \alpha}


For a positive integer $k$, let the set
$$
R_{n}=\left\{\begin{array}{l}
\{-k,-(k-1), \cdots,-1,1, \cdots, k-1, k\}, \quad n=2 k ; \\
\{-k,-(k-1), \cdots,-1,0,1, \cdots, k-1, k\}, \quad n=2 k+1 .
\end{array}\right.
$$

A device contains some balls and red or white strings connecting some pairs of balls. A "labeling" is to color each ball with one of the elements from $R_{n}$. A labeling is "good" if and only if the colors of any two balls connected by a string are different; a labeling is "wise" if and only if the colors of any two balls connected by a white string are different, and the sum of the colors of any two balls connected by a red string is not equal to 0.

For a fixed positive integer $n \geqslant 3$, assume that any device has a good labeling with respect to $R_{n}$, and also has a wise labeling with respect to $R_{m}$. Find the minimum value of the positive integer $m=m(n)$.

Answer: 2n - 1


In the figure, \( \triangle ABC \) has all sides as positive integers and has a perimeter of 35. \( G \) and \( I \) are the centroid and the incenter of \( \triangle ABC \) respectively, and \( \angle GIC = 90^\circ \). Find the length of side \( AB \).

Answer: 11


The areas of the projections of a body onto the coordinate planes are $S_{1}, S_{2}$, and $S_{3}$. Prove that its volume does not exceed $\sqrt{S_{1} S_{2} S_{3}}$.

Answer: V \leq \sqrt{S_1 S_2 S_3}


In a test, \( 3n \) students participate, who are located in three rows of \( n \) students in each. The students leave the test room one by one. If \( N_{1}(t), N_{2}(t), N_{3}(t) \) denote the numbers of students in the first, second, and third row respectively at time \( t \), find the probability that for each \( t \) during the test,
$$
|N_{i}(t) - N_{j}(t)| < 2, \quad i \neq j, \quad i, j = 1, 2, \ldots.
$$

Answer: \dfrac{6^n (n!)^3}{(3n)!}


Let $k$ and $a$ are positive constants. Denote by $V_1$ the volume of the solid generated by a rotation of the figure enclosed
by the curve $C: y=\frac{x}{x+k}\ (x\geq 0)$, the line $x=a$ and the $x$-axis around the $x$-axis, and denote by $V_2$ that of
the solid by a rotation of the figure enclosed by the curve $C$, the line $y=\frac{a}{a+k}$ and the $y$-axis around the $y$-axis.
Find the ratio $\frac{V_2}{V_1}.$

Answer: k


8. In a circle, three chords $A A_{1}, B B_{1}, C C_{1}$ intersect at one point. The angular measures of the arcs $A C_{1}, A B, C A_{1}$, and $A_{1} B_{1}$ are $150^{\circ}, 30^{\circ}, 60^{\circ}$, and $30^{\circ}$, respectively. Find the angular measure of the arc $B_{1} C_{1}$.

Answer: 60


## Task 4 - 300734

Someone wants to select as many different natural numbers from 1 to 1000 as possible according to the following rules:

The first number is to be chosen randomly from the numbers 1 to 6 by rolling a die and selecting the number shown on the die. The subsequent numbers are to be chosen such that the following applies:

When the selection of numbers is complete, any two of the overall selected numbers always have a sum that is divisible by 3.

Determine (depending on all possibilities of the first number) the maximum number of numbers that can be selected according to these rules!

Answer: 333


Galoikin A.i.

Nine digits: $1,2,3, \ldots, 9$ are written in some order (so that a nine-digit number is formed). Consider all triples of consecutive digits, and find the sum of the corresponding seven three-digit numbers. What is the maximum possible value of this sum?

Answer: 4648


8.3. $A B C D$ - a convex quadrilateral. It is known that $\angle C A D=\angle D B A=40^{\circ}, \angle C A B=60^{\circ}$, $\angle C B D=20^{\circ}$. Find the angle $C D B$.

Answer: 30


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

## Clues:
1. The person who uses an iPhone 13 is Alice.
2. The person who uses a Huawei P50 is in the first house.
3. The person who uses a OnePlus 9 is in the sixth house.
4. The person who uses a Google Pixel 6 is not in the second house.
5. The person who uses an iPhone 13 is not in the second house.
6. There is one house between Bob and Carol.
7. The person who uses a Huawei P50 is Eric.
8. The person who uses a Xiaomi Mi 11 is in the third house.
9. Alice is somewhere to the left of Carol.
10. Arnold is the person who uses a OnePlus 9.
 What is the value of attribute House for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Peter`, `Arnold`, `Eric`
 - Each person has a unique type of pet: `cat`, `dog`, `bird`, `fish`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`, `Kailyn`
 - Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`, `craftsman`
 - People have unique favorite sports: `soccer`, `basketball`, `swimming`, `tennis`

