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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`
- The mothers' names in different houses are unique: `Holly`, `Kailyn`, `Janelle`, `Aniya`
- They all have a unique favorite flower: `carnations`, `roses`, `lilies`, `daffodils`
## Clues:
1. Alice is The person whose mother's name is Kailyn.
2. The person whose mother's name is Janelle is somewhere to the right of Arnold.
3. Peter is somewhere to the right of the person who loves a carnations arrangement.
4. Eric is the person who loves a bouquet of daffodils.
5. Arnold is The person whose mother's name is Holly.
6. The person who loves a carnations arrangement is somewhere to the right of The person whose mother's name is Holly.
7. The person who loves the boquet of lilies is directly left of Alice.
8. Alice is in the third house.
What is the value of attribute Mother for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{} | Holly | 3/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Bob`, `Alice`, `Eric`, `Arnold`
- People use unique phone models: `oneplus 9`, `google pixel 6`, `samsung galaxy s21`, `iphone 13`, `huawei p50`
- Each person has an occupation: `lawyer`, `engineer`, `teacher`, `artist`, `doctor`
## Clues:
1. The person who uses a Samsung Galaxy S21 is directly left of Eric.
2. There are two houses between Alice and the person who is an artist.
3. The person who uses an iPhone 13 is directly left of Bob.
4. The person who is a lawyer is in the third house.
5. The person who is a doctor is Arnold.
6. The person who is an engineer is directly left of the person who is an artist.
7. The person who uses a OnePlus 9 is somewhere to the right of Eric.
8. The person who uses a Google Pixel 6 is Peter.
What is the value of attribute House for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{} | 2 | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Peter`, `Bob`, `Eric`, `Arnold`, `Carol`
- Each person has a unique level of education: `bachelor`, `high school`, `associate`, `doctorate`, `trade school`, `master`
- Everyone has something unique for lunch: `spaghetti`, `stir fry`, `stew`, `grilled cheese`, `pizza`, `soup`
- People have unique favorite sports: `baseball`, `swimming`, `tennis`, `volleyball`, `soccer`, `basketball`
- People have unique heights: `very short`, `average`, `very tall`, `super tall`, `tall`, `short`
## Clues:
1. Alice is somewhere to the left of Bob.
2. The person who loves tennis is the person with an associate's degree.
3. The person who is tall is not in the first house.
4. The person who loves the spaghetti eater is in the second house.
5. The person who loves baseball is in the third house.
6. Arnold is somewhere to the left of the person who is very tall.
7. Eric is the person with a bachelor's degree.
8. The person who loves the soup is the person who is very short.
9. The person who loves swimming is the person who loves the stew.
10. Arnold is somewhere to the right of the person who loves soccer.
11. The person with a doctorate is not in the sixth house.
12. The person who loves stir fry is Carol.
13. The person who has an average height is in the sixth house.
14. There is one house between the person who attended trade school and the person who has an average height.
15. The person who is very tall is directly left of the person who is super tall.
16. Alice is somewhere to the right of the person who attended trade school.
17. The person who is a pizza lover is somewhere to the left of Eric.
18. Alice is the person who loves basketball.
19. The person with a high school diploma is Arnold.
What is the value of attribute FavoriteSport for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{} | swimming | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Peter`, `Bob`, `Eric`, `Arnold`, `Alice`
- Each person prefers a unique type of vacation: `camping`, `cruise`, `beach`, `city`, `cultural`, `mountain`
- People have unique favorite sports: `volleyball`, `baseball`, `basketball`, `swimming`, `soccer`, `tennis`
## Clues:
1. The person who loves tennis and Peter are next to each other.
2. Bob is in the second house.
3. There is one house between the person who prefers city breaks and the person who loves tennis.
4. Peter is somewhere to the left of Alice.
5. Carol is the person who loves basketball.
6. The person who loves swimming is the person who likes going on cruises.
7. The person who loves tennis and the person who loves beach vacations are next to each other.
8. The person who loves swimming is Bob.
9. The person who loves volleyball is the person who enjoys camping trips.
10. Eric is in the first house.
11. Arnold is somewhere to the left of the person who enjoys mountain retreats.
12. Eric is the person who loves soccer.
13. The person who prefers city breaks is in the first house.
14. The person who enjoys camping trips is not in the sixth 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{} | 2 | 2/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Alice`, `Peter`, `Eric`
- Each mother is accompanied by their child: `Bella`, `Meredith`, `Fred`, `Samantha`
- Everyone has something unique for lunch: `pizza`, `spaghetti`, `grilled cheese`, `stew`
- Each person has a favorite color: `red`, `white`, `yellow`, `green`
## Clues:
1. The person who is a pizza lover is somewhere to the left of the person's child is named Samantha.
2. The person whose favorite color is red is directly left of the person who loves white.
3. Eric is somewhere to the right of the person who loves the stew.
4. The person who loves white is in the fourth house.
5. The person whose favorite color is green is not in the second house.
6. The person whose favorite color is red is the person's child is named Bella.
7. The person who loves eating grilled cheese is in the second house.
8. There is one house between the person's child is named Meredith and Alice.
9. There is one house between Peter and Alice.
10. Alice is not in the third house.
What is the value of attribute House for the person whose attribute Children is Samantha? Please reason step by step, and put your final answer within \boxed{} | 4 | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Eric`, `Peter`, `Bob`, `Arnold`
- Each person has a favorite color: `red`, `white`, `green`, `blue`, `yellow`
- Everyone has a favorite smoothie: `watermelon`, `dragonfruit`, `cherry`, `desert`, `lime`
- Each person has a unique birthday month: `feb`, `sept`, `april`, `mar`, `jan`
- People have unique favorite book genres: `romance`, `science fiction`, `mystery`, `fantasy`, `biography`
- People have unique heights: `very short`, `very tall`, `tall`, `short`, `average`
## Clues:
1. The person who drinks Lime smoothies is in the second house.
2. The person who loves fantasy books is directly left of the Dragonfruit smoothie lover.
3. The person whose birthday is in September is not in the third house.
4. There is one house between the person whose birthday is in March and Peter.
5. The person whose birthday is in February is the Desert smoothie lover.
6. The person who is tall is not in the fifth house.
7. The person whose birthday is in January is somewhere to the left of the person whose birthday is in February.
8. The person who is very short is the person who loves blue.
9. The person whose favorite color is red is Arnold.
10. The person who loves science fiction books is directly left of the person who loves biography books.
11. Bob is not in the fifth house.
12. The person whose birthday is in January is the person whose favorite color is green.
13. The person who has an average height is the person who likes Cherry smoothies.
14. The person who loves fantasy books is the person whose birthday is in February.
15. The person whose favorite color is red is directly left of the person who is very short.
16. The person who loves science fiction books is the person whose birthday is in March.
17. The person who is very tall is in the second house.
18. The person who drinks Lime smoothies is somewhere to the left of the person who loves mystery books.
19. Eric is in the third house.
20. The person who loves fantasy books is the person who loves white.
What is the value of attribute BookGenre for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{} | romance | 0/8 |
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`, `Eric`, `Peter`, `Carol`, `Bob`, `Arnold`
- Everyone has a favorite smoothie: `watermelon`, `blueberry`, `desert`, `cherry`, `dragonfruit`, `lime`
- Everyone has something unique for lunch: `stew`, `pizza`, `grilled cheese`, `stir fry`, `soup`, `spaghetti`
- People use unique phone models: `google pixel 6`, `iphone 13`, `xiaomi mi 11`, `huawei p50`, `samsung galaxy s21`, `oneplus 9`
- People own unique car models: `tesla model 3`, `honda civic`, `toyota camry`, `ford f150`, `chevrolet silverado`, `bmw 3 series`
- Each person lives in a unique style of house: `craftsman`, `ranch`, `modern`, `victorian`, `mediterranean`, `colonial`
