12. In a game, two players take turns to "eat squares" from a $5 \times 7$ grid chessboard. To "eat a square," a player selects an uneaten square and moves the piece to that square, then all the squares in the quadrant formed (along the left edge of the square upwards, and along the bottom edge of the square to the right) are eaten. For example, in the right figure, moving the piece to the shaded square results in the shaded square and the four squares marked with $\times$ being eaten (the squares with lines in them were previously eaten). The goal of the game is to make the opponent eat the last square. The figure above shows a situation that can occur during the game. How many different situations can appear at most during the game process?

Answer: 792


1B. Find the angle $\alpha$ of triangle $ABC$, if for its angles $\alpha, \beta, \gamma$ the equality $\sin \alpha=\frac{\sin \beta+\sin \gamma}{\cos \beta+\cos \gamma}$ holds.

Answer: \dfrac{\pi}{2}


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Nationality, Music-Genre, Hobby, Pet, Sport, Transport.
The attributes have the following possible values:
- Nationality: american, australian, malaysian, nigerian, pakistani, spanish
- Music-Genre: gospel, jazz, metal, pop, punk, rock
- Hobby: camping, cooking, dancing, fishing, singing, woodworking
- Pet: bird, chinchilla, fish, hamster, lizard, pony
- Sport: ice-hockey, rugby, sailing, skateboarding, soccer, surfing
- Transport: helicopter, motorbike, skateboard, train, trike, van

Given the following premises about the line of people:
- Sport:soccer is not to the right of Sport:rugby
- Sport:ice-hockey != Pet:pony or Sport:ice-hockey != Music-Genre:pop or both
- Music-Genre:metal != Pet:fish or Music-Genre:metal != Sport:sailing or both
- Hobby:cooking == Music-Genre:jazz or Hobby:cooking == Nationality:australian, but not both
- Nationality:malaysian == Hobby:dancing or Nationality:malaysian == Transport:van, but not both
- Music-Genre:metal is not to the left of Transport:motorbike
- Music-Genre:jazz != Transport:van or Sport:soccer != Music-Genre:jazz or both
- Sport:soccer and Music-Genre:jazz have different parity positions
- Sport:rugby is not to the left of Sport:sailing
- Sport:ice-hockey == Transport:train or Sport:ice-hockey == Nationality:spanish or both
- Music-Genre:jazz != Sport:surfing or Music-Genre:jazz != Transport:skateboard or both
- Nationality:australian != Sport:skateboarding or Sport:skateboarding != Pet:lizard or both
- Sport:skateboarding == Pet:bird or Sport:skateboarding == Hobby:woodworking, but not both
- Sport:sailing and Hobby:fishing have different parity positions
- Sport:sailing != Transport:motorbike or Sport:sailing != Nationality:malaysian or both
- Transport:trike and Pet:fish have the same parity positions
- Pet:bird is not to the right of Pet:hamster
- Sport:sailing is not to the right of Nationality:pakistani
- Sport:surfing and Transport:trike have different parity positions
- Sport:ice-hockey is not to the left of Music-Genre:rock
- Pet:chinchilla != Nationality:american or Pet:chinchilla != Music-Genre:pop or both
- Sport:sailing and Transport:helicopter have different parity positions
- Pet:hamster != Transport:motorbike or Pet:hamster != Nationality:australian or both
- Pet:chinchilla and Nationality:australian have the same parity positions
- Nationality:australian and Sport:ice-hockey have different parity positions
- Music-Genre:gospel == Transport:skateboard or Music-Genre:gospel == Sport:surfing or both
- Sport:ice-hockey is not to the right of Hobby:camping
- Transport:skateboard is not to the left of Transport:trike
- Nationality:nigerian == Sport:sailing or Nationality:nigerian == Pet:pony, but not both
- Pet:lizard and Sport:skateboarding have the same parity positions
- Nationality:pakistani is not to the left of Nationality:spanish
- Hobby:singing is not to the right of Nationality:nigerian
- Pet:pony and Transport:train have the same parity positions
- Sport:skateboarding is somewhere between Sport:soccer and Sport:rugby
- Transport:helicopter == Sport:rugby or Transport:helicopter == Nationality:american, but not both
- Sport:soccer and Hobby:woodworking have different parity positions
- Music-Genre:pop and Pet:bird have the same parity positions
- Music-Genre:punk and Hobby:dancing have the same parity positions
- Hobby:camping is somewhere between Pet:pony and Pet:fish
- Pet:lizard is not to the right of Hobby:camping
- Music-Genre:rock == Hobby:fishing or Hobby:fishing == Sport:sailing or both
- Music-Genre:punk != Transport:helicopter or Transport:helicopter != Pet:pony or both
- Hobby:singing is not to the right of Transport:motorbike
- Music-Genre:jazz and Hobby:camping have different parity positions
- Transport:skateboard is not to the left of Hobby:cooking
- Nationality:pakistani == Hobby:camping or Hobby:camping == Transport:motorbike, but not both
- Music-Genre:metal is not to the right of Hobby:dancing
- Transport:trike and Sport:skateboarding have different parity positions
- Pet:lizard and Sport:rugby have different parity positions
- Transport:trike is not to the left of Music-Genre:jazz
- Transport:motorbike == Hobby:camping or Nationality:malaysian == Transport:motorbike or both
- Nationality:australian is somewhere between Nationality:pakistani and Hobby:cooking
- Music-Genre:metal is somewhere between Nationality:spanish and Music-Genre:gospel
- Sport:soccer is not to the right of Hobby:woodworking
- Hobby:woodworking and Pet:lizard have the same parity positions
- Hobby:camping != Transport:motorbike or Sport:skateboarding != Hobby:camping or both
- Sport:sailing != Nationality:spanish or Sport:sailing != Music-Genre:pop or both
- Music-Genre:metal is not to the left of Sport:surfing
- Sport:sailing is not to the left of Hobby:cooking
- Pet:fish != Transport:helicopter or Pet:fish != Nationality:australian or both
- Hobby:singing is not to the left of Transport:trike
- Pet:bird != Transport:helicopter or Pet:bird != Hobby:cooking or both
- Transport:helicopter == Hobby:cooking or Pet:chinchilla == Transport:helicopter, but not both
- Pet:pony != Music-Genre:punk or Nationality:american != Pet:pony or both
- Nationality:malaysian != Sport:soccer or Nationality:malaysian != Pet:lizard or both
- Music-Genre:punk is not to the left of Hobby:singing
- Transport:motorbike != Pet:pony or Music-Genre:punk != Transport:motorbike or both
- Nationality:nigerian is not to the right of Music-Genre:rock
- Transport:train and Sport:ice-hockey have the same parity positions
- Pet:pony != Nationality:australian or Pet:pony != Hobby:singing or both
- Music-Genre:jazz is not to the right of Transport:helicopter
- Sport:soccer is not to the right of Pet:fish
- Transport:helicopter != Nationality:pakistani or Transport:helicopter != Music-Genre:gospel or both
- Nationality:nigerian is somewhere between Pet:chinchilla and Pet:fish
- Transport:van is somewhere between Music-Genre:gospel and Hobby:cooking
- Music-Genre:pop != Nationality:spanish or Music-Genre:pop != Sport:ice-hockey or both
- Transport:trike == Music-Genre:punk or Transport:trike == Hobby:woodworking or both
- Nationality:pakistani and Music-Genre:metal have different parity positions
- Nationality:american and Pet:hamster have the same parity positions
- Transport:skateboard is not to the left of Pet:fish
- Music-Genre:gospel is not to the right of Transport:skateboard
- Sport:skateboarding is not to the left of Nationality:malaysian
- Music-Genre:jazz is not to the right of Hobby:singing
- Music-Genre:metal is not to the right of Hobby:woodworking
- Transport:trike is not to the left of Transport:helicopter
- Sport:ice-hockey == Nationality:spanish or Nationality:spanish == Transport:motorbike or both
- Hobby:dancing and Pet:hamster have different parity positions
- Music-Genre:jazz is not to the right of Sport:ice-hockey
- Pet:pony == Nationality:australian or Music-Genre:rock == Pet:pony or both
- Pet:hamster != Sport:skateboarding or Pet:hamster != Nationality:pakistani or both
- Transport:helicopter != Hobby:camping or Hobby:camping != Music-Genre:metal or both

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is bird??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pop


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Nationality, Music-Genre, Pet, Transport.
The attributes have the following possible values:
- Nationality: argentine, brazilian, chinese, japanese, spanish
- Music-Genre: d&b, folk, hip-hop, pop, trance
- Pet: fish, goldfish, hamster, hedgehog, mouse
- Transport: airplane, bike, bus, scooter, skateboard

Given the following premises about the line of people:
- Transport:bus is somewhere to the left of Pet:hedgehog
- Transport:bike is somewhere to the right of Transport:scooter
- Music-Genre:hip-hop is somewhere between Pet:hedgehog and Nationality:chinese
- Pet:goldfish and Transport:bus have different parity positions
- Transport:bike is not to the right of Transport:airplane
- Music-Genre:d&b is on the left of Nationality:argentine
- Pet:hedgehog is not to the right of Pet:hamster
- Transport:bike == Music-Genre:folk
- Music-Genre:pop is between Nationality:argentine and Nationality:spanish
- Pet:mouse == Music-Genre:folk
- Music-Genre:pop and Pet:goldfish have different parity positions
- Nationality:japanese == Transport:skateboard or Nationality:japanese == Pet:goldfish, but not both

Answer the following question:

Question: Question: What is the Nationality of the person who has/is hedgehog??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: japanese


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Beverage, Movie-Genre, Music-Genre, Nationality.
The attributes have the following possible values:
- Job: accountant, firefighter, journalist, manager
- Food: asparagus, cucumber, lemon, raspberry
- Beverage: fanta, iced-tea, tea, water
- Movie-Genre: adventure, disaster, horror, satire
- Music-Genre: d&b, dubstep, folk, jazz
- Nationality: brazilian, british, colombian, turkish