## Clues:
1. The person who loves soccer is Alice.
2. The person whose mother's name is Kailyn is somewhere to the left of the person in a Craftsman-style house.
3. The person with an aquarium of fish and The person whose mother's name is Janelle are next to each other.
4. Alice is the person who keeps a pet bird.
5. The person who loves swimming is the person in a ranch-style home.
6. Eric is in the first house.
7. Eric is the person residing in a Victorian house.
8. Arnold is the person in a ranch-style home.
9. Arnold is not in the second house.
10. The person whose mother's name is Holly is somewhere to the left of the person who owns a dog.
11. The person whose mother's name is Janelle is in the fourth house.
12. The person whose mother's name is Kailyn is the person who loves tennis.
13. Alice is The person whose mother's name is Janelle.
 What is the value of attribute House for the person whose attribute Pet is cat? 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: `Peter`, `Eric`, `Arnold`, `Carol`, `Bob`, `Alice`
 - People have unique heights: `super tall`, `very tall`, `tall`, `very short`, `short`, `average`

## Clues:
1. Carol is not in the sixth house.
2. There is one house between Bob and the person who is very tall.
3. The person who is super tall is not in the sixth house.
4. Eric is the person who is very tall.
5. Peter is not in the sixth house.
6. The person who is short is not in the first house.
7. The person who is short is not in the third house.
8. The person who is short is directly left of Eric.
9. The person who is very short is somewhere to the right of the person who is very tall.
10. The person who is tall is Alice.
11. Carol is not in the second house.
12. There are two houses between the person who is super tall and Eric.
 What is the value of attribute House for the person whose attribute Height is very short? Please reason step by step, and put your final answer within \boxed{}

Answer: 6


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

## Clues:
1. Eric is the person who has red hair.
2. The person who loves classical music is directly left of the person who has blonde hair.
3. The person who has brown hair is not in the first house.
4. The person who loves pop music is not in the third house.
5. The person who loves classical music is in the first house.
6. The person who loves jazz music is the person who has red hair.
7. The person who loves rock music is Arnold.
8. Peter is somewhere to the right of the person who loves rock music.
 What is the value of attribute House for the person whose attribute HairColor is red? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


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

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

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Carol`, `Alice`, `Bob`, `Arnold`
 - The people are of nationalities: `brit`, `norwegian`, `swede`, `chinese`, `german`, `dane`
 - Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `lime`, `desert`, `watermelon`, `blueberry`

## Clues:
1. The Chinese is somewhere to the right of the Swedish person.
2. The Desert smoothie lover is the German.
3. The person who drinks Blueberry smoothies is Bob.
4. The person who drinks Blueberry smoothies is somewhere to the right of Eric.
5. Peter and Carol are next to each other.
6. The Swedish person is the Dragonfruit smoothie lover.
7. Arnold is the Norwegian.
8. The Dane is the person who likes Cherry smoothies.
9. Peter is directly left of the Watermelon smoothie lover.
10. Arnold is not in the third house.
11. The Norwegian is somewhere to the left of the Chinese.
12. The Dane is in the first house.
13. The German is in the sixth house.
14. The Chinese is not in the fifth house.
 What is the value of attribute House for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


There are 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`, `Alice`, `Bob`, `Arnold`
 - The people keep unique animals: `cat`, `horse`, `fish`, `dog`, `bird`
 - The mothers' names in different houses are unique: `Penny`, `Holly`, `Janelle`, `Kailyn`, `Aniya`

## Clues:
1. The person whose mother's name is Janelle and The person whose mother's name is Penny are next to each other.
2. There are two houses between the fish enthusiast and The person whose mother's name is Kailyn.
3. There are two houses between Peter and Bob.
4. The bird keeper is in the second house.
5. The person who keeps horses is directly left of the dog owner.
6. The fish enthusiast and Peter are next to each other.
7. The bird keeper is somewhere to the right of Alice.
8. The person whose mother's name is Aniya is somewhere to the left of The person whose mother's name is Penny.
9. The person whose mother's name is Janelle is in the second house.
10. Arnold is directly left of the person who keeps horses.
 What is the value of attribute Mother for the person whose attribute Animal is horse? Please reason step by step, and put your final answer within \boxed{}

Answer: Kailyn


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 have unique heights: `very tall`, `average`, `tall`, `very short`, `short`
 - Everyone has something unique for lunch: `stew`, `grilled cheese`, `spaghetti`, `pizza`, `stir fry`

## Clues:
1. Alice is the person who is short.
2. The person who is tall is in the third house.
3. The person who has an average height is not in the second house.
4. The person who has an average height is somewhere to the left of the person who loves the stew.
5. The person who loves stir fry is Arnold.
6. The person who is a pizza lover is the person who is tall.
7. Eric is the person who is tall.
8. Bob is somewhere to the right of Arnold.
9. The person who loves eating grilled cheese is somewhere to the right of Eric.
10. The person who is very short is somewhere to the left of Arnold.
 What is the value of attribute Food for the person whose attribute Height is tall? Please reason step by step, and put your final answer within \boxed{}

Answer: pizza


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`, `Peter`, `Arnold`, `Eric`
 - Each person has a unique type of pet: `cat`, `dog`, `bird`, `fish`
 - The mothers' names in different houses are unique: `Holly`, `Janelle`, `Aniya`, `Kailyn`
 - Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`, `craftsman`
 - People have unique favorite sports: `soccer`, `basketball`, `swimming`, `tennis`