## Clues:
1. Bob is the person who uses a Xiaomi Mi 11.
2. The person who loves the soup is in the fourth house.
3. The Dragonfruit smoothie lover is somewhere to the left of the person in a ranch-style home.
4. There is one house between the person who owns a Chevrolet Silverado and the person residing in a Victorian house.
5. The person in a Mediterranean-style villa is the person who drinks Lime smoothies.
6. Eric is in the sixth house.
7. The Desert smoothie lover is the person who is a pizza lover.
8. The person living in a colonial-style house is the person who drinks Blueberry smoothies.
9. The Dragonfruit smoothie lover and the person who uses a Google Pixel 6 are next to each other.
10. The person who loves the soup is Peter.
11. Alice is somewhere to the right of the person who owns a BMW 3 Series.
12. The person who loves stir fry is the person in a ranch-style home.
13. The person who owns a Ford F-150 is the person living in a colonial-style house.
14. The person in a Craftsman-style house is somewhere to the right of the person in a modern-style house.
15. The person who loves the stew is directly left of the person in a ranch-style home.
16. The person who owns a Tesla Model 3 is directly left of the person who loves stir fry.
17. The person who loves eating grilled cheese is the person who owns a Honda Civic.
18. The person in a Mediterranean-style villa is the person who uses a Google Pixel 6.
19. The person in a Craftsman-style house is the Watermelon smoothie lover.
20. The person in a modern-style house is Carol.
21. The person who uses an iPhone 13 is in the first house.
22. The person who owns a Honda Civic is somewhere to the left of the person who owns a BMW 3 Series.
23. The person who uses a Xiaomi Mi 11 is the person who is a pizza lover.
24. The person who uses a Samsung Galaxy S21 is the person who loves stir fry.
25. The person residing in a Victorian house is directly left of the person who uses a OnePlus 9.
What is the value of attribute House for the person whose attribute HouseStyle is craftsman? Please reason step by step, and put your final answer within \boxed{} | 5 | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`
- The people are of nationalities: `brit`, `swede`, `norwegian`, `dane`
- They all have a unique favorite flower: `carnations`, `lilies`, `roses`, `daffodils`
- Each person has a unique level of education: `high school`, `bachelor`, `master`, `associate`
## Clues:
1. The Norwegian is directly left of the person who loves the rose bouquet.
2. The person with a high school diploma is Eric.
3. Arnold is not in the first house.
4. The person with an associate's degree is the person who loves a carnations arrangement.
5. The Dane is not in the third house.
6. Peter is the person who loves the rose bouquet.
7. The Swedish person and the Norwegian are next to each other.
8. Eric is in the second house.
9. The person who loves the boquet of lilies is the person with a master's degree.
10. The person who loves the boquet of lilies is the Swedish person.
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{} | 4 | 1/8 |
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`, `Bob`, `Arnold`, `Carol`, `Alice`
- Each person has a unique birthday month: `may`, `sept`, `jan`, `mar`, `feb`, `april`
- People have unique hair colors: `brown`, `blonde`, `red`, `auburn`, `black`, `gray`
- Each mother is accompanied by their child: `Alice`, `Samantha`, `Fred`, `Meredith`, `Timothy`, `Bella`
- Everyone has a favorite smoothie: `blueberry`, `cherry`, `watermelon`, `lime`, `dragonfruit`, `desert`
- The mothers' names in different houses are unique: `Sarah`, `Aniya`, `Janelle`, `Holly`, `Kailyn`, `Penny`
## Clues:
1. The person whose birthday is in September and the person's child is named Alice are next to each other.
2. The person whose birthday is in April is the person who is the mother of Timothy.
3. The person who likes Cherry smoothies is the person who has gray hair.
4. Alice is somewhere to the right of Arnold.
5. The person's child is named Alice is somewhere to the right of The person whose mother's name is Sarah.
6. Peter is the person who drinks Blueberry smoothies.
7. The person whose mother's name is Janelle is the person whose birthday is in May.
8. The person whose birthday is in January is somewhere to the left of The person whose mother's name is Sarah.
9. The Watermelon smoothie lover is the person who has brown hair.
10. The person who has red hair is somewhere to the right of the person who has gray hair.
11. The person who drinks Lime smoothies is in the fifth house.
12. The person who has black hair and the person's child is named Meredith are next to each other.
13. The person whose birthday is in March is somewhere to the right of the person who has red hair.
14. The person whose mother's name is Sarah is somewhere to the left of the person who has auburn hair.
15. The person who has black hair is directly left of The person whose mother's name is Penny.
16. The person's child is named Samantha is The person whose mother's name is Holly.
17. The person who has blonde hair and Bob are next to each other.
18. The person who has gray hair is the person whose birthday is in January.
19. The person who has black hair is in the first house.
20. The person whose mother's name is Sarah is the person who has blonde hair.
21. The person whose mother's name is Kailyn is Arnold.
22. The person whose birthday is in January is The person whose mother's name is Kailyn.
23. The person whose birthday is in September is Carol.
24. The person who drinks Lime smoothies is somewhere to the right of the Desert smoothie lover.
25. The person's child is named Fred is not in the third house.
What is the value of attribute Birthday for the person whose attribute HairColor is auburn? Please reason step by step, and put your final answer within \boxed{} | mar | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Peter`, `Eric`, `Arnold`, `Carol`, `Bob`
- People have unique heights: `very short`, `very tall`, `short`, `super tall`, `tall`, `average`
- Everyone has something unique for lunch: `grilled cheese`, `stir fry`, `pizza`, `spaghetti`, `soup`, `stew`
- The mothers' names in different houses are unique: `Holly`, `Janelle`, `Penny`, `Aniya`, `Kailyn`, `Sarah`
- Each person has a unique favorite drink: `tea`, `water`, `milk`, `coffee`, `boba tea`, `root beer`
- Each person has a unique type of pet: `rabbit`, `fish`, `bird`, `hamster`, `cat`, `dog`
## Clues:
1. Arnold is the person who loves the stew.
2. The person who owns a dog is directly left of the person who has a cat.
3. The person whose mother's name is Holly is in the sixth house.
4. The tea drinker is somewhere to the left of the boba tea drinker.
5. The tea drinker is in the second house.
6. The person who is very tall is Bob.
7. The person who has a cat is The person whose mother's name is Penny.
8. The person who is very short is directly left of Alice.
9. Carol is the person who is a pizza lover.
10. The person who has an average height is not in the sixth house.
11. The person who loves stir fry is Bob.
12. The person with a pet hamster is not in the third house.
13. The person whose mother's name is Janelle is somewhere to the left of the person with a pet hamster.
14. Eric is the person who loves the soup.
15. The person whose mother's name is Kailyn is directly left of the person who keeps a pet bird.
16. The one who only drinks water is somewhere to the right of the person who likes milk.
17. The person who owns a rabbit is the person who loves the stew.
18. The person who is tall is The person whose mother's name is Aniya.
19. The person who is very short is somewhere to the left of the person who likes milk.
20. The person who is tall is not in the fifth house.
21. The person who is very short is in the second house.
22. The person who loves the stew is the root beer lover.
23. The person whose mother's name is Kailyn is the boba tea drinker.
24. The person who is tall is not in the fourth house.
25. The person who is super tall is directly left of the person who loves eating grilled cheese.
26. Carol is directly left of the root beer lover.
What is the value of attribute Food for the person whose attribute Name is Carol? Please reason step by step, and put your final answer within \boxed{} | pizza | 0/8 |
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Eric`
- People have unique favorite music genres: `classical`, `rock`, `pop`
- Each person has a unique type of pet: `cat`, `fish`, `dog`
- The mothers' names in different houses are unique: `Janelle`, `Aniya`, `Holly`
- The people keep unique animals: `cat`, `bird`, `horse`
## Clues:
1. The person whose mother's name is Aniya is not in the first house.
2. The person whose mother's name is Aniya is directly left of The person whose mother's name is Holly.
3. The person whose mother's name is Janelle is Peter.
4. The person who loves pop music is directly left of the person who owns a dog.
5. The person who keeps horses is in the first house.
6. Peter and the cat lover are next to each other.
7. Eric is the person who loves rock music.
8. The person whose mother's name is Janelle and the person who has a cat are next to each other.
What is the value of attribute Pet for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{} | fish | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
- Everyone has something unique for lunch: `spaghetti`, `pizza`, `stew`, `grilled cheese`
- Each person has a unique favorite drink: `coffee`, `milk`, `tea`, `water`
- Everyone has a favorite smoothie: `cherry`, `desert`, `dragonfruit`, `watermelon`
## Clues:
1. The Dragonfruit smoothie lover is the person who likes milk.
2. The Watermelon smoothie lover is not in the fourth house.
3. The person who loves eating grilled cheese is directly left of Peter.
4. The person who loves the stew is Alice.
5. The person who is a pizza lover is the Dragonfruit smoothie lover.
6. The tea drinker is directly left of the coffee drinker.
7. The person who loves the stew is the Watermelon smoothie lover.
8. The person who likes Cherry smoothies is Eric.
9. Eric is in the first house.
10. Alice is somewhere to the right of the person who is a pizza lover.
What is the value of attribute House for the person whose attribute Drink is water? Please reason step by step, and put your final answer within \boxed{} | 1 | 3/8 |
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 Nationality for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{} | norwegian | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
- Everyone has a favorite smoothie: `dragonfruit`, `cherry`, `desert`, `watermelon`
- Everyone has a unique favorite cigar: `blue master`, `pall mall`, `dunhill`, `prince`
- People have unique heights: `tall`, `average`, `short`, `very short`
- People use unique phone models: `google pixel 6`, `samsung galaxy s21`, `iphone 13`, `oneplus 9`
## Clues:
1. The Dragonfruit smoothie lover is Eric.
2. The Dunhill smoker is the person who likes Cherry smoothies.
3. The person who uses a Samsung Galaxy S21 is directly left of the person who uses an iPhone 13.
4. The Dunhill smoker is somewhere to the right of the person who is very short.
5. The Watermelon smoothie lover is somewhere to the right of the Desert smoothie lover.
6. The Prince smoker is the person who uses a OnePlus 9.
7. The person who is tall is in the third house.
8. The person who is very short is the person who uses an iPhone 13.
9. The person who smokes Blue Master is not in the first house.
10. The Dunhill smoker is the person who is short.
11. Peter is not in the third house.
12. Arnold is the person who uses a Google Pixel 6.
13. The Dragonfruit smoothie lover is the person partial to Pall Mall.
What is the value of attribute PhoneModel for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{} | iphone 13 | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`, `Bob`
- Each person has a unique type of pet: `cat`, `dog`, `bird`, `fish`, `hamster`
- Everyone has a unique favorite cigar: `pall mall`, `blends`, `prince`, `dunhill`, `blue master`
- Everyone has a favorite smoothie: `watermelon`, `desert`, `dragonfruit`, `cherry`, `lime`
- People use unique phone models: `google pixel 6`, `oneplus 9`, `samsung galaxy s21`, `iphone 13`, `huawei p50`
- People have unique favorite sports: `baseball`, `soccer`, `basketball`, `swimming`, `tennis`