Given the following premises about the line of people:
- Music-Genre:folk is on the right of Job:accountant
- Nationality:colombian and Music-Genre:jazz have the same parity positions
- Job:firefighter != Food:raspberry
- Beverage:water == Movie-Genre:adventure
- Nationality:brazilian == Movie-Genre:horror
- Movie-Genre:satire is on the right of Nationality:british
- Food:raspberry is on the right of Food:asparagus
- Nationality:colombian == Food:raspberry or Food:raspberry == Beverage:fanta or both
- Food:cucumber == Job:firefighter or Food:cucumber == Music-Genre:dubstep or both
- Job:manager is not to the left of Music-Genre:jazz
- Music-Genre:d&b and Food:raspberry have the same parity positions
- Movie-Genre:disaster and Beverage:iced-tea have different parity positions
- Music-Genre:jazz == Movie-Genre:satire or Food:raspberry == Music-Genre:jazz, but not both
- Nationality:british is on the right of Music-Genre:folk
- Nationality:colombian == Movie-Genre:adventure
- Beverage:water == Food:raspberry or Food:raspberry == Music-Genre:d&b or both

Answer the following question:

Question: Question: What is the Job of the person who has/is iced-tea??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: manager


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Food, Music-Genre, Sport, Transport.
The attributes have the following possible values:
- Food: avocado, cherry, lime, pineapple, zucchini
- Music-Genre: classical, dubstep, gospel, pop, techno
- Sport: climbing, lacrosse, rugby, soccer, tennis
- Transport: car, scooter, ship, train, trike

Given the following premises about the line of people:
- Transport:train is on the right of Transport:trike
- Sport:rugby is on the left or right of Food:avocado
- Food:lime == Sport:lacrosse
- Sport:rugby is on the far left or far right
- Music-Genre:dubstep is somewhere to the left of Sport:lacrosse
- Music-Genre:pop is on the left or right of Music-Genre:techno
- Sport:tennis == Food:pineapple
- Music-Genre:techno is on the left or right of Transport:ship
- Food:zucchini is on the left of Food:avocado
- Sport:soccer is on the far left or far right
- Transport:ship == Music-Genre:gospel
- Music-Genre:pop is on the right of Sport:tennis
- Transport:car is on the left of Music-Genre:pop
- Music-Genre:techno is in the middle

Answer the following question:

Question: Question: What is the Food of the person who has/is techno??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pineapple


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Food, Movie-Genre, Pet, Transport.
The attributes have the following possible values:
- Food: artichoke, avocado, grapefruit, pear
- Movie-Genre: disaster, family, musical, mystery
- Pet: chinchilla, frog, hamster, pony
- Transport: boat, jet-ski, train, tram

Given the following premises about the line of people:
- Transport:boat is in an odd position
- Pet:frog is somewhere to the left of Food:avocado
- Movie-Genre:disaster is between Pet:hamster and Pet:frog
- Movie-Genre:mystery is somewhere to the right of Transport:train
- Pet:chinchilla is somewhere to the left of Pet:pony
- Transport:tram is on the left or right of Pet:pony
- Pet:hamster is in an odd position
- Food:pear is on the far right
- Pet:pony is on the left or right of Food:grapefruit
- Movie-Genre:musical == Transport:jet-ski

Answer the following question:

Question: Question: What is the Movie-Genre of the person who has/is pear??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: musical


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Nationality, Movie-Genre, Food, Transport.
The attributes have the following possible values:
- Nationality: brazilian, british, german, indonesian, turkish
- Movie-Genre: crime, documentary, musical, romance, thriller
- Food: cherry, lettuce, mango, potato, pumpkin
- Transport: airplane, bus, snowmobile, taxi, van

Given the following premises about the line of people:
- Food:lettuce is somewhere to the left of Movie-Genre:thriller
- Food:pumpkin is somewhere between Movie-Genre:thriller and Food:cherry
- Nationality:turkish is somewhere to the left of Nationality:german
- Movie-Genre:documentary and Transport:bus have different parity positions
- Transport:bus is not to the right of Movie-Genre:romance
- Movie-Genre:musical and Transport:bus have the same parity positions
- Nationality:german and Transport:airplane have different parity positions
- Transport:snowmobile == Nationality:indonesian or Transport:snowmobile == Food:potato or both
- Food:mango and Movie-Genre:crime have different parity positions
- Nationality:brazilian is somewhere to the left of Transport:bus
- Transport:snowmobile is somewhere to the left of Movie-Genre:musical
- Food:lettuce and Transport:airplane have different parity positions
- Transport:airplane is somewhere to the right of Nationality:british
- Transport:taxi == Food:cherry or Nationality:indonesian == Transport:taxi, but not both
- Movie-Genre:musical is somewhere to the left of Food:lettuce
- Food:mango != Nationality:german

Answer the following question:

Question: Question: What is the Movie-Genre of the person who has/is mango??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: thriller


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Job, Hobby, Movie-Genre, Music-Genre, Transport.
The attributes have the following possible values:
- Job: accountant, doctor, musician, paramedic, teacher, videographer
- Hobby: drawing, reading, rock-climbing, singing, sudoku, writing
- Movie-Genre: adventure, documentary, epic, horror, western, zombie
- Music-Genre: folk, indie, pop, reggae, salsa, techno
- Transport: boat, car, jet-ski, snowmobile, tram, trike

Given the following premises about the line of people:
- Job:accountant is somewhere to the right of Job:musician
- Movie-Genre:adventure is on the left of Job:teacher
- Movie-Genre:documentary is on the right of Music-Genre:techno
- Transport:snowmobile is on the right of Movie-Genre:zombie
- Hobby:rock-climbing == Music-Genre:pop
- Transport:trike is on the left of Hobby:singing
- Hobby:writing is somewhere to the right of Movie-Genre:horror
- Music-Genre:salsa is somewhere to the left of Job:teacher
- Music-Genre:indie == Job:teacher
- Movie-Genre:horror is in an odd position
- Job:videographer is on the left or right of Movie-Genre:documentary
- Hobby:singing is between Transport:jet-ski and Job:doctor
- Job:paramedic is on the left or right of Music-Genre:pop
- Transport:jet-ski is somewhere to the left of Transport:boat
- Transport:jet-ski is somewhere to the right of Transport:tram
- Hobby:rock-climbing is somewhere to the left of Job:paramedic
- Hobby:reading is on the left of Music-Genre:folk
- Job:videographer == Hobby:reading
- Hobby:drawing == Music-Genre:indie
- Movie-Genre:western is on the far left or far right
- Movie-Genre:adventure is on the right of Movie-Genre:horror
- Transport:tram is somewhere to the right of Transport:car

Answer the following question:

Question: Question: What is the Job of the person who has/is sudoku??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: musician


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Beverage, Hobby, Music-Genre, Pet.
The attributes have the following possible values:
- Beverage: coffee, hot-chocolate, juice, mirinda, soy-milk, water
- Hobby: baking, card-games, drawing, fishing, photography, singing
- Music-Genre: ambient, blues, d&b, disco, dubstep, soul
- Pet: bird, fish, goldfish, guinea-pig, lizard, pony

Given the following premises about the line of people:
- Music-Genre:disco is on the left or right of Hobby:fishing
- Hobby:fishing is on the left of Beverage:mirinda
- Beverage:hot-chocolate is somewhere to the left of Beverage:coffee
- Pet:bird is somewhere to the right of Pet:fish
- Music-Genre:dubstep is on the left or right of Beverage:hot-chocolate
- Music-Genre:blues == Hobby:baking
- Music-Genre:blues is on the left or right of Music-Genre:ambient
- Hobby:card-games is on the left of Pet:bird
- Pet:pony is on the left of Hobby:card-games
- Pet:guinea-pig is somewhere to the left of Hobby:drawing
- Pet:pony is on the right of Pet:lizard
- Pet:goldfish == Hobby:photography
- Music-Genre:disco is on the left or right of Beverage:soy-milk
- Hobby:drawing is on the left or right of Beverage:coffee
- Music-Genre:d&b is on the right of Pet:goldfish
- Beverage:water is somewhere to the left of Music-Genre:d&b
- Hobby:card-games is on the left of Music-Genre:blues
- Beverage:soy-milk is on the left or right of Beverage:coffee

Answer the following question:

Question: Question: What is the Beverage of the person who has/is blues??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: juice


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Nationality, Hobby, Sport, Transport.
The attributes have the following possible values:
- Nationality: chinese, colombian, french, japanese, pakistani
- Hobby: board-games, card-games, dancing, filmmaking, photography
- Sport: biathlon, cricket, lacrosse, parkour, surfing
- Transport: boat, motorbike, roller, train, tram

Given the following premises about the line of people:
- Sport:cricket is somewhere to the left of Sport:biathlon
- Nationality:pakistani is somewhere to the right of Transport:motorbike
- Hobby:photography == Nationality:chinese or Transport:motorbike == Hobby:photography, but not both
- Sport:cricket is on the left or right of Nationality:french
- Transport:motorbike is on the far left or far right
- Hobby:filmmaking is somewhere to the right of Hobby:board-games
- Transport:train is in an odd position
- Hobby:board-games and Transport:boat have different parity positions
- Nationality:french is somewhere to the right of Transport:train
- Transport:train is on the left or right of Transport:roller
- Sport:parkour is in an odd position
- Hobby:dancing is on the left or right of Sport:surfing
- Nationality:french is somewhere between Transport:boat and Hobby:photography
- Nationality:pakistani is on the left or right of Sport:lacrosse
- Nationality:colombian is on the left or right of Transport:motorbike
- Transport:boat is not to the left of Hobby:dancing
- Sport:parkour is somewhere to the left of Nationality:french
- Nationality:colombian and Hobby:board-games have different parity positions

Answer the following question:

Question: Question: What is the Nationality of the person who has/is lacrosse??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: french