## Clues:
1. The person who loves soccer is Alice.
2. The person whose mother's name is Kailyn is somewhere to the left of the person in a Craftsman-style house.
3. The person with an aquarium of fish and The person whose mother's name is Janelle are next to each other.
4. Alice is the person who keeps a pet bird.
5. The person who loves swimming is the person in a ranch-style home.
6. Eric is in the first house.
7. Eric is the person residing in a Victorian house.
8. Arnold is the person in a ranch-style home.
9. Arnold is not in the second house.
10. The person whose mother's name is Holly is somewhere to the left of the person who owns a dog.
11. The person whose mother's name is Janelle is in the fourth house.
12. The person whose mother's name is Kailyn is the person who loves tennis.
13. Alice is The person whose mother's name is Janelle.
 What is the value of attribute Mother for the person whose attribute HouseStyle is victorian? Please reason step by step, and put your final answer within \boxed{}

Answer: Holly


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

## Clues:
1. The person who loves the rose bouquet and the person who loves yellow are next to each other.
2. The person who loves a carnations arrangement is Peter.
3. The person who loves the rose bouquet is not in the third house.
4. The person whose favorite color is green is not in the fifth house.
5. The person who loves a bouquet of daffodils is Alice.
6. The person who loves yellow is Eric.
7. The person who has blonde hair is in the fifth house.
8. The person who has black hair is directly left of Arnold.
9. The person who loves yellow is the person who has brown hair.
10. Alice is the person whose favorite color is green.
11. The person who has red hair is the person who loves blue.
12. The person whose favorite color is red is somewhere to the right of the person who loves blue.
13. The person who has black hair is the person who loves the vase of tulips.
 What is the value of attribute 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 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Peter`
 - Each person has a unique hobby: `cooking`, `photography`, `gardening`
 - The people are of nationalities: `dane`, `brit`, `swede`
 - Everyone has something unique for lunch: `pizza`, `spaghetti`, `grilled cheese`
 - Everyone has a favorite smoothie: `cherry`, `desert`, `watermelon`

## Clues:
1. The Desert smoothie lover is the person who enjoys gardening.
2. The photography enthusiast is the Swedish person.
3. Peter is somewhere to the left of the Desert smoothie lover.
4. The person who is a pizza lover is in the third house.
5. The person who enjoys gardening is the Dane.
6. There is one house between the person who loves eating grilled cheese and Arnold.
7. Arnold is the Swedish person.
8. The Watermelon smoothie lover is somewhere to the left of the person who likes Cherry smoothies.
 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: 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: `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 PhoneModel for the person whose attribute Nationality is norwegian? Please reason step by step, and put your final answer within \boxed{}

Answer: oneplus 9


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Carol`, `Bob`, `Peter`, `Eric`, `Arnold`
 - They all have a unique favorite flower: `lilies`, `tulips`, `roses`, `daffodils`, `iris`, `carnations`
 - The people are of nationalities: `norwegian`, `dane`, `swede`, `german`, `brit`, `chinese`
 - Everyone has a favorite smoothie: `cherry`, `watermelon`, `desert`, `dragonfruit`, `blueberry`, `lime`
 - Each person has a unique hobby: `photography`, `cooking`, `knitting`, `woodworking`, `painting`, `gardening`
 - Each person has a unique type of pet: `rabbit`, `hamster`, `fish`, `cat`, `bird`, `dog`

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

Answer: 5


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Arnold`, `Eric`
 - Each person lives in a unique style of house: `victorian`, `ranch`, `craftsman`, `colonial`
 - People have unique favorite music genres: `pop`, `classical`, `rock`, `jazz`
 - They all have a unique favorite flower: `roses`, `lilies`, `carnations`, `daffodils`
 - Each person prefers a unique type of vacation: `city`, `beach`, `mountain`, `cruise`
 - Each person has a favorite color: `red`, `white`, `yellow`, `green`

## Clues:
1. The person who loves classical music is Peter.
2. The person in a ranch-style home is not in the fourth house.
3. The person who loves a bouquet of daffodils is the person living in a colonial-style house.
4. The person living in a colonial-style house is the person who loves white.
5. The person who prefers city breaks and the person whose favorite color is red are next to each other.
6. The person who loves the rose bouquet is not in the fourth house.
7. The person who likes going on cruises is in the second house.
8. The person who prefers city breaks is the person who loves rock music.
9. The person who loves pop music is Alice.
10. The person who loves the rose bouquet is the person who prefers city breaks.
11. Eric is the person who enjoys mountain retreats.
12. The person who enjoys mountain retreats is directly left of the person who loves a bouquet of daffodils.
13. The person who loves yellow is somewhere to the left of the person who likes going on cruises.
14. The person who enjoys mountain retreats is the person residing in a Victorian house.
15. The person who loves classical music is the person who likes going on cruises.
16. Peter is somewhere to the right of the person who loves the boquet of lilies.
 What is the value of attribute House for the person whose attribute Color is red? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


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

Answer: science fiction