## Clues:
1. The person who loves swimming is directly left of the Prince smoker.
2. The person who smokes Blue Master is somewhere to the right of Eric.
3. The person who uses a OnePlus 9 is Arnold.
4. Arnold is somewhere to the right of the person with a pet hamster.
5. The person who owns a dog is Peter.
6. Eric is the Desert smoothie lover.
7. The person who loves basketball is not in the fifth house.
8. The person who has a cat is the person who uses a Samsung Galaxy S21.
9. The person who loves baseball is directly left of Peter.
10. There is one house between the Desert smoothie lover and the Dunhill smoker.
11. The person who loves baseball and the person who uses a Google Pixel 6 are next to each other.
12. The person who keeps a pet bird is in the second house.
13. The person who uses a Huawei P50 is in the fourth house.
14. The person who drinks Lime smoothies is in the fourth house.
15. The person partial to Pall Mall is in the fifth house.
16. The Dragonfruit smoothie lover is in the second house.
17. The person who loves tennis is the person with a pet hamster.
18. Bob is somewhere to the right of the person who owns a dog.
19. The Watermelon smoothie lover is Arnold.
20. The Prince smoker is somewhere to the left of the Dunhill smoker.
What is the value of attribute Cigar for the person whose attribute Pet is fish? Please reason step by step, and put your final answer within \boxed{} | pall mall | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
- Each person lives in a unique style of house: `victorian`, `ranch`, `colonial`, `craftsman`
- Each person has an occupation: `teacher`, `engineer`, `doctor`, `artist`
- Everyone has a unique favorite cigar: `prince`, `dunhill`, `pall mall`, `blue master`
- People have unique favorite music genres: `pop`, `rock`, `classical`, `jazz`
- People have unique heights: `very short`, `tall`, `average`, `short`
## Clues:
1. The person who loves classical music is the person living in a colonial-style house.
2. The person who smokes Blue Master is the person in a ranch-style home.
3. The person who loves rock music is the person who smokes Blue Master.
4. The Dunhill smoker is directly left of Peter.
5. Eric is in the first house.
6. The person residing in a Victorian house is in the third house.
7. The person who loves rock music and the person who loves classical music are next to each other.
8. The person who is a teacher is the person who is short.
9. The person who loves classical music is the Prince smoker.
10. The person who is a doctor is somewhere to the left of the person who is very short.
11. Arnold is the person who is an artist.
12. The person who smokes Blue Master is in the first house.
13. The person who is tall is directly left of the person who loves pop music.
14. The person residing in a Victorian house is the person who is a teacher.
What is the value of attribute House for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{} | 2 | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Bob`, `Eric`, `Arnold`, `Alice`
- People have unique hair colors: `brown`, `black`, `gray`, `blonde`, `red`
- Everyone has a unique favorite cigar: `pall mall`, `dunhill`, `prince`, `blue master`, `blends`
- Each person has a unique favorite drink: `milk`, `coffee`, `water`, `tea`, `root beer`
- People have unique favorite music genres: `rock`, `classical`, `pop`, `jazz`, `hip hop`
## Clues:
1. The person who has gray hair and Bob are next to each other.
2. Arnold is not in the first house.
3. The person who has blonde hair is not in the second house.
4. Peter is not in the first house.
5. The Dunhill smoker is the person who likes milk.
6. Arnold is the one who only drinks water.
7. The person who loves classical music is the person partial to Pall Mall.
8. The person who loves pop music is directly left of the person who loves jazz music.
9. The person who has brown hair is Bob.
10. The person who has red hair is the person who loves hip-hop music.
11. The root beer lover is Alice.
12. The person who has black hair is in the third house.
13. There are two houses between the coffee drinker and Arnold.
14. The person who smokes Blue Master is somewhere to the right of the person who loves hip-hop music.
15. The person who has blonde hair is the person who smokes many unique blends.
16. Alice is the person who loves classical music.
17. The Dunhill smoker is the person who loves jazz music.
What is the value of attribute Drink for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{} | tea | 0/8 |
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`
- Each person has a unique level of education: `associate`, `bachelor`, `high school`, `master`, `doctorate`
- People have unique favorite sports: `swimming`, `basketball`, `tennis`, `baseball`, `soccer`
- Each person prefers a unique type of vacation: `camping`, `cruise`, `city`, `mountain`, `beach`
- People use unique phone models: `google pixel 6`, `huawei p50`, `oneplus 9`, `samsung galaxy s21`, `iphone 13`
## Clues:
1. The person who uses a Huawei P50 is not in the second house.
2. The person with a master's degree is the person who uses a Google Pixel 6.
3. The person who loves swimming is the person with a high school diploma.
4. The person with a bachelor's degree is directly left of the person who loves tennis.
5. The person who enjoys camping trips is the person who loves tennis.
6. Bob is the person who uses a Samsung Galaxy S21.
7. The person with a high school diploma is not in the third house.
8. The person who loves swimming is directly left of the person who loves beach vacations.
9. The person who likes going on cruises is Arnold.
10. Bob is the person with an associate's degree.
11. The person who uses a OnePlus 9 is directly left of the person who loves basketball.
12. The person who enjoys camping trips and the person who prefers city breaks are next to each other.
13. Eric is the person who loves swimming.
14. The person who loves basketball is the person who enjoys mountain retreats.
15. The person who loves tennis is somewhere to the left of Alice.
16. Arnold is the person who loves soccer.
What is the value of attribute Vacation for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{} | mountain | 0/8 |
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 Vacation is city? Please reason step by step, and put your final answer within \boxed{} | 3 | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Peter`, `Bob`, `Arnold`
- Each person has a unique type of pet: `hamster`, `fish`, `cat`, `dog`, `bird`
- Each person has an occupation: `doctor`, `engineer`, `artist`, `lawyer`, `teacher`
- Each person has a favorite color: `green`, `blue`, `yellow`, `red`, `white`
- The people keep unique animals: `bird`, `cat`, `horse`, `fish`, `dog`
## Clues:
1. The person who owns a dog is Arnold.
2. The bird keeper is in the fourth house.
3. The person who keeps a pet bird is directly left of the dog owner.
4. The person who loves white is somewhere to the left of the person who is a lawyer.
5. The person who loves yellow is directly left of the person whose favorite color is green.
6. The cat lover is Bob.
7. The cat lover is somewhere to the left of Eric.
8. The person who keeps horses is in the fifth house.
9. The person who is a lawyer is directly left of the person who is a teacher.
10. The person who is a doctor is in the first house.
11. Alice is the person who loves yellow.
12. The person who loves blue is directly left of the person with an aquarium of fish.
13. The person who loves yellow is in the first house.
14. The person with a pet hamster is the person who is an artist.
15. Eric is the dog owner.
What is the value of attribute Pet for the person whose attribute Animal is dog? Please reason step by step, and put your final answer within \boxed{} | hamster | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Alice`, `Arnold`, `Bob`, `Eric`
- Each person has a unique hobby: `photography`, `cooking`, `knitting`, `gardening`, `painting`
- Each person has a unique favorite drink: `root beer`, `milk`, `water`, `coffee`, `tea`
## Clues:
1. Eric is the coffee drinker.
2. The tea drinker is the person who paints as a hobby.
3. The person who enjoys knitting is not in the fourth house.
4. Peter is not in the fourth house.
5. Eric is somewhere to the right of the root beer lover.
6. Arnold is the person who loves cooking.
7. The one who only drinks water is somewhere to the right of the person who enjoys gardening.
8. There is one house between Bob and the person who paints as a hobby.
9. The person who enjoys gardening is directly left of the root beer lover.
10. The photography enthusiast is the one who only drinks water.
What is the value of attribute Drink for the person whose attribute Name is Peter? Please reason step by step, and put your final answer within \boxed{} | tea | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Eric`, `Bob`, `Arnold`, `Peter`
- The people keep unique animals: `horse`, `bird`, `dog`, `cat`, `fish`
- Each person has an occupation: `lawyer`, `teacher`, `doctor`, `engineer`, `artist`
## Clues:
1. The dog owner is not in the first house.
2. The bird keeper is somewhere to the right of the person who is an engineer.
3. Arnold is the fish enthusiast.
4. The bird keeper is directly left of the cat lover.
5. The person who is a teacher is not in the second house.
6. The fish enthusiast is the person who is a lawyer.
7. The person who is an engineer is Alice.
8. The fish enthusiast is in the fourth house.
9. The person who is a doctor is Peter.
10. Bob is the person who is a teacher.
11. Peter is somewhere to the right of Arnold.
What is the value of attribute Animal for the person whose attribute Occupation is lawyer? Please reason step by step, and put your final answer within \boxed{} | fish | 4/8 |
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 MusicGenre for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{} | hip hop | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Eric`, `Alice`
- Each person prefers a unique type of vacation: `mountain`, `cruise`, `beach`, `city`
- Each person lives in a unique style of house: `craftsman`, `ranch`, `victorian`, `colonial`
- The mothers' names in different houses are unique: `Kailyn`, `Holly`, `Aniya`, `Janelle`
- They all have a unique favorite flower: `daffodils`, `roses`, `lilies`, `carnations`