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Nationality, Hobby, Food, Pet.
The attributes have the following possible values:
- Nationality: australian, french, japanese, mexican, pakistani
- Hobby: chess, dancing, gardening, singing, video-games
- Food: avocado, corn, kiwi, papaya, plum
- Pet: cat, frog, lizard, rabbit, snake

Given the following premises about the line of people:
- Hobby:gardening is somewhere to the left of Hobby:video-games
- Pet:lizard and Food:papaya have the same parity positions
- Pet:rabbit is not to the left of Hobby:singing
- Nationality:australian is on the left or right of Nationality:pakistani
- Nationality:japanese == Food:kiwi
- Nationality:french is on the left of Nationality:japanese
- Pet:frog == Food:corn
- Pet:snake is on the right of Food:plum
- Hobby:chess and Food:avocado have the same parity positions
- Food:avocado is somewhere between Pet:lizard and Food:plum
- Food:avocado == Nationality:pakistani
- Hobby:dancing is on the far right
- Food:plum is somewhere between Hobby:gardening and Hobby:singing
- Pet:frog and Nationality:pakistani have the same parity positions

Answer the following question:

Question: Question: What is the Nationality of the person who has/is chess??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pakistani


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Nationality, Hobby, Movie-Genre, Music-Genre, Food, Transport.
The attributes have the following possible values:
- Nationality: argentine, chinese, egyptian, indonesian
- Hobby: fishing, gardening, puzzles, woodworking
- Movie-Genre: comedy, horror, musical, romance
- Music-Genre: dubstep, gospel, jazz, punk
- Food: apple, blueberry, broccoli, corn
- Transport: airplane, car, motorbike, snowmobile

Given the following premises about the line of people:
- Movie-Genre:romance and Music-Genre:gospel have different parity positions
- Food:broccoli != Transport:car
- Food:blueberry == Movie-Genre:horror or Hobby:gardening == Food:blueberry, but not both
- Transport:car == Food:blueberry or Transport:car == Hobby:puzzles, but not both
- Movie-Genre:comedy == Transport:motorbike or Food:corn == Movie-Genre:comedy, but not both
- Transport:snowmobile is in an even position
- Hobby:gardening is somewhere to the right of Music-Genre:dubstep
- Movie-Genre:musical is somewhere to the left of Nationality:argentine
- Nationality:egyptian is on the left or right of Transport:car
- Food:broccoli is in an even position
- Transport:airplane is somewhere to the left of Hobby:fishing
- Nationality:egyptian is somewhere to the right of Music-Genre:jazz
- Transport:snowmobile and Nationality:indonesian have different parity positions
- Movie-Genre:comedy is somewhere to the right of Nationality:egyptian
- Nationality:argentine is somewhere between Nationality:egyptian and Music-Genre:jazz

Answer the following question:

Question: Question: What is the Movie-Genre of the person who has/is punk??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: romance


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Beverage, Food, Movie-Genre, Transport.
The attributes have the following possible values:
- Beverage: coffee, cola, juice, milk, soy-milk, water
- Food: banana, cauliflower, grapefruit, papaya, radish, raspberry
- Movie-Genre: animation, horror, martial-arts, romance, time-travel, western
- Transport: car, jet-ski, scooter, snowmobile, subway, train

Given the following premises about the line of people:
- Beverage:milk and Transport:jet-ski have the same parity positions
- Food:papaya == Movie-Genre:western or Food:papaya == Transport:snowmobile, but not both
- Beverage:soy-milk is somewhere between Beverage:milk and Movie-Genre:martial-arts
- Food:radish is on the left or right of Transport:jet-ski
- Beverage:water is on the far left or far right
- Transport:car is somewhere between Transport:subway and Transport:scooter
- Transport:snowmobile == Food:raspberry or Transport:snowmobile == Beverage:milk or both
- Movie-Genre:horror is somewhere to the right of Movie-Genre:animation
- Food:raspberry is somewhere to the left of Transport:scooter
- Transport:subway is somewhere to the right of Movie-Genre:romance
- Transport:jet-ski is not to the left of Food:grapefruit
- Transport:snowmobile is between Beverage:juice and Movie-Genre:western
- Beverage:cola is on the far left
- Movie-Genre:animation == Food:cauliflower or Beverage:coffee == Movie-Genre:animation, but not both
- Transport:snowmobile is somewhere to the left of Movie-Genre:romance
- Movie-Genre:animation is not to the left of Food:banana
- Movie-Genre:martial-arts is on the left or right of Food:cauliflower
- Movie-Genre:time-travel == Food:raspberry or Movie-Genre:time-travel == Beverage:coffee, but not both

Answer the following question:

Question: Question: What is the Food of the person who has/is martial-arts??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: radish


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Beverage, Food, Movie-Genre, Music-Genre, Sport.
The attributes have the following possible values:
- Beverage: cola, fanta, hot-chocolate, soy-milk, tea
- Food: apricot, cranberry, mango, papaya, peas
- Movie-Genre: adventure, horror, musical, romance, sports
- Music-Genre: ambient, disco, house, indie, jazz
- Sport: baseball, basketball, cycling, rugby, weightlifting

Given the following premises about the line of people:
- Movie-Genre:romance is on the left or right of Beverage:tea
- Food:mango == Sport:rugby or Music-Genre:house == Food:mango or both
- Sport:baseball and Music-Genre:ambient have the same parity positions
- Food:apricot is somewhere to the right of Sport:baseball
- Beverage:tea == Music-Genre:jazz or Movie-Genre:sports == Beverage:tea or both
- Sport:weightlifting and Movie-Genre:sports have different parity positions
- Food:apricot == Beverage:tea or Music-Genre:indie == Food:apricot, but not both
- Movie-Genre:musical is not to the right of Sport:weightlifting
- Food:papaya is on the left or right of Beverage:cola
- Sport:rugby is not to the left of Music-Genre:house
- Food:mango is somewhere to the right of Movie-Genre:romance
- Beverage:tea and Movie-Genre:adventure have different parity positions
- Beverage:soy-milk is not to the right of Food:cranberry
- Food:papaya == Music-Genre:indie or Food:papaya == Movie-Genre:musical or both
- Music-Genre:jazz == Beverage:fanta or Music-Genre:jazz == Food:cranberry or both
- Beverage:soy-milk == Movie-Genre:romance or Beverage:soy-milk == Music-Genre:disco, but not both
- Food:apricot and Movie-Genre:musical have different parity positions
- Music-Genre:indie is somewhere to the left of Music-Genre:house
- Movie-Genre:adventure and Beverage:soy-milk have different parity positions
- Sport:rugby is somewhere between Beverage:soy-milk and Sport:basketball
- Movie-Genre:musical == Beverage:cola or Movie-Genre:musical == Music-Genre:jazz, but not both

Answer the following question:

Question: Question: What is the Beverage of the person who has/is jazz??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: fanta


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Food, Movie-Genre, Sport, Transport.
The attributes have the following possible values:
- Food: artichoke, blueberry, grapes, mango
- Movie-Genre: animation, drama, epic, family
- Sport: badminton, rowing, soccer, volleyball
- Transport: bike, bus, ship, skateboard

Given the following premises about the line of people:
- Food:artichoke == Transport:bike
- Sport:soccer != Transport:bus
- Movie-Genre:epic is somewhere to the right of Movie-Genre:drama
- Movie-Genre:family is somewhere to the right of Movie-Genre:epic
- Movie-Genre:drama == Transport:bus
- Transport:bike is between Food:grapes and Sport:volleyball
- Food:blueberry is not to the right of Transport:bus
- Food:grapes is somewhere between Movie-Genre:animation and Sport:badminton
- Transport:ship == Food:blueberry

Answer the following question:

Question: Question: What is the Sport of the person who has/is animation??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: soccer


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Hobby, Beverage, Movie-Genre, Sport.
The attributes have the following possible values:
- Job: freelancer, manager, nurse, project-manager
- Food: artichoke, cabbage, corn, zucchini
- Hobby: hiking, magic-tricks, singing, skydiving
- Beverage: iced-tea, juice, mirinda, sprite
- Movie-Genre: adventure, epic, musical, satire
- Sport: badminton, climbing, skateboarding, swimming

Given the following premises about the line of people:
- Sport:climbing is not to the right of Job:project-manager
- Sport:climbing and Food:corn have different parity positions
- Movie-Genre:satire is on the right of Movie-Genre:musical
- Food:cabbage is between Sport:swimming and Hobby:skydiving
- Sport:climbing is somewhere to the right of Beverage:juice
- Beverage:iced-tea is somewhere to the right of Job:project-manager
- Food:corn and Job:manager have different parity positions
- Hobby:skydiving and Food:zucchini have different parity positions
- Hobby:singing is on the left of Beverage:sprite
- Sport:skateboarding and Movie-Genre:adventure have the same parity positions
- Food:corn is somewhere to the right of Job:freelancer
- Beverage:iced-tea == Movie-Genre:musical
- Sport:skateboarding is not to the right of Movie-Genre:adventure
- Food:zucchini is not to the right of Hobby:magic-tricks

Answer the following question:

Question: Question: What is the Job of the person who has/is epic??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: project-manager


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Beverage, Movie-Genre, Music-Genre, Sport.
The attributes have the following possible values:
- Job: paramedic, pilot, scientist, teacher
- Hobby: chess, rock-climbing, skydiving, traveling
- Beverage: 7up, cola, hot-chocolate, milk
- Movie-Genre: animation, documentary, family, zombie
- Music-Genre: disco, folk, house, jazz
- Sport: cricket, cycling, ice-hockey, lacrosse