- Each person has a favorite color: `green`, `white`, `yellow`, `red`
## Clues:
1. Alice is directly left of the person whose favorite color is red.
2. The person who loves a bouquet of daffodils is The person whose mother's name is Janelle.
3. Eric is not in the first house.
4. The person who loves the boquet of lilies is directly left of the person living in a colonial-style house.
5. The person residing in a Victorian house is in the second house.
6. The person who loves the rose bouquet is the person who loves yellow.
7. The person whose mother's name is Aniya is the person who loves yellow.
8. The person who enjoys mountain retreats is in the first house.
9. The person who likes going on cruises is the person whose favorite color is red.
10. The person who loves yellow is in the second house.
11. The person who loves white is the person who prefers city breaks.
12. The person whose mother's name is Holly is not in the fourth house.
13. The person whose favorite color is red is directly left of Peter.
14. The person who loves a bouquet of daffodils is the person in a ranch-style home.
What is the value of attribute HouseStyle for the person whose attribute Vacation is mountain? Please reason step by step, and put your final answer within \boxed{} | ranch | 0/8 |
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`, `Bob`, `Alice`
- People have unique hair colors: `brown`, `blonde`, `black`, `gray`, `red`
- Each person prefers a unique type of vacation: `beach`, `camping`, `city`, `cruise`, `mountain`
- Each person has an occupation: `doctor`, `lawyer`, `engineer`, `teacher`, `artist`
- People have unique favorite music genres: `jazz`, `pop`, `hip hop`, `classical`, `rock`
## Clues:
1. Alice is the person who has brown hair.
2. The person who is a teacher is somewhere to the right of the person who is an artist.
3. The person who has blonde hair is in the first house.
4. The person who prefers city breaks is not in the fourth house.
5. The person who enjoys mountain retreats is in the third house.
6. The person who loves beach vacations is somewhere to the right of the person who is a lawyer.
7. Eric is the person who has black hair.
8. The person who is an engineer is the person who has red hair.
9. The person who loves classical music is Bob.
10. The person who loves hip-hop music is in the fifth house.
11. The person who has blonde hair is the person who enjoys camping trips.
12. The person who has red hair is in the second house.
13. The person who is a teacher is the person who has gray hair.
14. The person who loves jazz music is the person who has black hair.
15. There is one house between the person who likes going on cruises and the person who has gray hair.
16. The person who loves rock music is the person who has red hair.
17. The person who is a lawyer is not in the third house.
18. The person who has blonde hair is Arnold.
What is the value of attribute House for the person whose attribute Vacation is camping? Please reason step by step, and put your final answer within \boxed{} | 1 | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
- Each person has a unique type of pet: `hamster`, `fish`, `bird`, `cat`, `dog`
- Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`, `modern`, `craftsman`
- Each person has a unique birthday month: `mar`, `sept`, `jan`, `feb`, `april`
- The people keep unique animals: `dog`, `cat`, `fish`, `bird`, `horse`
## Clues:
1. There is one house between Alice and the fish enthusiast.
2. The person in a ranch-style home is not in the fifth house.
3. The person whose birthday is in March is Alice.
4. The person in a ranch-style home is not in the fourth house.
5. Arnold is somewhere to the right of the person whose birthday is in April.
6. The person who has a cat is the person who keeps horses.
7. There are two houses between the cat lover and the person living in a colonial-style house.
8. Eric is somewhere to the left of the person whose birthday is in September.
9. The person whose birthday is in April is directly left of the person who keeps horses.
10. Alice is the person residing in a Victorian house.
11. The person whose birthday is in March and the cat lover are next to each other.
12. Peter is the person whose birthday is in February.
13. The cat lover is the person who owns a dog.
14. The bird keeper is somewhere to the left of the person who keeps a pet bird.
15. Bob is the person who keeps a pet bird.
16. Eric is in the fourth house.
17. The person who has a cat is somewhere to the left of the person with a pet hamster.
18. The person who keeps a pet bird is the person in a modern-style house.
What is the value of attribute Animal for the person whose attribute Name is Bob? Please reason step by step, and put your final answer within \boxed{} | fish | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Eric`, `Arnold`, `Peter`
- Each person has a unique hobby: `painting`, `gardening`, `photography`, `cooking`
- People have unique favorite book genres: `romance`, `science fiction`, `mystery`, `fantasy`
- Each person prefers a unique type of vacation: `city`, `beach`, `mountain`, `cruise`
- People have unique favorite music genres: `rock`, `pop`, `classical`, `jazz`
- Each person has a unique level of education: `high school`, `associate`, `bachelor`, `master`
## Clues:
1. The person who loves science fiction books is somewhere to the right of the person who loves fantasy books.
2. The person who paints as a hobby is the person who loves fantasy books.
3. Arnold is the person who loves fantasy books.
4. The person with a high school diploma is the person who loves pop music.
5. The person who loves cooking is somewhere to the right of Eric.
6. There are two houses between the photography enthusiast and the person who loves beach vacations.
7. The person who loves romance books is Peter.
8. The person who enjoys mountain retreats is not in the second house.
9. The person with a bachelor's degree is somewhere to the right of the person with a high school diploma.
10. The person who loves classical music is not in the third house.
11. The person who prefers city breaks is the person who loves science fiction books.
12. The person who loves rock music is Peter.
13. The person with a bachelor's degree is not in the fourth house.
14. The person with a master's degree is the person who loves jazz music.
15. The person who enjoys gardening is the person who loves romance books.
What is the value of attribute Education for the person whose attribute Vacation is city? Please reason step by step, and put your final answer within \boxed{} | master | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
- Each person has a unique birthday month: `sept`, `april`, `feb`, `jan`
- Everyone has something unique for lunch: `pizza`, `spaghetti`, `grilled cheese`, `stew`
- Each person has a unique hobby: `cooking`, `gardening`, `painting`, `photography`
- Each person has an occupation: `teacher`, `artist`, `engineer`, `doctor`
- Each mother is accompanied by their child: `Bella`, `Samantha`, `Fred`, `Meredith`
## Clues:
1. The person who is a teacher is the person who loves cooking.
2. The person whose birthday is in January is directly left of Eric.
3. The person who is an artist is not in the fourth house.
4. The person who loves the spaghetti eater is not in the third house.
5. The person's child is named Bella is the person who paints as a hobby.
6. The person whose birthday is in January is the person who is a teacher.
7. The person who paints as a hobby is the person who is a doctor.
8. The person whose birthday is in September is directly left of Arnold.
9. The person who is a pizza lover is Peter.
10. The person who loves the stew is somewhere to the left of the photography enthusiast.
11. Arnold is the person's child is named Meredith.
12. The person whose birthday is in January is directly left of the person whose birthday is in September.
13. The person whose birthday is in April is in the fourth house.
14. The person's child is named Fred is directly left of the person whose birthday is in April.
15. Alice is in the first house.
16. The person whose birthday is in April is the person who enjoys gardening.
What is the value of attribute Children for the person whose attribute Occupation is artist? Please reason step by step, and put your final answer within \boxed{} | Fred | 0/8 |
There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Eric`, `Alice`, `Peter`, `Arnold`
- Each person lives in a unique style of house: `victorian`, `ranch`, `craftsman`, `colonial`
- Everyone has a unique favorite cigar: `pall mall`, `dunhill`, `blue master`, `prince`
- Each person has an occupation: `doctor`, `teacher`, `engineer`, `artist`
- They all have a unique favorite flower: `lilies`, `daffodils`, `roses`, `carnations`
- The people keep unique animals: `horse`, `bird`, `fish`, `cat`
## Clues:
1. The fish enthusiast is somewhere to the right of Eric.
2. The person who is an engineer is Arnold.
3. The person who loves a carnations arrangement is the person in a ranch-style home.
4. Alice is the person in a Craftsman-style house.
5. The person partial to Pall Mall is the person who loves a bouquet of daffodils.
6. The cat lover is Arnold.
7. The Dunhill smoker is Peter.
8. The person living in a colonial-style house is not in the fourth house.
9. The person who is a teacher is the bird keeper.
10. The person residing in a Victorian house is Peter.
11. The person who loves the boquet of lilies is the person who smokes Blue Master.
12. Peter is somewhere to the right of the person who is an artist.
13. The person who is an engineer and the person who is a teacher are next to each other.
14. The person who is a doctor is the person who loves a carnations arrangement.
15. The person partial to Pall Mall is the person living in a colonial-style house.
What is the value of attribute Flower for the person whose attribute HouseStyle is craftsman? Please reason step by step, and put your final answer within \boxed{} | lilies | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Carol`, `Peter`, `Alice`, `Eric`, `Arnold`
- They all have a unique favorite flower: `daffodils`, `iris`, `lilies`, `roses`, `tulips`, `carnations`
- People have unique hair colors: `gray`, `red`, `blonde`, `auburn`, `brown`, `black`
- Each person has a favorite color: `white`, `blue`, `green`, `purple`, `red`, `yellow`
- People own unique car models: `tesla model 3`, `ford f150`, `honda civic`, `toyota camry`, `chevrolet silverado`, `bmw 3 series`
- The mothers' names in different houses are unique: `Janelle`, `Holly`, `Kailyn`, `Sarah`, `Penny`, `Aniya`
## Clues:
1. There is one house between Arnold and the person who loves blue.
2. The person whose mother's name is Janelle is directly left of the person who has auburn hair.
3. The person who owns a Chevrolet Silverado and the person who owns a BMW 3 Series are next to each other.
4. Carol is the person who loves a carnations arrangement.
5. The person who loves the boquet of iris is the person who has gray hair.
6. The person who loves the rose bouquet is The person whose mother's name is Kailyn.
7. Bob is the person who loves the boquet of lilies.
8. The person who loves a bouquet of daffodils is somewhere to the left of the person who owns a Chevrolet Silverado.
9. Bob is in the third house.
10. The person who owns a Honda Civic is in the sixth house.
11. The person who loves the vase of tulips is somewhere to the left of The person whose mother's name is Penny.
12. The person who has brown hair is in the fourth house.
13. The person who has brown hair is somewhere to the left of the person who has blonde hair.
14. The person whose mother's name is Holly is Bob.
15. The person who owns a Ford F-150 is in the third house.
16. Eric is directly left of the person who has auburn hair.
17. The person who owns a Tesla Model 3 is the person who loves yellow.
18. There are two houses between the person who loves purple and The person whose mother's name is Aniya.
19. The person who loves purple is in the first house.
20. The person whose favorite color is green is not in the fourth house.
21. The person who has gray hair is the person who owns a BMW 3 Series.
22. The person who has gray hair is somewhere to the left of Alice.
23. The person whose mother's name is Holly is somewhere to the left of the person who loves the vase of tulips.
24. The person who has red hair is the person who loves white.
What is the value of attribute HairColor for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{} | red | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Alice`, `Eric`, `Peter`, `Arnold`
- People have unique heights: `average`, `short`, `very tall`, `very short`, `tall`
- Each person has an occupation: `engineer`, `artist`, `doctor`, `lawyer`, `teacher`
- The mothers' names in different houses are unique: `Janelle`, `Aniya`, `Holly`, `Penny`, `Kailyn`
- Each person has a unique birthday month: `mar`, `april`, `jan`, `feb`, `sept`
- Each person has a unique type of pet: `hamster`, `fish`, `bird`, `dog`, `cat`
## Clues:
1. The person who is a doctor is somewhere to the left of the person with a pet hamster.
2. Arnold is in the first house.
3. The person who is an engineer is the person who owns a dog.
4. The person whose birthday is in March is somewhere to the left of Peter.
5. The person who is an artist is in the third house.
6. The person who is a lawyer is in the fifth house.
7. The person who has a cat is The person whose mother's name is Kailyn.
8. Alice is directly left of Eric.
9. The person whose birthday is in February is directly left of The person whose mother's name is Holly.
10. The person whose birthday is in April is somewhere to the right of the person who is a teacher.
11. The person whose birthday is in February is The person whose mother's name is Kailyn.
12. Peter is in the fourth house.
13. The person with an aquarium of fish is the person who is very short.
14. The person whose mother's name is Kailyn and the person with an aquarium of fish are next to each other.
15. The person who is short is directly left of the person who is a lawyer.
16. The person whose mother's name is Aniya and the person who is a lawyer are next to each other.
17. The person whose birthday is in January is The person whose mother's name is Penny.
18. The person who has an average height is the person who keeps a pet bird.
19. The person who is tall is the person who is an engineer.
What is the value of attribute Birthday for the person whose attribute Pet is cat? Please reason step by step, and put your final answer within \boxed{} | feb | 0/8 |
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 have unique hair colors: `black`, `red`, `blonde`, `brown`
- Each person has an occupation: `engineer`, `artist`, `doctor`, `teacher`
- Each person has a unique favorite drink: `coffee`, `water`, `tea`, `milk`
## Clues:
1. The person who has brown hair is not in the second house.
2. The person who is a doctor is Peter.
3. The person who is a doctor is the one who only drinks water.
4. The person who is an artist is somewhere to the left of the person who is an engineer.
5. The person who likes milk is the person who has blonde hair.
6. The person who has red hair is Alice.
7. The person who is an artist and Arnold are next to each other.
8. The person who is an artist is in the third house.
9. The person who likes milk is somewhere to the left of the tea drinker.
10. Arnold is somewhere to the right of Eric.
11. The person who has black hair is the coffee drinker.
What is the value of attribute House for the person whose attribute HairColor is black? Please reason step by step, and put your final answer within \boxed{} | 4 | 2/8 |
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 Color for the person whose attribute HouseStyle is colonial? Please reason step by step, and put your final answer within \boxed{} | white | 0/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Alice`, `Peter`, `Arnold`, `Eric`, `Bob`
- Everyone has a unique favorite cigar: `dunhill`, `prince`, `blue master`, `blends`, `pall mall`
- People have unique favorite sports: `tennis`, `soccer`, `basketball`, `swimming`, `baseball`
## Clues:
1. The person who loves baseball is the person partial to Pall Mall.
2. The person who smokes many unique blends and Eric are next to each other.
3. The person who loves basketball is Peter.
4. Arnold is the person who loves baseball.
5. The person who loves basketball is somewhere to the right of the Dunhill smoker.
6. The person who smokes Blue Master is the person who loves tennis.
7. The person who loves soccer is somewhere to the right of Arnold.
8. Peter is in the third house.
9. Bob is not in the fifth house.
10. Alice is in the first house.
What is the value of attribute FavoriteSport for the person whose attribute Name is Eric? Please reason step by step, and put your final answer within \boxed{} | tennis | 1/8 |
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Arnold`, `Eric`
- People have unique favorite book genres: `science fiction`, `mystery`, `romance`
- Everyone has a favorite smoothie: `watermelon`, `desert`, `cherry`
- Each person has a unique birthday month: `april`, `jan`, `sept`
- People have unique heights: `average`, `very short`, `short`
## Clues:
1. The person who likes Cherry smoothies is not in the second house.
2. Arnold is the person who loves mystery books.
3. The person whose birthday is in January is not in the first house.
4. The person who is very short is the person who loves romance books.
5. The person who loves mystery books is the person whose birthday is in September.
6. The person who has an average height is the Desert smoothie lover.
7. Eric is in the first house.
8. The Watermelon smoothie lover is the person who is short.
9. The Watermelon smoothie lover is Eric.
What is the value of attribute House for the person whose attribute Birthday is jan? Please reason step by step, and put your final answer within \boxed{} | 3 | 4/8 |
There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Peter`, `Alice`, `Arnold`, `Bob`, `Eric`
- Each person has a unique hobby: `photography`, `cooking`, `knitting`, `gardening`, `painting`
- Each person has a unique favorite drink: `root beer`, `milk`, `water`, `coffee`, `tea`
## Clues:
1. Eric is the coffee drinker.
2. The tea drinker is the person who paints as a hobby.
3. The person who enjoys knitting is not in the fourth house.
4. Peter is not in the fourth house.
5. Eric is somewhere to the right of the root beer lover.
6. Arnold is the person who loves cooking.
7. The one who only drinks water is somewhere to the right of the person who enjoys gardening.
8. There is one house between Bob and the person who paints as a hobby.
9. The person who enjoys gardening is directly left of the root beer lover.
10. The photography enthusiast is the one who only drinks water.
What is the value of attribute House for the person whose attribute Hobby is gardening? Please reason step by step, and put your final answer within \boxed{} | 1 | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Carol`, `Arnold`, `Bob`, `Alice`, `Peter`, `Eric`
- People use unique phone models: `samsung galaxy s21`, `oneplus 9`, `google pixel 6`, `iphone 13`, `xiaomi mi 11`, `huawei p50`
- Each person has a unique type of pet: `dog`, `cat`, `fish`, `rabbit`, `hamster`, `bird`
- They all have a unique favorite flower: `daffodils`, `tulips`, `carnations`, `lilies`, `iris`, `roses`
- People own unique car models: `toyota camry`, `chevrolet silverado`, `bmw 3 series`, `tesla model 3`, `honda civic`, `ford f150`
## Clues:
1. There is one house between the person who owns a Tesla Model 3 and the person who uses a OnePlus 9.
2. There are two houses between the person who owns a dog and the person who owns a Honda Civic.
3. There is one house between the person who uses an iPhone 13 and the person who uses a Xiaomi Mi 11.
4. The person who loves the vase of tulips is somewhere to the right of the person who loves a bouquet of daffodils.
5. The person who owns a Chevrolet Silverado is directly left of the person who loves the rose bouquet.
6. Alice is the person who owns a dog.
7. There are two houses between the person who uses a Google Pixel 6 and the person who uses a Huawei P50.
8. There are two houses between the person who owns a Ford F-150 and the person who loves the boquet of lilies.
9. The person who uses a Google Pixel 6 is somewhere to the left of the person who has a cat.
10. The person who loves a bouquet of daffodils is not in the first house.
11. There is one house between the person with a pet hamster and the person who has a cat.
12. The person who uses a OnePlus 9 is Peter.
13. The person who uses a Xiaomi Mi 11 is the person who has a cat.
14. The person who loves the boquet of lilies is Eric.
15. The person who owns a Tesla Model 3 and the person who uses a Google Pixel 6 are next to each other.
16. The person who owns a rabbit is not in the second house.
17. The person who loves a carnations arrangement is in the second house.
18. The person who loves the boquet of lilies is somewhere to the right of the person who owns a Honda Civic.
19. There are two houses between Arnold and the person who owns a Chevrolet Silverado.
20. There are two houses between Peter and Bob.
21. The person who keeps a pet bird is in the fifth house.
22. The person who owns a Toyota Camry is the person who has a cat.
What is the value of attribute Flower for the person whose attribute CarModel is toyota camry? Please reason step by step, and put your final answer within \boxed{} | roses | 0/8 |
Problem 8.6. Vasya thought of three natural numbers with a sum of 1003. Calculating their product, Vasya noticed that it ends with $N$ zeros. What is the maximum value that
$N$ can take? | 7 | 2/8 |
5. For a convex polyhedron, the internal dihedral angle at each edge is acute. How many faces can the polyhedron have? | 4 | 2/8 |
The sum of two numbers is 173,717. The prime factors of the four-digit difference between the two numbers do not include any single-digit numbers. One of the numbers is divisible by 1558. Which are these two numbers? | 91143 | 4/8 |
7. For what values of the parameter $a$ will the minimum value of the function
$$
f(x)=|7 x-3 a+8|+|5 x+4 a-6|+|x-a-8|-24
$$
be the smallest. | \dfrac{82}{43} | 4/8 |
Problem 3. Find all real numbers $a$ such that $4[a n]=n+[a[a n]]$ for any positive integer $n$ ( $[x]$ denotes the largest integer less than or equal to $x$ ).