Given the following premises about the line of people:
- Movie-Genre:family == Job:paramedic
- Job:pilot is somewhere to the right of Beverage:milk
- Movie-Genre:zombie is somewhere to the left of Job:paramedic
- Hobby:traveling == Music-Genre:disco
- Sport:cycling is on the left or right of Sport:lacrosse
- Music-Genre:folk == Movie-Genre:documentary
- Music-Genre:jazz == Hobby:rock-climbing
- Beverage:hot-chocolate is somewhere to the left of Sport:ice-hockey
- Job:teacher == Music-Genre:house
- Hobby:rock-climbing is on the left of Sport:lacrosse
- Sport:cycling is somewhere to the left of Movie-Genre:zombie
- Hobby:chess == Beverage:milk
- Beverage:hot-chocolate is between Beverage:7up and Job:paramedic

Answer the following question:

Question: Question: What is the Beverage of the person who has/is house??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: hot-chocolate


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Nationality, Food, Movie-Genre, Beverage, Transport.
The attributes have the following possible values:
- Nationality: german, italian, japanese, mexican, spanish, thai
- Food: cauliflower, cranberry, kale, lettuce, pomegranate, raspberry
- Movie-Genre: animation, disaster, family, martial-arts, sports, zombie
- Beverage: almond-milk, cola, fanta, milk, mirinda, tea
- Transport: bus, ship, skateboard, snowmobile, tram, van

Given the following premises about the line of people:
- Beverage:milk is on the left or right of Beverage:mirinda
- Transport:bus is not to the right of Movie-Genre:martial-arts
- Nationality:japanese is somewhere to the right of Nationality:german
- Transport:bus == Food:raspberry or Movie-Genre:family == Transport:bus, but not both
- Transport:snowmobile != Food:raspberry or Nationality:italian != Transport:snowmobile or both
- Transport:tram is not to the left of Transport:snowmobile
- Nationality:german is somewhere to the right of Nationality:thai
- Nationality:italian is between Transport:tram and Nationality:spanish
- Food:cranberry is not to the right of Movie-Genre:zombie
- Transport:bus and Movie-Genre:sports have different parity positions
- Food:lettuce and Beverage:mirinda have different parity positions
- Food:cranberry is somewhere between Movie-Genre:sports and Nationality:italian
- Nationality:italian is on the left or right of Beverage:almond-milk
- Nationality:japanese is not to the right of Beverage:fanta
- Nationality:spanish is not to the right of Nationality:thai
- Beverage:milk and Food:kale have the same parity positions
- Transport:tram == Movie-Genre:zombie or Transport:tram == Beverage:milk, but not both
- Transport:skateboard != Movie-Genre:sports
- Beverage:mirinda is not to the right of Food:lettuce
- Beverage:fanta and Transport:van have different parity positions
- Beverage:tea is not to the right of Transport:tram
- Movie-Genre:animation is somewhere to the right of Nationality:japanese
- Movie-Genre:martial-arts is between Food:pomegranate and Nationality:thai
- Food:cauliflower and Movie-Genre:sports have different parity positions
- Beverage:tea == Transport:ship or Beverage:tea == Food:pomegranate or both

Answer the following question:

Question: Question: What is the Beverage of the person who has/is pomegranate??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: tea


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Job, Hobby, Movie-Genre, Pet.
The attributes have the following possible values:
- Job: accountant, bartender, coach, police-officer, scientist
- Hobby: dancing, reading, rock-climbing, sudoku, writing
- Movie-Genre: crime, fantasy, musical, romance, satire
- Pet: hamster, hedgehog, lizard, rat, turtle

Given the following premises about the line of people:
- Pet:rat is on the right of Movie-Genre:musical
- Pet:hamster is on the far left or far right
- Job:coach is on the far left
- Pet:hedgehog is somewhere to the left of Job:bartender
- Job:coach is on the left of Movie-Genre:romance
- Hobby:rock-climbing is in the middle
- Hobby:dancing is somewhere to the left of Job:bartender
- Movie-Genre:musical is in the middle
- Movie-Genre:satire is on the left of Hobby:reading
- Job:accountant is in an odd position
- Movie-Genre:crime is somewhere between Pet:turtle and Pet:lizard
- Hobby:writing is on the left of Job:police-officer
- Movie-Genre:romance is on the left or right of Pet:lizard
- Job:scientist is on the left or right of Movie-Genre:fantasy

Answer the following question:

Question: Question: What is the Movie-Genre of the person who has/is rock-climbing??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: musical


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Nationality, Food, Hobby, Beverage, Pet, Transport.
The attributes have the following possible values:
- Nationality: french, japanese, malaysian, polish
- Food: asparagus, lemon, mango, potato
- Hobby: camping, chess, hiking, traveling
- Beverage: iced-tea, juice, soy-milk, water
- Pet: cat, goldfish, horse, pony
- Transport: motorbike, ship, snowmobile, van

Given the following premises about the line of people:
- Food:asparagus is not to the left of Pet:horse
- Transport:snowmobile != Pet:horse
- Beverage:water is somewhere to the right of Food:asparagus
- Food:potato == Pet:pony or Pet:pony == Beverage:water or both
- Hobby:chess is somewhere to the right of Hobby:camping
- Beverage:juice is not to the right of Food:potato
- Nationality:japanese is not to the left of Pet:pony
- Pet:cat is not to the left of Nationality:french
- Transport:snowmobile is somewhere to the left of Nationality:malaysian
- Hobby:chess is somewhere to the left of Transport:motorbike
- Hobby:camping is not to the left of Pet:goldfish
- Transport:snowmobile and Food:lemon have different parity positions
- Pet:horse is not to the left of Hobby:traveling
- Beverage:soy-milk is not to the right of Pet:goldfish
- Beverage:soy-milk is somewhere between Hobby:chess and Beverage:iced-tea
- Nationality:malaysian is not to the right of Beverage:soy-milk
- Transport:ship == Beverage:soy-milk or Transport:ship == Nationality:malaysian or both

Answer the following question:

Question: Question: What is the Nationality of the person who has/is juice??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: polish


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Beverage, Food, Hobby, Music-Genre, Sport.
The attributes have the following possible values:
- Beverage: almond-milk, cola, iced-tea, lemonade, sprite
- Food: cabbage, garlic, orange, plum, zucchini
- Hobby: drawing, filmmaking, fishing, rock-climbing, video-games
- Music-Genre: classical, indie, punk, techno, trance
- Sport: badminton, climbing, cricket, golf, soccer

Given the following premises about the line of people:
- Beverage:lemonade is not to the right of Food:cabbage
- Food:plum == Sport:climbing or Food:plum == Music-Genre:indie, but not both
- Beverage:almond-milk is in an odd position
- Sport:golf is not to the left of Food:orange
- Hobby:filmmaking == Music-Genre:techno or Hobby:filmmaking == Beverage:lemonade or both
- Hobby:video-games is not to the right of Music-Genre:techno
- Beverage:almond-milk is somewhere to the left of Hobby:rock-climbing
- Beverage:sprite is somewhere between Hobby:video-games and Sport:climbing
- Music-Genre:techno is somewhere to the left of Beverage:sprite
- Food:plum is somewhere to the left of Food:garlic
- Food:plum is somewhere to the right of Sport:soccer
- Hobby:rock-climbing and Beverage:almond-milk have different parity positions
- Food:zucchini is somewhere to the left of Food:orange
- Beverage:cola is somewhere to the right of Sport:golf
- Music-Genre:trance is somewhere to the left of Music-Genre:techno
- Music-Genre:punk and Sport:badminton have different parity positions
- Sport:soccer != Hobby:drawing
- Music-Genre:trance and Hobby:drawing have the same parity positions
- Beverage:iced-tea != Hobby:filmmaking
- Music-Genre:classical is somewhere to the left of Sport:soccer
- Sport:soccer is in an even position

Answer the following question:

Question: Question: What is the Beverage of the person who has/is cabbage??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: lemonade


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Job, Hobby, Music-Genre, Pet.
The attributes have the following possible values:
- Job: architect, entrepreneur, journalist, manager, nurse, project-manager
- Hobby: baking, camping, chess, magic-tricks, video-games, writing
- Music-Genre: dubstep, funk, gospel, indie, rock, soul
- Pet: goat, hedgehog, lizard, mouse, rat, turtle

Given the following premises about the line of people:
- Hobby:baking is not to the left of Hobby:writing
- Hobby:magic-tricks is between Job:architect and Job:journalist
- Hobby:writing and Pet:mouse have the same parity positions
- Music-Genre:soul == Pet:rat or Music-Genre:soul == Hobby:magic-tricks, but not both
- Job:manager and Pet:turtle have different parity positions
- Job:manager is not to the right of Pet:turtle
- Job:entrepreneur is somewhere to the left of Hobby:writing
- Job:nurse is somewhere between Hobby:writing and Hobby:chess
- Music-Genre:indie is on the right of Job:architect
- Job:project-manager is somewhere to the left of Job:manager
- Job:manager is between Hobby:camping and Job:journalist
- Pet:rat and Music-Genre:dubstep have the same parity positions
- Hobby:baking is somewhere to the left of Hobby:magic-tricks
- Job:architect is not to the left of Music-Genre:dubstep
- Music-Genre:funk is between Job:entrepreneur and Pet:hedgehog
- Music-Genre:gospel == Pet:goat or Music-Genre:gospel == Job:nurse, but not both

Answer the following question:

Question: Question: What is the Job of the person who has/is funk??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: project-manager


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Beverage, Hobby, Music-Genre, Pet, Sport.
The attributes have the following possible values:
- Beverage: iced-tea, milk, mirinda, tea
- Hobby: baking, board-games, fishing, singing
- Music-Genre: d&b, dubstep, folk, punk
- Pet: goldfish, horse, pony, rat
- Sport: handball, rugby, skiing, surfing

Given the following premises about the line of people:
- Pet:rat is on the right of Music-Genre:punk
- Sport:skiing is not to the left of Beverage:mirinda
- Hobby:singing is on the left or right of Pet:goldfish
- Music-Genre:folk is not to the left of Hobby:fishing
- Sport:surfing and Beverage:iced-tea have the same parity positions
- Hobby:singing is somewhere to the right of Hobby:board-games
- Pet:pony is on the far right
- Pet:pony is on the right of Pet:horse
- Hobby:fishing and Sport:handball have different parity positions
- Beverage:milk is somewhere between Music-Genre:d&b and Sport:skiing
- Music-Genre:folk is in an odd position
- Hobby:board-games is on the left of Sport:rugby