Nikolai Nikolov | 2 + \sqrt{3} | 4/8 |
Let $f^1(x)=x^3-3x$. Let $f^n(x)=f(f^{n-1}(x))$. Let $\mathcal{R}$ be the set of roots of $\tfrac{f^{2022}(x)}{x}$. If
\[\sum_{r\in\mathcal{R}}\frac{1}{r^2}=\frac{a^b-c}{d}\]
for positive integers $a,b,c,d$, where $b$ is as large as possible and $c$ and $d$ are relatively prime, find $a+b+c+d$. | 4060 | 0/8 |
[
Two tangents drawn from one point
Auxiliary similar triangles Properties and characteristics of isosceles triangles.
Inscribed and circumscribed circles
Pythagorean theorem (direct and inverse)
In an isosceles triangle \(ABC (AB = BC)\), a circle is inscribed. A line parallel to side \(BC\) and tangent to the circle intersects side \(AB\) at a point \(N\) such that \(AN = \frac{3}{8} AB\). Find the radius of the circle if the area of triangle \(ABC\) is 12.
# | \dfrac{3}{2} | 3/8 |
II. (25 points) As shown in Figure 4, the incircle $\odot I$ of $\triangle ABC$ touches $AB$ and $AC$ at points $D$ and $E$, respectively. Extend $DI$ to $M$ and $EI$ to $N$ such that $IM = IN = 9IE$. Points $B$, $I$, $C$, $M$, and $N$ are concyclic. The ratio of the perimeter of $\triangle ABC$ to side $BC$ is the simplest fraction $\frac{m}{n}$ (where $m$ and $n$ are coprime positive integers). Find the value of $100m + n$. | 2009 | 1/8 |
Kalinin A.
Anya and Borya, whose speeds are constant but not necessarily the same, simultaneously set out from villages A and B towards each other. If Anya had set out 30 minutes earlier, they would have met 2 km closer to village B. If Borya had set out 30 minutes earlier, the meeting would have taken place closer to village A. By how much? | 2 | 4/8 |
Find prime numbers $p , q , r$ such that $p+q^2+r^3=200$. Give all the possibilities.
Remember that the number $1$ is not prime. | (23, 13, 2) | 1/8 |
Example 7 Given $x \geqslant 0, x^{2}+(y-2)^{2}=1$. Find
$$
W=\frac{3 x^{2}+2 \sqrt{3} x y+5 y^{2}}{x^{2}+y^{2}}
$$
the maximum and minimum values. | 6 | 0/8 |
Problem 4. Point $O$ is the center of the circumcircle of triangle $ABC$ with sides $AB=8$ and $AC=5$. Find the length of side $BC$ if the length of the vector $\overrightarrow{OA}+3 \overrightarrow{OB}-4 \overrightarrow{OC}$ is 10. | 4 | 5/8 |
3. In rectangle $A B C D$, $A B=4, A D=3$, fold the rectangle along diagonal $A C$ so that the projection of point $D$ on plane $A B C$, point $E$, falls on line $A B$. At this moment, the dihedral angle $B-A C-D$ is $\qquad$ | \arccos \frac{9}{16} | 4/8 |
3. Alice and Bob are independently trying to figure out a secret password to Cathy's bitcoin wallet. Both of them have already figured out that:
- it is a 4-digit number whose first digit is 5;
- it is a multiple of 9 ;
- The larger number is more likely to be a password than a smaller number.
Moreover, Alice figured out the second and the third digits of the password and Bob figured out the third and the fourth digits. They told this information to each other but not actual digits. After that the conversation followed:
Alice: "I have no idea what the number is."
Bob: "I have no idea too."
After that both of them knew which number they should try first. Identify this number. | 5949 | 1/8 |
Consider the sequence of polynomials $P_0(x) = 2$ , $P_1(x) = x$ and $P_n(x) = xP_{n-1}(x) - P_{n-2}(x)$ for $n \geq 2$ . Let $x_n$ be the greatest zero of $P_n$ in the the interval $|x| \leq 2$ . Show that $$ \lim \limits_{n \to \infty}n^2\left(4-2\pi +n^2\int \limits_{x_n}^2P_n(x)dx\right)=2\pi - 4-\frac{\pi^3}{12} $$ | 2\pi - 4 - \frac{\pi^3}{12} | 1/8 |
Let $X = \{-5,-4,-3,-2,-1,0,1,2,3,4,5\}$ and $S = \{(a,b) \in X \times X : x^2 + ax + b \text{ and } x^3 + bx + a \text{ have at least a common real zero.}\}$.
How many elements are there in $S$? | 24 | 5/8 |
A parliament consists of $n$ senators. These senators are organized into 10 parties and 10 committees. Each senator belongs to exactly one party and one committee.
Determine the smallest possible value of $n$ such that it is possible to label the parties and the committees with numbers from 1 to 10, ensuring that there are at least 11 senators for which the party and committee numbers match. | 101 | 1/8 |
Let $p(x) = x^4 - 5773x^3 - 46464x^2 - 5773x + 46$. Determine the sum of $\arctan$ of its real roots. | 0 | 2/8 |
Consider an infinite sequence $x_1, x_2, \dots$ of positive integers such that, for every integer $n \geq 1$:
- If $x_n$ is even, then $x_{n+1} = \frac{x_n}{2}$.
- If $x_n$ is odd, then $x_{n+1} = \frac{x_n - 1}{2} + 2^{k-1}$, where $2^{k-1} \leq x_n < 2^k$.
Determine the smallest possible value of $x_1$ for which $2020$ is in the sequence. | 1183 | 1/8 |
Suppose we have $10$ balls and $10$ colors. For each ball, we independently color it with one of the $10$ colors, then group the balls together by color at the end. If $S$ is the expected value of the square of the number of distinct colors used on the balls, find the sum of the digits of $S$ written as a decimal. | 55 | 4/8 |
Cat and Claire are having a conversation about Cat’s favorite number. Cat says, "My favorite number is a two-digit perfect square!"
Claire asks, "If you picked a digit of your favorite number at random and revealed it to me without telling me which place it was in, is there any chance I’d know for certain what it is?"
Cat says, "Yes! Moreover, if I told you a number and identified it as the sum of the digits of my favorite number, or if I told you a number and identified it as the positive difference of the digits of my favorite number, you wouldn’t know my favorite number."
Claire says, "Now I know your favorite number!" What is Cat’s favorite number? | 36 | 4/8 |
A function $f$ defined on the positive integers (and taking positive integer values) is given by:
$$\begin{align*}
f(1) &= 1, \\
f(3) &= 3, \\
f(2 \cdot n) &= f(n), \\
f(4 \cdot n + 1) &= 2 \cdot f(2 \cdot n + 1) - f(n), \\
f(4 \cdot n + 3) &= 3 \cdot f(2 \cdot n + 1) - 2 \cdot f(n),
\end{align*}$$
for all positive integers $n$. Determine with proof the number of positive integers $\leq 1988$ for which $f(n) = n$. | 92 | 0/8 |
Let $ABCD$ be a convex quadrilateral with positive integer side lengths. Given that $\angle A = \angle B = 120^{\circ}$, $|AD - BC| = 42$, and $CD = 98$, find the maximum possible value of $AB$. | 69 | 1/8 |
We choose 100 points in the coordinate plane. Let $N$ be the number of triples $(A, B, C)$ of distinct chosen points such that $A$ and $B$ have the same $y$-coordinate, and $B$ and $C$ have the same $x$-coordinate. Find the greatest value that $N$ can attain considering all possible ways to choose the points. | 8100 | 4/8 |
At the Lexington High School, each student is given a unique five-character ID consisting of uppercase letters. Compute the number of possible IDs that contain the string "LMT". | 2028 | 4/8 |
A mouse has a wheel of cheese which is cut into $2018$ slices. The mouse also has a $2019$-sided die, with faces labeled $0, 1, 2, \ldots, 2018$, and with each face equally likely to come up. Every second, the mouse rolls the die. If the die lands on $k$, and the mouse has at least $k$ slices of cheese remaining, then the mouse eats $k$ slices of cheese; otherwise, the mouse does nothing. What is the expected number of seconds until all the cheese is gone? | 2019 | 4/8 |
Suppose tetrahedron $PABC$ has volume $420$ and satisfies $AB = 13$, $BC = 14$, and $CA = 15$. The minimum possible surface area of $PABC$ can be written as $m+n\sqrt{k}$, where $m$, $n$, and $k$ are positive integers, and $k$ is not divisible by the square of any prime. Compute $m+n+k$. | 346 | 4/8 |
Let $\triangle ABC$ satisfy $AB = 17$, $AC = \frac{70}{3}$, and $BC = 19$. Let $I$ be the incenter of $\triangle ABC$ and $E$ be the excenter of $\triangle ABC$ opposite $A$. (Note: this means that the circle tangent to ray $AB$ beyond $B$, ray $AC$ beyond $C$, and side $BC$ is centered at $E$.) Suppose the circle with diameter $IE$ intersects $AB$ beyond $B$ at $D$. If $BD = \frac{a}{b}$ where $a, b$ are coprime positive integers, find $a + b$. | 22 | 0/8 |
Given triangle $ABC$. Let $A_1B_1$, $A_2B_2$, $\ldots$, $A_{2008}B_{2008}$ be $2008$ lines parallel to $AB$ which divide triangle $ABC$ into $2009$ equal areas. Calculate the value of $$ \left\lfloor \frac{A_1B_1}{2A_2B_2} + \frac{A_1B_1}{2A_3B_3} + \ldots + \frac{A_1B_1}{2A_{2008}B_{2008}} \right\rfloor$$ | 43 | 5/8 |
Caltech's 900 students are evenly spaced along the circumference of a circle. How many equilateral triangles can be formed with at least two Caltech students as vertices? | 808500 | 1/8 |
An infinite sequence of real numbers $a_1, a_2, \dots$ satisfies the recurrence
\[ a_{n+3} = a_{n+2} - 2a_{n+1} + a_n \]for every positive integer $n$. Given that $a_1 = a_3 = 1$ and $a_{98} = a_{99}$, compute $a_1 + a_2 + \dots + a_{100}$. | 3 | 1/8 |
Euclid, Pythagoras, Ptolemy, and Hypatia are playing a game where they all have to think of a number, and then cube that number 20 times. Hypatia doesn't want to cube large numbers, so she chooses the number 1. Euclid thinks the same thing and also chooses the number 1. However, Pythagoras and Ptolemy don't think ahead and Pythagoras chooses 2 and Ptolemy chooses -2. After they finish cubing their numbers (Pythagoras and Ptolemy take a while), all four players write their final numbers on a piece of paper. What is the sum of the numbers they wrote on the piece of paper? | 2 | 5/8 |
Let $k$ be the smallest positive integer such that the binomial coefficient $\binom{10^9}{k}$ is less than the binomial coefficient $\binom{10^9 + 1}{k - 1}$. Let $a$ be the first (from the left) digit of $k$ and let $b$ be the second (from the left) digit of $k$. What is the value of $10a + b$? | 38 | 3/8 |
In $\vartriangle ABC, \angle A = 52^o$ and $\angle B = 57^o$. One circle passes through the points $B, C$, and the incenter of $\vartriangle ABC$, and a second circle passes through the points $A, C$, and the circumcenter of $\vartriangle ABC$. Find the degree measure of the acute angle at which the two circles intersect. | 59 | 1/8 |
Let $P$ be the set of positive integers that are prime numbers. Find the number of subsets of $P$ that have the property that the sum of their elements is $34$ such as $\{3, 31\}$. | 9 | 2/8 |
Six different small books and three different large books sit on a shelf. Three children may each take either two small books or one large book. Find the number of ways the three children can select their books. | 1176 | 4/8 |
A storage depot is a pyramid with height $30$ and a square base with side length $40$. Determine how many cubical $3\times 3\times 3$ boxes can be stored in this depot if the boxes are always packed so that each of their edges is parallel to either an edge of the base or the altitude of the pyramid. | 471 | 2/8 |
Fiona had a solid rectangular block of cheese that measured $6$ centimeters from left to right, $5$ centimeters from front to back, and $4$ centimeters from top to bottom. Fiona took a sharp knife and sliced off a $1$ centimeter thick slice from the left side of the block and a $1$ centimeter slice from the right side of the block. After that, she sliced off a $1$ centimeter thick slice from the front side of the remaining block and a $1$ centimeter slice from the back side of the remaining block. Finally, Fiona sliced off a $1$ centimeter slice from the top of the remaining block and a $1$ centimeter slice from the bottom of the remaining block. Fiona now has $7$ blocks of cheese. Find the total surface area of those seven blocks of cheese measured in square centimeters. | 340 | 2/8 |
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`
- People have unique heights: `tall`, `short`, `very short`, `average`
- Each person has a unique hobby: `photography`, `painting`, `cooking`, `gardening`
## Clues:
1. Alice is somewhere to the right of Peter.
2. There are two houses between the person who paints as a hobby and the person who has an average height.
3. Peter is somewhere to the left of the person who loves cooking.
4. Arnold is the person who is very short.
5. The person who is tall and Alice are next to each other.
6. The person who loves cooking is not in the third house.
7. The photography enthusiast is Peter.
8. The photography enthusiast and the person who enjoys gardening are next to each other.
9. The person who loves cooking is Eric.
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{} | 4 | 4/8 |
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`, `Eric`, `Bob`
- Each person has a unique type of pet: `cat`, `bird`, `fish`, `dog`, `hamster`, `rabbit`
- People have unique heights: `super tall`, `average`, `tall`, `very short`, `very tall`, `short`
- People have unique favorite sports: `baseball`, `tennis`, `soccer`, `swimming`, `basketball`, `volleyball`
## Clues:
1. There is one house between the person who has an average height and the person who is short.
2. The person with an aquarium of fish is in the fifth house.
3. The person who has a cat is the person who is tall.
4. The person who is very tall is the person who loves soccer.
5. Peter is in the first house.
6. The person who loves tennis is in the sixth house.
7. Carol is somewhere to the right of the person who is very tall.
8. The person who loves volleyball is directly left of the person who loves soccer.
9. The person who loves baseball is directly left of the person who is super tall.
10. Carol and Bob are next to each other.
11. The person who is super tall is not in the sixth house.
12. The person who is short is not in the fourth house.
13. There is one house between the person who loves swimming and Bob.
14. The person who loves basketball is somewhere to the left of the person who owns a dog.
15. The person who owns a rabbit is somewhere to the left of the person who is short.
16. The person who keeps a pet bird is the person who is short.
17. Arnold is not in the second house.
18. Bob is directly left of Eric.
19. The person who owns a rabbit and the person who is very tall are next to each other.
What is the value of attribute Name for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{} | Peter | 0/8 |
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`, `Arnold`, `Bob`, `Peter`, `Alice`
- Each person has a unique birthday month: `feb`, `sept`, `april`, `mar`, `jan`
## Clues:
1. The person whose birthday is in March is somewhere to the left of the person whose birthday is in January.
2. Arnold is the person whose birthday is in January.
3. The person whose birthday is in March is directly left of Alice.
4. The person whose birthday is in September and the person whose birthday is in January are next to each other.
5. Eric is not in the fourth house.
6. The person whose birthday is in January is not in the fourth house.
7. Peter is in the first house.
8. Alice is directly left of the person whose birthday is in April.
What is the value of attribute Birthday for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{} | jan | 0/8 |
There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Bob`, `Arnold`, `Eric`, `Peter`, `Carol`, `Alice`
- Each person has a unique hobby: `cooking`, `woodworking`, `gardening`, `knitting`, `photography`, `painting`
## Clues:
1. Alice is directly left of Bob.
2. The photography enthusiast is not in the fourth house.
3. The person who paints as a hobby and the woodworking hobbyist are next to each other.
4. The person who loves cooking is somewhere to the left of the person who enjoys knitting.
5. The woodworking hobbyist is not in the fourth house.
6. Arnold is in the fifth house.
7. There are two houses between Peter and the person who enjoys knitting.
8. The person who loves cooking is in the third house.
9. Bob is not in the third house.
10. There is one house between the woodworking hobbyist and Carol.
What is the value of attribute Hobby for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{} | woodworking | 0/8 |
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`
- Each person has a unique hobby: `cooking`, `gardening`, `painting`, `photography`, `knitting`
- People have unique favorite sports: `swimming`, `tennis`, `soccer`, `baseball`, `basketball`
- Each person lives in a unique style of house: `ranch`, `craftsman`, `victorian`, `modern`, `colonial`
- Each mother is accompanied by their child: `Timothy`, `Samantha`, `Bella`, `Meredith`, `Fred`
- People have unique heights: `average`, `very tall`, `very short`, `short`, `tall`