Answer the following question:

Question: Question: What is the Beverage of the person who has/is pony??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: tea


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Beverage, Pet, Sport.
The attributes have the following possible values:
- Job: analyst, chef, fisherman, police-officer
- Food: kiwi, nectarine, orange, peas
- Beverage: almond-milk, juice, tea, water
- Pet: cat, guinea-pig, hamster, lizard
- Sport: cricket, parkour, sailing, snowboarding

Given the following premises about the line of people:
- Pet:hamster is not to the right of Job:fisherman
- Beverage:tea is not to the left of Sport:sailing
- Food:orange == Sport:snowboarding or Food:orange == Beverage:water or both
- Food:nectarine is on the left or right of Job:analyst
- Food:kiwi is somewhere to the right of Beverage:water
- Pet:cat is somewhere to the right of Beverage:tea
- Pet:cat and Sport:snowboarding have different parity positions
- Pet:guinea-pig is not to the right of Sport:sailing
- Job:fisherman == Food:orange or Sport:sailing == Job:fisherman or both
- Pet:guinea-pig is somewhere to the right of Sport:parkour
- Food:nectarine == Sport:sailing or Job:fisherman == Food:nectarine or both
- Sport:snowboarding and Food:kiwi have the same parity positions
- Beverage:juice == Food:nectarine or Job:chef == Beverage:juice or both
- Job:chef is somewhere to the left of Beverage:juice

Answer the following question:

Question: Question: What is the Job of the person who has/is cat??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: police-officer


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Beverage, Food, Movie-Genre, Music-Genre, Pet, Sport.
The attributes have the following possible values:
- Beverage: coffee, fanta, hot-chocolate, mirinda, sprite
- Food: apple, garlic, kiwi, pear, zucchini
- Movie-Genre: horror, satire, sports, western, zombie
- Music-Genre: country, hip-hop, house, jazz, salsa
- Pet: bird, dog, fish, goat, rabbit
- Sport: biathlon, climbing, handball, soccer, swimming

Given the following premises about the line of people:
- Beverage:fanta and Movie-Genre:sports have different parity positions
- Pet:goat == Music-Genre:country or Music-Genre:country == Movie-Genre:sports or both
- Movie-Genre:horror == Food:pear or Food:pear == Pet:bird or both
- Movie-Genre:zombie == Pet:rabbit or Pet:rabbit == Food:apple or both
- Food:pear != Music-Genre:country
- Beverage:fanta == Sport:handball or Beverage:fanta == Music-Genre:house or both
- Beverage:mirinda == Sport:climbing or Beverage:mirinda == Music-Genre:house or both
- Beverage:hot-chocolate == Music-Genre:country or Food:garlic == Beverage:hot-chocolate or both
- Pet:fish is somewhere to the left of Food:garlic
- Beverage:mirinda is not to the left of Food:apple
- Beverage:hot-chocolate != Sport:biathlon or Movie-Genre:western != Beverage:hot-chocolate or both
- Pet:bird == Music-Genre:salsa or Pet:bird == Movie-Genre:zombie, but not both
- Sport:swimming is somewhere between Music-Genre:salsa and Food:pear
- Beverage:hot-chocolate and Pet:fish have different parity positions
- Beverage:fanta is not to the left of Sport:biathlon
- Sport:climbing is in an even position
- Beverage:coffee is somewhere to the left of Beverage:sprite
- Sport:biathlon == Pet:rabbit or Sport:biathlon == Music-Genre:salsa or both
- Sport:climbing == Movie-Genre:horror or Sport:climbing == Music-Genre:salsa, but not both
- Movie-Genre:satire == Pet:bird or Movie-Genre:satire == Food:apple or both
- Beverage:mirinda is not to the right of Food:garlic
- Beverage:hot-chocolate != Food:garlic or Music-Genre:salsa != Beverage:hot-chocolate or both
- Food:kiwi is not to the left of Food:zucchini
- Movie-Genre:horror is somewhere between Movie-Genre:western and Movie-Genre:satire
- Pet:dog is not to the right of Sport:biathlon
- Food:zucchini and Sport:handball have different parity positions
- Sport:swimming is not to the left of Pet:fish
- Music-Genre:house != Pet:rabbit or Food:apple != Music-Genre:house or both
- Music-Genre:country is somewhere to the left of Music-Genre:hip-hop
- Music-Genre:hip-hop == Food:pear or Music-Genre:hip-hop == Beverage:hot-chocolate, but not both
- Movie-Genre:zombie != Beverage:coffee
- Food:zucchini is somewhere between Food:garlic and Food:apple
- Sport:biathlon and Music-Genre:salsa have the same parity positions

Answer the following question:

Question: Question: What is the Beverage of the person who has/is goat??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: hot-chocolate


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Job, Food, Beverage, Movie-Genre, Sport.
The attributes have the following possible values:
- Job: bartender, dancer, firefighter, manager, security-guard
- Food: avocado, kale, lettuce, spinach, tomato
- Beverage: almond-milk, iced-tea, lemonade, mirinda, tea
- Movie-Genre: adventure, comedy, crime, musical, satire
- Sport: biathlon, cycling, ice-hockey, rowing, soccer

Given the following premises about the line of people:
- Food:lettuce and Job:security-guard have the same parity positions
- Sport:soccer is not to the right of Beverage:iced-tea
- Sport:biathlon is not to the left of Movie-Genre:satire
- Job:dancer is somewhere to the left of Food:avocado
- Sport:cycling != Movie-Genre:satire or Sport:cycling != Food:lettuce or both
- Sport:biathlon == Movie-Genre:musical or Sport:biathlon == Beverage:mirinda or both
- Job:security-guard and Beverage:mirinda have different parity positions
- Food:tomato is not to the left of Job:security-guard
- Food:spinach == Job:manager or Food:spinach == Sport:biathlon or both
- Beverage:lemonade is somewhere to the left of Job:bartender
- Sport:cycling == Food:lettuce or Sport:cycling == Job:security-guard or both
- Beverage:lemonade is on the left or right of Sport:rowing
- Beverage:mirinda is somewhere to the left of Sport:rowing
- Sport:ice-hockey and Movie-Genre:musical have different parity positions
- Movie-Genre:crime is on the left or right of Beverage:almond-milk
- Sport:soccer and Job:bartender have different parity positions
- Job:dancer is somewhere to the right of Food:tomato
- Movie-Genre:comedy is not to the left of Food:spinach
- Food:lettuce is somewhere to the left of Food:spinach
- Food:avocado is in an even position
- Job:manager and Food:lettuce have different parity positions
- Sport:biathlon and Beverage:lemonade have the same parity positions

Answer the following question:

Question: Question: What is the Beverage of the person who has/is satire??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: mirinda


There are 5 people standing in a line numbered 1 through 5 in a left to right order.
Each person has the following attributes:  Job, Hobby, Food, Movie-Genre, Pet, Sport.
The attributes have the following possible values:
- Job: engineer, librarian, manager, paramedic, photographer
- Hobby: cooking, filmmaking, reading, skydiving, woodworking
- Food: apricot, cherry, cranberry, lettuce, peas
- Movie-Genre: disaster, documentary, musical, mystery, satire
- Pet: chinchilla, frog, lizard, rabbit, rat
- Sport: basketball, golf, rowing, skiing, tennis

Given the following premises about the line of people:
- Pet:lizard is not to the right of Movie-Genre:satire
- Job:photographer != Pet:chinchilla or Sport:basketball != Job:photographer or both
- Job:photographer != Sport:basketball
- Food:peas == Hobby:filmmaking or Sport:basketball == Food:peas or both
- Job:photographer and Pet:rabbit have the same parity positions
- Food:cherry != Sport:skiing
- Job:manager is not to the left of Pet:rabbit
- Food:cherry != Hobby:reading or Food:cherry != Movie-Genre:musical or both
- Pet:rat != Food:peas or Pet:rat != Movie-Genre:disaster or both
- Food:peas == Pet:rat or Job:librarian == Food:peas, but not both
- Hobby:filmmaking != Pet:chinchilla or Sport:golf != Hobby:filmmaking or both
- Job:manager != Sport:rowing
- Hobby:filmmaking is somewhere between Hobby:skydiving and Pet:rabbit
- Movie-Genre:satire == Food:cherry or Food:cherry == Sport:tennis or both
- Hobby:filmmaking and Sport:tennis have the same parity positions
- Job:engineer == Hobby:cooking or Job:engineer == Food:lettuce or both
- Hobby:filmmaking != Pet:lizard or Food:apricot != Hobby:filmmaking or both
- Job:paramedic is somewhere between Sport:basketball and Hobby:woodworking
- Job:manager != Pet:chinchilla
- Hobby:woodworking != Pet:chinchilla or Hobby:woodworking != Food:lettuce or both
- Food:cranberry is not to the left of Job:paramedic
- Movie-Genre:documentary != Food:apricot or Food:apricot != Job:photographer or both
- Hobby:filmmaking != Movie-Genre:documentary or Hobby:filmmaking != Food:cranberry or both
- Hobby:cooking is not to the right of Hobby:filmmaking
- Hobby:reading == Movie-Genre:disaster or Hobby:reading == Job:manager or both
- Food:cherry is not to the left of Movie-Genre:mystery
- Sport:rowing == Job:engineer or Sport:rowing == Pet:lizard or both
- Sport:tennis != Hobby:cooking or Job:photographer != Sport:tennis or both
- Job:photographer is not to the right of Movie-Genre:disaster
- Food:cranberry != Movie-Genre:disaster
- Job:photographer and Hobby:cooking have the same parity positions
- Job:photographer is not to the right of Movie-Genre:mystery
- Job:photographer == Sport:basketball or Job:photographer == Hobby:skydiving or both
- Food:cherry is not to the left of Sport:skiing
- Job:engineer != Sport:golf
- Movie-Genre:mystery is not to the left of Food:peas
- Movie-Genre:documentary != Job:manager
- Food:peas is not to the left of Food:apricot
- Sport:basketball != Movie-Genre:musical or Sport:basketball != Job:paramedic or both
- Job:manager != Sport:skiing or Job:manager != Pet:lizard or both
- Pet:chinchilla == Sport:basketball or Sport:basketball == Food:apricot, but not both
- Job:photographer and Movie-Genre:musical have the same parity positions
- Job:paramedic != Food:lettuce or Sport:golf != Job:paramedic or both
- Food:cherry and Hobby:reading have the same parity positions
- Hobby:woodworking != Job:photographer or Job:photographer != Sport:rowing or both
- Hobby:woodworking == Pet:lizard or Movie-Genre:musical == Hobby:woodworking or both
- Pet:rat is somewhere between Movie-Genre:documentary and Movie-Genre:disaster
- Food:cranberry is somewhere between Sport:rowing and Pet:frog
- Hobby:filmmaking and Movie-Genre:documentary have the same parity positions
- Sport:skiing != Food:cherry or Job:engineer != Sport:skiing or both
- Hobby:skydiving == Movie-Genre:mystery or Job:manager == Hobby:skydiving, but not both
- Sport:tennis != Hobby:skydiving or Movie-Genre:mystery != Sport:tennis or both
- Movie-Genre:mystery != Job:manager or Hobby:reading != Movie-Genre:mystery or both
- Movie-Genre:disaster is not to the left of Pet:frog
- Pet:lizard != Hobby:filmmaking
- Hobby:filmmaking != Sport:golf
- Sport:golf is not to the right of Sport:golf
- Sport:skiing is somewhere between Pet:frog and Hobby:woodworking
- Job:manager is not to the left of Food:apricot
- Pet:rat is not to the right of Movie-Genre:mystery
- Sport:golf is somewhere between Sport:rowing and Job:photographer
- Pet:chinchilla != Hobby:cooking or Sport:tennis != Pet:chinchilla or both
- Food:peas == Hobby:filmmaking or Food:peas == Sport:basketball or both
- Movie-Genre:musical != Sport:basketball or Food:lettuce != Movie-Genre:musical or both
- Pet:rat != Movie-Genre:documentary
- Pet:chinchilla != Movie-Genre:mystery
- Sport:tennis == Movie-Genre:disaster or Sport:tennis == Food:lettuce or both
- Hobby:filmmaking != Pet:frog
- Sport:skiing != Pet:rat or Sport:skiing != Food:peas or both
- Pet:rat is not to the left of Job:engineer
- Pet:lizard is not to the right of Pet:rabbit
- Food:peas is not to the left of Pet:rabbit
- Hobby:cooking and Sport:skiing have the same parity positions
- Sport:basketball == Movie-Genre:mystery or Sport:basketball == Food:peas, but not both
- Hobby:reading is not to the left of Movie-Genre:musical
- Job:photographer and Movie-Genre:mystery have the same parity positions
- Food:apricot != Pet:frog
- Pet:rabbit and Movie-Genre:satire have different parity positions
- Pet:rabbit is somewhere between Pet:frog and Movie-Genre:documentary
- Pet:rabbit != Food:lettuce
- Hobby:cooking is not to the right of Pet:rabbit

Answer the following question:

Question: Question: What is the Hobby of the person who is manager??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: reading


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Nationality, Hobby, Beverage, Transport.
The attributes have the following possible values:
- Nationality: egyptian, pakistani, polish, russian
- Hobby: board-games, reading, rock-climbing, writing
- Beverage: coffee, cola, mirinda, sprite
- Transport: airplane, bike, taxi, van

Given the following premises about the line of people:
- Transport:bike is somewhere between Hobby:board-games and Transport:van
- Transport:airplane is not to the left of Transport:taxi
- Hobby:writing is somewhere to the right of Beverage:cola
- Beverage:mirinda is on the far left or far right
- Transport:taxi is somewhere to the right of Nationality:pakistani
- Nationality:polish is not to the right of Hobby:reading
- Nationality:pakistani != Beverage:cola
- Hobby:rock-climbing is somewhere between Hobby:reading and Transport:taxi
- Beverage:sprite is somewhere to the right of Nationality:egyptian

Answer the following question:

Question: Question: What is the Nationality of the person who has/is coffee??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pakistani


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Hobby, Movie-Genre, Music-Genre, Transport.
The attributes have the following possible values:
- Job: accountant, architect, journalist, photographer
- Hobby: cooking, photography, puzzles, woodworking
- Movie-Genre: documentary, epic, mystery, western
- Music-Genre: d&b, house, jazz, trance
- Transport: motorbike, quad-bike, ship, taxi

Given the following premises about the line of people:
- Movie-Genre:documentary is not to the right of Music-Genre:house
- Hobby:puzzles is somewhere to the right of Transport:motorbike
- Music-Genre:jazz is not to the left of Hobby:puzzles
- Music-Genre:d&b == Job:photographer
- Movie-Genre:epic is somewhere between Movie-Genre:documentary and Job:photographer
- Transport:motorbike is on the left or right of Movie-Genre:documentary
- Job:accountant is on the right of Transport:taxi
- Movie-Genre:mystery != Transport:quad-bike
- Hobby:woodworking is not to the left of Job:journalist
- Hobby:photography == Music-Genre:d&b
- Hobby:woodworking is on the right of Hobby:photography
- Hobby:cooking is somewhere to the left of Hobby:puzzles
- Music-Genre:d&b and Movie-Genre:western have different parity positions

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is western??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: jazz


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Hobby, Music-Genre, Pet, Sport, Transport.
The attributes have the following possible values:
- Hobby: baking, filmmaking, photography, reading, skydiving, video-games
- Music-Genre: ambient, country, jazz, punk, techno, trance
- Pet: cat, dog, ferret, goat, horse, turtle
- Sport: climbing, cricket, golf, ice-hockey, soccer, surfing
- Transport: boat, bus, helicopter, snowmobile, tram, van

Given the following premises about the line of people:
- Transport:boat is on the left of Music-Genre:punk
- Pet:goat is somewhere to the left of Sport:ice-hockey
- Hobby:reading == Sport:climbing
- Music-Genre:techno is somewhere to the right of Music-Genre:jazz
- Hobby:video-games is on the far left or far right
- Pet:goat is somewhere to the left of Music-Genre:country
- Pet:horse == Hobby:filmmaking
- Sport:surfing is on the far left or far right
- Transport:tram == Sport:surfing
- Sport:golf is on the left or right of Music-Genre:trance
- Hobby:video-games == Transport:bus
- Sport:golf is somewhere to the left of Pet:turtle
- Music-Genre:trance is somewhere to the right of Transport:boat
- Hobby:baking is somewhere to the left of Pet:dog
- Music-Genre:ambient is between Hobby:reading and Sport:soccer
- Hobby:photography is on the left of Transport:snowmobile
- Transport:boat is on the right of Transport:van
- Music-Genre:punk is on the right of Pet:goat
- Hobby:filmmaking is on the left or right of Transport:helicopter
- Pet:cat is on the left of Hobby:photography

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is turtle??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: trance


There are 6 people standing in a line numbered 1 through 6 in a left to right order.
Each person has the following attributes:  Job, Hobby, Movie-Genre, Music-Genre, Transport.
The attributes have the following possible values:
- Job: bartender, chef, coach, journalist, lawyer, librarian
- Hobby: board-games, camping, card-games, collecting, gardening, singing
- Movie-Genre: animation, disaster, satire, sports, superhero, zombie
- Music-Genre: d&b, disco, indie, jazz, punk, soul
- Transport: airplane, bike, scooter, ship, snowmobile, taxi

Given the following premises about the line of people:
- Job:coach == Transport:ship
- Movie-Genre:satire is on the left or right of Music-Genre:soul
- Movie-Genre:zombie is on the left of Transport:airplane
- Movie-Genre:disaster == Hobby:board-games
- Movie-Genre:animation == Job:librarian
- Music-Genre:soul is somewhere to the left of Movie-Genre:satire
- Movie-Genre:animation is on the right of Hobby:card-games
- Hobby:board-games is between Hobby:card-games and Transport:snowmobile
- Movie-Genre:superhero is on the right of Job:lawyer
- Job:journalist is on the left or right of Hobby:camping
- Transport:snowmobile is between Transport:airplane and Music-Genre:disco
- Hobby:board-games is on the right of Hobby:singing
- Movie-Genre:sports is somewhere to the left of Hobby:collecting
- Music-Genre:indie is on the left or right of Hobby:collecting
- Job:chef is on the far left
- Music-Genre:d&b == Movie-Genre:superhero
- Transport:taxi is somewhere to the right of Music-Genre:jazz
- Hobby:board-games == Transport:bike

Answer the following question:

Question: Question: What is the Music-Genre of the person who has/is sports??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: indie


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Food, Movie-Genre, Sport.
The attributes have the following possible values:
- Job: bartender, dancer, dressmaker, musician
- Food: carrot, cranberry, pepper, radish
- Movie-Genre: adventure, comedy, superhero, thriller
- Sport: basketball, surfing, tennis, water-polo

Given the following premises about the line of people:
- Movie-Genre:thriller and Sport:basketball have the same parity positions
- Sport:basketball is not to the left of Sport:surfing
- Food:pepper and Sport:surfing have different parity positions
- Job:musician and Movie-Genre:comedy have different parity positions
- Job:bartender is not to the left of Movie-Genre:adventure
- Job:dressmaker is somewhere between Sport:surfing and Sport:water-polo
- Job:bartender == Food:radish or Job:bartender == Movie-Genre:superhero or both
- Job:dancer is not to the left of Movie-Genre:superhero
- Sport:surfing is somewhere between Sport:tennis and Food:cranberry
- Food:pepper is not to the left of Job:bartender
- Food:cranberry and Job:dancer have different parity positions