## Clues:
1. The person who has an average height is the person's child is named Meredith.
2. The person who is tall is in the second house.
3. Peter is directly left of the person residing in a Victorian house.
4. Alice is the person who is tall.
5. The person who loves baseball is the person who is very tall.
6. The person's child is named Meredith and the person who is the mother of Timothy are next to each other.
7. Bob is the person who paints as a hobby.
8. The person who enjoys gardening is in the second house.
9. The person who is very short is somewhere to the right of Eric.
10. The person who loves tennis is the person's child is named Samantha.
11. The person who loves soccer is not in the first house.
12. The person's child is named Samantha is the person in a modern-style house.
13. The person in a Craftsman-style house is the person who has an average height.
14. The person's child is named Fred is the person residing in a Victorian house.
15. The person who is short is the person who loves basketball.
16. Peter is the person who is very tall.
17. The person in a ranch-style home is somewhere to the left of the person who loves cooking.
18. The person who enjoys knitting and the person who enjoys gardening are next to each other.
19. The person in a modern-style house is the person who loves cooking.
20. The person residing in a Victorian house is in the fifth house.
What is the value of attribute FavoriteSport for the person whose attribute Hobby is cooking? Please reason step by step, and put your final answer within \boxed{} | tennis | 0/8 |
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`, `Peter`, `Arnold`
- Everyone has a favorite smoothie: `cherry`, `watermelon`, `desert`
- They all have a unique favorite flower: `carnations`, `lilies`, `daffodils`
- The people keep unique animals: `cat`, `horse`, `bird`
- Each person has a unique hobby: `photography`, `cooking`, `gardening`
## Clues:
1. The person who keeps horses and the photography enthusiast are next to each other.
2. The bird keeper is the person who likes Cherry smoothies.
3. The person who loves cooking is the Desert smoothie lover.
4. The person who enjoys gardening is the person who loves a carnations arrangement.
5. The person who loves cooking is directly left of Peter.
6. The person who loves a bouquet of daffodils is the Desert smoothie lover.
7. The Watermelon smoothie lover is the person who keeps horses.
8. The photography enthusiast is Eric.
What is the value of attribute Animal for the person whose attribute Hobby is gardening? Please reason step by step, and put your final answer within \boxed{} | horse | 1/8 |
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 favorite book genres: `mystery`, `fantasy`, `romance`, `science fiction`
- Each person prefers a unique type of vacation: `cruise`, `mountain`, `city`, `beach`
- They all have a unique favorite flower: `roses`, `daffodils`, `carnations`, `lilies`
- People have unique favorite music genres: `pop`, `rock`, `jazz`, `classical`
## Clues:
1. Alice is the person who loves jazz music.
2. Eric is the person who loves romance books.
3. The person who loves a carnations arrangement is in the first house.
4. The person who loves a bouquet of daffodils is the person who loves science fiction books.
5. The person who enjoys mountain retreats is in the third house.
6. The person who enjoys mountain retreats is the person who loves mystery books.
7. The person who loves science fiction books is Peter.
8. The person who prefers city breaks is in the second house.
9. The person who prefers city breaks and the person who loves classical music are next to each other.
10. The person who loves beach vacations is not in the first house.
11. The person who loves romance books is the person who loves pop music.
12. The person who loves romance books is somewhere to the left of Alice.
13. The person who loves the boquet of lilies is the person who loves mystery books.
14. Peter is somewhere to the left of Alice.
What is the value of attribute MusicGenre for the person whose attribute Vacation is cruise? Please reason step by step, and put your final answer within \boxed{} | pop | 2/8 |
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`, `Arnold`, `Alice`, `Bob`, `Peter`
- Each person lives in a unique style of house: `colonial`, `modern`, `ranch`, `victorian`, `craftsman`
- People have unique favorite sports: `tennis`, `basketball`, `soccer`, `baseball`, `swimming`
- People have unique favorite music genres: `pop`, `classical`, `jazz`, `rock`, `hip hop`
## Clues:
1. The person in a Craftsman-style house and the person who loves basketball are next to each other.
2. Alice is the person living in a colonial-style house.
3. Peter is somewhere to the right of the person who loves swimming.
4. The person living in a colonial-style house is the person who loves soccer.
5. The person in a ranch-style home is the person who loves baseball.
6. The person who loves pop music is somewhere to the left of the person who loves swimming.
7. The person who loves baseball is not in the second house.
8. The person in a modern-style house is in the fourth house.
9. The person who loves basketball and Peter are next to each other.
10. The person in a Craftsman-style house is somewhere to the left of Arnold.
11. The person who loves jazz music is not in the fourth house.
12. There are two houses between the person who loves tennis and the person in a ranch-style home.
13. Eric is not in the third house.
14. The person who loves hip-hop music is the person in a ranch-style home.
15. The person who loves tennis is the person who loves classical music.
What is the value of attribute House for the person whose attribute MusicGenre is jazz? Please reason step by step, and put your final answer within \boxed{} | 3 | 2/8 |
There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
- Each person has a unique name: `Arnold`, `Eric`, `Peter`
- People have unique favorite book genres: `science fiction`, `mystery`, `romance`
- Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`
- People have unique hair colors: `black`, `blonde`, `brown`
- Each person has a unique level of education: `high school`, `associate`, `bachelor`
- They all have a unique favorite flower: `daffodils`, `lilies`, `carnations`
## Clues:
1. The person who loves the boquet of lilies is directly left of the person who loves romance books.
2. Peter is the person with a high school diploma.
3. The person who loves the boquet of lilies is the person who has brown hair.
4. The person's child is named Bella is Arnold.
5. The person who loves science fiction books is the person's child is named Fred.
6. The person's child is named Fred is the person who loves the boquet of lilies.
7. The person who has black hair is the person with an associate's degree.
8. The person's child is named Meredith is not in the first house.
9. The person with a high school diploma is the person who loves a carnations arrangement.
10. Peter is not in the third house.
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{} | 3 | 2/8 |
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 use unique phone models: `samsung galaxy s21`, `huawei p50`, `oneplus 9`, `iphone 13`, `google pixel 6`
- Everyone has a favorite smoothie: `desert`, `dragonfruit`, `watermelon`, `cherry`, `lime`
- The mothers' names in different houses are unique: `Janelle`, `Holly`, `Penny`, `Aniya`, `Kailyn`
- Each person has an occupation: `doctor`, `lawyer`, `engineer`, `teacher`, `artist`
## Clues:
1. The person whose mother's name is Kailyn is Peter.
2. The Dragonfruit smoothie lover is not in the fourth house.
3. The person who uses an iPhone 13 is the person who is an artist.
4. The person whose mother's name is Aniya is Arnold.
5. The person whose mother's name is Aniya is the Desert smoothie lover.
6. The person whose mother's name is Aniya is in the second house.
7. The person who drinks Lime smoothies is in the first house.
8. The person who uses a Huawei P50 is the person who is a doctor.
9. Eric is the person who drinks Lime smoothies.
10. There is one house between the person who is a teacher and Bob.
11. The person whose mother's name is Aniya is the person who is a lawyer.
12. The person who uses an iPhone 13 is the person who likes Cherry smoothies.
13. Arnold is the person who uses a OnePlus 9.
14. The person who is a doctor is The person whose mother's name is Penny.
15. Peter is the person who uses a Samsung Galaxy S21.
16. Bob is not in the third house.
17. The person whose mother's name is Holly is directly left of Peter.
What is the value of attribute House for the person whose attribute PhoneModel is samsung galaxy s21? Please reason step by step, and put your final answer within \boxed{} | 4 | 0/8 |
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`, `Alice`, `Bob`, `Arnold`
- The people are of nationalities: `norwegian`, `brit`, `swede`, `dane`, `german`
- Each person prefers a unique type of vacation: `cruise`, `mountain`, `camping`, `beach`, `city`
- Each person has a unique level of education: `bachelor`, `master`, `associate`, `doctorate`, `high school`
- Each person has an occupation: `artist`, `doctor`, `engineer`, `teacher`, `lawyer`
## Clues:
1. The person who likes going on cruises is the person who is a lawyer.
2. The person who loves beach vacations is directly left of Arnold.
3. The person with a doctorate is somewhere to the left of Bob.
4. The person with an associate's degree is the person who likes going on cruises.
5. Peter is not in the first house.
6. The person who is an artist is Peter.
7. The person who enjoys camping trips is the person with a master's degree.
8. The Dane is somewhere to the right of the person who is a doctor.
9. The person with an associate's degree is directly left of the person who is an engineer.
10. The person who enjoys camping trips is the British person.
11. The Norwegian and the person with a bachelor's degree are next to each other.
12. The person who is an artist is the Swedish person.
13. Bob is not in the fourth house.
14. The person who enjoys camping trips is Eric.
15. Alice is the German.
16. The person who loves beach vacations is somewhere to the left of the person who prefers city breaks.
17. The person who enjoys mountain retreats is in the fifth house.
18. The person who likes going on cruises is somewhere to the right of the person who loves beach vacations.
19. The person with a bachelor's degree is in the third house.
What is the value of attribute Name for the person whose attribute Occupation is artist? Please reason step by step, and put your final answer within \boxed{} | Peter | 0/8 |
Given the positive integers \( x_{1}, x_{2}, x_{3}, x_{4}, x_{5} \). Any set of four numbers selected and summed results in the set \(\{44, 45, 46, 47\}\). Determine these five numbers. | 10, 11, 11, 12, 13 | 2/8 |
Let \( a, b, c \in \left[\frac{1}{2}, 1\right] \). Define \( s = \frac{a+b}{1+c} + \frac{b+c}{1+a} + \frac{c+a}{1+b} \). What is the range of possible values for \( s \)? | [2, 3] | 4/8 |
We start with the numbers \( a, b, c, d \). We then replace them with \( a' = a - b \), \( b' = b - c \), \( c' = c - d \), \( d' = d - a \). We carry out this process 1996 times. Is it possible to end up with numbers \( A, B, C, D \) such that \( |BC - AD| \), \( |AC - BD| \), \( |AB - CD| \) are all primes? | \text{No} | 4/8 |
Problem 4. Find the number of all natural numbers $n, 4 \leq n \leq$ 1023, such that their binary representations do not contain three consecutive equal digits.
Emil Kolev | 228 | 2/8 |
3. As shown in Figure 4, it is known that quadrilateral $ABCD$ is inscribed in $\odot O$, $AB$ is the diameter, $AD=DC$, and $BA$, $CD$ are extended to intersect at point $E$, $BF \perp EC$ intersects the extension of $EC$ at point $F$. If $AE=AO, BC=6$, then the length of $CF$ is $\qquad$. | \dfrac{3\sqrt{2}}{2} | 3/8 |
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