Answer the following question:

Question: Question: What is the Food of the person who is dressmaker??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: pepper


There are 4 people standing in a line numbered 1 through 4 in a left to right order.
Each person has the following attributes:  Job, Beverage, Movie-Genre, Nationality, Sport, Transport.
The attributes have the following possible values:
- Job: entrepreneur, lawyer, social-worker, software-developer
- Beverage: almond-milk, cola, hot-chocolate, water
- Movie-Genre: horror, mystery, scientific, time-travel
- Nationality: indonesian, italian, russian, turkish
- Sport: climbing, rowing, snowboarding, weightlifting
- Transport: bus, quad-bike, skateboard, train

Given the following premises about the line of people:
- Movie-Genre:time-travel is on the right of Sport:snowboarding
- Nationality:russian is on the left or right of Beverage:almond-milk
- Beverage:cola is on the left of Movie-Genre:scientific
- Beverage:cola == Job:lawyer
- Sport:climbing != Transport:train
- Transport:skateboard is on the left of Transport:bus
- Transport:bus is somewhere to the left of Nationality:italian
- Nationality:indonesian is between Sport:weightlifting and Beverage:water
- Beverage:almond-milk is between Movie-Genre:scientific and Movie-Genre:horror
- Transport:train is on the left of Job:social-worker
- Job:software-developer is between Job:entrepreneur and Job:lawyer

Answer the following question:

Question: Question: What is the Movie-Genre of the person who is turkish??
 Please provide your answer in the format: \boxed{X}, where X is the answer.

Answer: mystery


Example 9. Given the dihedral angle $C-A B=D=120^{\circ}$, $\angle C B A=60^{\circ}, \angle D A B=30^{\circ}, A B=\sqrt{37} \mathrm{~cm}$ (Figure 17). Find the distance $d$ between the skew lines $B C, A D$.

Answer: 3


Find the number of functions $f(x)$ from $\{1, 2, 3, 4, 5\}$ to $\{1, 2, 3, 4, 5\}$ that satisfy $f(f(x)) = f(f(f(x)))$ for all $x$ in $\{1, 2, 3, 4, 5\}$ .
Please give the answer directly without any intermediate steps.

Answer: 756


2. At the parade of the royal musketeers, seeing that they could not be arranged in rows of 11 musketeers, D'Artagnan decided to arrange the musketeers in rows of 10 musketeers, but it turned out that there was one empty place in the last row. Then he tried to arrange them in rows of 9, 8, 7, 6, 5, 4, 3, 2 musketeers, but each time there was one empty place in the last row. Finally, the musketeers marched in a single file, which caused a burst of laughter among the spectators. Determine how many musketeers participated in the parade, given that there were no more than 7000.

Answer: 5039


6. As shown in the figure, given that the area of the equilateral $\triangle A B C$ is $S, D$ is the midpoint of $A B, D E \perp B C, E F \perp A C, F G \perp$ $A B$. Then the area of quadrilateral $D E F G$ is ${ }^{\circ}$ . $\qquad$

Answer: \dfrac{51}{128} S


# Problem 2. (2 points)

In a positive non-constant geometric progression, the arithmetic mean of the third, fourth, and eighth terms is equal to some term of this progression. What is the minimum possible number of this term?

Answer: 4


5. Daisies grew along the path. Between every two daisies, a cornflower grew, and then between each cornflower and daisy - a dandelion. It turned out that now 101 flowers grow along the path. How many daisies grow along the path?

Answer: 26


## Task 2 - 220812

For a 22-digit number $z$, the following properties are required:

$z$ has the unit digit 7; if this last digit is removed and placed in front of the remaining 21 digits, the result is the same as the multiplication $7 \cdot z$.

Prove that there is exactly one such number $z$! Determine this number!


10. The edge length of the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$ is 3, and points $P, Q, R$ are on the edges $A A_{1}, B B_{1}, C_{1} D_{1}$ respectively, with $A_{1} P=1, B_{1} Q=2, C_{1} R=1$. Let the dihedral angle (acute) between plane $P Q R$ and plane $A B C D$ be $\alpha$, find $\alpha$.

Answer: \arctan \frac{\sqrt{34}}{9}


Given \( n \) points on a plane, where no three points are collinear, and some of these points are connected by line segments, let \( N_{k} \) denote the number of complete graphs of \( k \) points. Prove that:

$$
\frac{N_{k+1}}{N_{k}} \geqslant \frac{1}{k^{2}-1}\left(\frac{k^{2} N_{k}}{N_{k+1}}-n\right),
$$

for \( k \in \{2,3, \cdots, n-1\} \) and \( N_{k} \neq 0 \).

Answer: \frac{N_{k+1}}{N_{k}} \geqslant \frac{1}{k^{2}-1}\left(\frac{k^{2} N_{k}}{N_{k+1}}-n\right)


In a circle,  let $AB$ and $BC$ be chords , with  $AB =\sqrt3,  BC =3\sqrt3, \angle ABC =60^o$. Find the length of the circle chord that divides angle $ \angle ABC$ in half.

Answer: 4


Task 2. Mom baked a cake for Anya's birthday, which weighs an integer number of grams. Before decorating it, Mom weighed the cake on digital scales that round the weight to the nearest ten grams (if the weight ends in 5, the scales round it down). The result was 1440 g. When Mom decorated the cake with identical candles, the number of which was equal to Anya's age, the scales showed 1610 g. It is known that the weight of each candle is an integer number of grams, and if you put one candle on the scales, they will show 40 g. How old can Anya be? List all possible answers and explain why there are no others. (20 points)

Answer: 4


4. Find the number of finite increasing sequences of natural numbers $a_{1}, a_{2}, \ldots, a_{k}$, of all possible lengths $k$, for which $a_{1}=1, a_{i} \mid a_{i+1}$ for $i=1,2, \ldots, k-1$, and $a_{k}=969969$.

Answer: 4683


6. Let the complex number $z$ satisfy $|z|=1$, such that the equation $z x^{2}+2 \bar{z} x+2=0$ has real roots, then the sum of such complex numbers $z$ is $\qquad$ .

Answer: -\dfrac{3}{2}


Circles \( S_1 \) and \( S_2 \) intersect at points \( A_1 \) and \( A_4 \), circles \( S_2 \) and \( S_3 \) intersect at points \( A_2 \) and \( A_5 \), circles \( S_3 \) and \( S_1 \) intersect at points \( A_3 \) and \( A_6 \). A broken line \( M_1 M_2 M_3 M_4 M_5 M_6 M_7 \) has the property that each segment \( M_k M_{k+1} \) contains the point \( A_k \). Additionally, \( M_k \) and \( M_{k+1} \) lie on the circumferences of the two circles intersecting at point \( A_k \), and point \( M_{k+1} \) is distinct from point \( A_{k+1} \). Prove that points \( M_1 \) and \( M_7 \) coincide.

Answer: M_1 \text{ and } M_7 \text{ coincide}


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`
 - People have unique favorite music genres: `classical`, `rock`, `pop`, `jazz`
 - Each person has a unique level of education: `master`, `associate`, `bachelor`, `high school`

## Clues:
1. Alice is directly left of the person with a high school diploma.
2. The person with a master's degree and the person with a high school diploma are next to each other.
3. Eric is not in the fourth house.
4. The person who loves pop music is somewhere to the left of the person with a bachelor's degree.
5. The person who loves rock music is in the second house.
6. Peter is the person with a high school diploma.
7. Alice is somewhere to the right of the person who loves jazz music.
 What is the value of attribute MusicGenre for the person whose attribute Education is high school? Please reason step by step, and put your final answer within \boxed{}

Answer: pop


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Peter`, `Eric`
 - Each person prefers a unique type of vacation: `beach`, `mountain`, `city`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`
 - Everyone has something unique for lunch: `grilled cheese`, `spaghetti`, `pizza`
 - The people keep unique animals: `bird`, `cat`, `horse`

## Clues:
1. The bird keeper is not in the second house.
2. The person who loves beach vacations is somewhere to the left of Arnold.
3. The bird keeper and the person who keeps horses are next to each other.
4. The bird keeper is not in the third house.
5. The person who is a pizza lover is not in the second house.
6. The person who prefers city breaks is the bird keeper.
7. The person who smokes Blue Master is not in the second house.
8. The person who loves the spaghetti eater is in the third house.
9. Eric is the person who smokes Blue Master.
10. The person who loves eating grilled cheese is directly left of the Prince smoker.
 What is the value of attribute Food for the person whose attribute Cigar is pall mall? Please reason step by step, and put your final answer within \boxed{}

Answer: grilled cheese


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`, `Eric`, `Peter`
 - Everyone has something unique for lunch: `stew`, `spaghetti`, `grilled cheese`, `pizza`, `stir fry`
 - Each person has a favorite color: `green`, `blue`, `yellow`, `red`, `white`
 - The people are of nationalities: `swede`, `brit`, `dane`, `german`, `norwegian`
 - People have unique favorite book genres: `fantasy`, `biography`, `romance`, `mystery`, `science fiction`
 - Each mother is accompanied by their child: `Timothy`, `Samantha`, `Meredith`, `Fred`, `Bella`

## Clues:
1. The Swedish person is the person's child is named Bella.
2. There is one house between the person who loves science fiction books and the person who loves the stew.
3. The person who is a pizza lover is the person's child is named Fred.
4. The person who loves white is not in the fourth house.
5. The person who loves yellow is Peter.
6. The person who loves eating grilled cheese is directly left of the person's child is named Meredith.
7. The German is the person who loves the spaghetti eater.
8. The person who loves romance books is the person who loves the stew.
9. The person's child is named Samantha is directly left of the German.
10. Alice is the Swedish person.
11. Arnold is the person whose favorite color is green.
12. Arnold is in the third house.
13. The person's child is named Meredith is the person who loves biography books.
14. The Norwegian is the person whose favorite color is red.
15. The person who loves romance books is not in the third house.
16. The person who loves the spaghetti eater is Eric.
17. The Dane is somewhere to the left of the person who loves yellow.
18. The person who loves mystery books is directly left of the person whose favorite color is red.
19. The person's child is named Fred is not in the third house.
 What is the value of attribute House for the person whose attribute Children is Bella? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


There are 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`, `Peter`, `Carol`, `Bob`, `Alice`
 - Everyone has a favorite smoothie: `blueberry`, `watermelon`, `cherry`, `lime`, `dragonfruit`, `desert`
 - The people keep unique animals: `bird`, `cat`, `fish`, `horse`, `dog`, `rabbit`

## Clues:
1. The Desert smoothie lover is directly left of Arnold.
2. Carol is the rabbit owner.
3. The Watermelon smoothie lover is the cat lover.
4. The dog owner is somewhere to the right of Peter.
5. The person who keeps horses is directly left of Carol.
6. Eric is not in the fifth house.
7. The person who drinks Lime smoothies is in the sixth house.
8. Carol is in the sixth house.
9. The bird keeper and the person who keeps horses are next to each other.
10. Alice is in the second house.
11. Arnold is in the third house.
12. The Dragonfruit smoothie lover is the dog owner.
13. The person who drinks Blueberry smoothies is not in the fifth house.
 What is the value of attribute Animal for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: fish


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 own unique car models: `honda civic`, `tesla model 3`, `ford f150`, `toyota camry`
 - Each person has a unique type of pet: `bird`, `cat`, `fish`, `dog`
 - People use unique phone models: `oneplus 9`, `iphone 13`, `google pixel 6`, `samsung galaxy s21`

## Clues:
1. The person who uses an iPhone 13 is the person who owns a dog.
2. Alice is not in the second house.
3. The person who uses an iPhone 13 is the person who owns a Toyota Camry.
4. The person who uses a Google Pixel 6 is not in the fourth house.
5. The person who owns a Ford F-150 is not in the second house.
6. The person with an aquarium of fish is directly left of the person who keeps a pet bird.
7. Peter is the person who uses a Google Pixel 6.
8. The person who owns a Tesla Model 3 is directly left of the person who uses an iPhone 13.
9. Eric is not in the second house.
10. Eric is not in the first house.
11. The person who uses a Google Pixel 6 and the person who owns a Ford F-150 are next to each other.
12. The person who uses a OnePlus 9 is somewhere to the left of the person who owns a Ford F-150.
 What is the value of attribute CarModel for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: honda civic


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

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

Answer: 5


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

## Clues:
1. The person who loves the vase of tulips is somewhere to the left of Eric.
2. Bob and Eric are next to each other.
3. The person who has black hair and the person who has blonde hair are next to each other.
4. Arnold is the person who loves the rose bouquet.
5. Arnold is the person who has blonde hair.
6. The person who has brown hair is not in the first house.
7. Arnold is somewhere to the right of the person who loves the boquet of lilies.
8. The person who has red hair is Eric.
9. There is one house between the person who loves the boquet of lilies and the person who has brown hair.
10. Bob is in the third house.
11. The person who has black hair is not in the third house.
12. Alice is the person who loves a carnations arrangement.
 What is the value of attribute Flower for the person whose attribute HairColor is blonde? Please reason step by step, and put your final answer within \boxed{}

Answer: roses


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Carol`, `Bob`, `Alice`, `Eric`, `Arnold`, `Peter`
 - Each person has a unique type of pet: `hamster`, `cat`, `fish`, `rabbit`, `dog`, `bird`
 - Each person has a favorite color: `blue`, `purple`, `yellow`, `white`, `red`, `green`

## Clues:
1. The person who has a cat is not in the third house.
2. Arnold is not in the first house.
3. The person who owns a dog is the person whose favorite color is green.
4. The person who loves yellow is somewhere to the left of Bob.
5. The person who loves blue is the person who has a cat.
6. There are two houses between the person with an aquarium of fish and Eric.
7. The person who owns a dog is Carol.
8. The person who loves yellow is the person with a pet hamster.
9. The person who loves white and the person who keeps a pet bird are next to each other.
10. The person who owns a rabbit is somewhere to the left of the person who loves white.
11. The person who owns a dog is directly left of the person who loves blue.
12. The person who loves purple is directly left of Carol.
13. Bob is not in the third house.
14. Alice is the person who loves purple.
 What is the value of attribute Color for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: yellow


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 Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: mystery


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `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 House for the person whose attribute Education is master? Please reason step by step, and put your final answer within \boxed{}

Answer: 5


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Peter`
 - People own unique car models: `honda civic`, `tesla model 3`, `toyota camry`, `ford f150`
 - They all have a unique favorite flower: `roses`, `daffodils`, `lilies`, `carnations`
 - Each person has a unique favorite drink: `milk`, `water`, `tea`, `coffee`
 - People have unique heights: `very short`, `average`, `tall`, `short`
 - Each person has a favorite color: `red`, `white`, `yellow`, `green`

## Clues:
1. The person who owns a Toyota Camry is somewhere to the left of the person who owns a Ford F-150.
2. The coffee drinker is the person who owns a Ford F-150.
3. The person who has an average height is in the third house.
4. The person whose favorite color is green and the person who owns a Tesla Model 3 are next to each other.
5. There are two houses between the person who loves the rose bouquet and the person who owns a Tesla Model 3.
6. The person who is very short is the tea drinker.
7. Alice is the person who loves white.
8. The person who loves the boquet of lilies is the person who owns a Tesla Model 3.
9. Peter is the person whose favorite color is red.
10. The person who owns a Toyota Camry is Eric.
11. The person who is short is somewhere to the left of the person who loves the boquet of lilies.
12. The person who loves a bouquet of daffodils is the person who loves white.
13. The coffee drinker is in the second house.
14. The person who owns a Tesla Model 3 is the person who likes milk.
 What is the value of attribute Color for the person whose attribute Flower is daffodils? Please reason step by step, and put your final answer within \boxed{}

Answer: white


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Peter`, `Carol`, `Bob`, `Eric`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`, `cruise`, `camping`, `cultural`
 - Everyone has a unique favorite cigar: `yellow monster`, `pall mall`, `prince`, `dunhill`, `blue master`, `blends`
 - People have unique favorite sports: `swimming`, `soccer`, `tennis`, `basketball`, `volleyball`, `baseball`

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

Answer: prince


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

## Clues:
1. There is one house between the boba tea drinker and Bob.
2. There are two houses between the person who uses a Google Pixel 6 and the person who enjoys camping trips.
3. The person who goes on cultural tours is Carol.
4. The person who enjoys camping trips is Eric.
5. The person who uses a Google Pixel 6 is not in the fifth house.
6. The person who uses a OnePlus 9 and the person who goes on cultural tours are next to each other.
7. The person who has gray hair and the person who goes on cultural tours are next to each other.
8. The person who uses a Samsung Galaxy S21 is somewhere to the right of the person who has red hair.
9. The person who enjoys mountain retreats is somewhere to the right of the person who uses a Xiaomi Mi 11.
10. The person who uses a OnePlus 9 is Peter.
11. The person who likes going on cruises is the person who has brown hair.
12. The coffee drinker is the person who goes on cultural tours.
13. The person who likes milk is directly left of the person who has black hair.
14. The person who uses a Xiaomi Mi 11 is directly left of the person who uses a Samsung Galaxy S21.
15. The person who prefers city breaks is not in the sixth house.
16. The person who has blonde hair is Arnold.
17. The person who goes on cultural tours is not in the sixth house.
18. The one who only drinks water and the person who goes on cultural tours are next to each other.
19. The tea drinker is somewhere to the left of the person who enjoys mountain retreats.
20. The person who likes milk is the person who uses a Huawei P50.
21. The person who has blonde hair is directly left of the person who has gray hair.
22. Bob is not in the third house.
23. Peter is the person who prefers city breaks.
 What is the value of attribute House for the person whose attribute Vacation is beach? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


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

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

Answer: water


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Peter`, `Bob`, `Alice`, `Carol`
 - People have unique favorite music genres: `jazz`, `country`, `pop`, `classical`, `rock`, `hip hop`
 - Each person lives in a unique style of house: `mediterranean`, `modern`, `colonial`, `ranch`, `victorian`, `craftsman`
 - People have unique favorite sports: `tennis`, `baseball`, `soccer`, `volleyball`, `swimming`, `basketball`
 - People have unique favorite book genres: `science fiction`, `historical fiction`, `mystery`, `biography`, `fantasy`, `romance`

## Clues:
1. The person who loves baseball is Arnold.
2. Alice is somewhere to the left of the person living in a colonial-style house.
3. The person who loves country music is directly left of the person who loves hip-hop music.
4. Peter is the person residing in a Victorian house.
5. The person who loves fantasy books is Peter.
6. The person who loves baseball is the person who loves romance books.
7. The person who loves hip-hop music is somewhere to the left of the person who loves biography books.
8. The person in a ranch-style home is somewhere to the left of the person who loves romance books.
9. Bob is the person who loves swimming.
10. The person who loves romance books is somewhere to the left of the person who loves mystery books.
11. The person who loves basketball is in the fourth house.
12. Bob is the person who loves jazz music.
13. The person in a Craftsman-style house is the person who loves mystery books.
14. Peter is somewhere to the left of the person who loves basketball.
15. The person who loves volleyball is somewhere to the right of the person in a Mediterranean-style villa.
16. The person in a Mediterranean-style villa is Alice.
17. The person who loves historical fiction books is directly left of the person living in a colonial-style house.
18. Carol is directly left of the person who loves pop music.
19. There is one house between the person who loves pop music and the person who loves classical music.
20. There are two houses between the person who loves tennis and Alice.
 What is the value of attribute House for the person whose attribute MusicGenre is classical? Please reason step by step, and put your final answer within \boxed{}

Answer: 5