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, Sport, Transport.
The attributes have the following possible values:
- Beverage: 7up, hot-chocolate, mirinda, water
- Hobby: fishing, hiking, reading, writing
- Music-Genre: classical, gospel, indie, salsa
- Sport: basketball, climbing, handball, skiing
- Transport: airplane, bike, bus, helicopter

Given the following premises about the line of people:
- Beverage:7up and Transport:helicopter have different parity positions
- Sport:handball is somewhere between Music-Genre:indie and Sport:basketball
- Hobby:reading is somewhere to the left of Hobby:fishing
- Sport:climbing is on the left or right of Hobby:fishing
- Music-Genre:indie is not to the left of Transport:bike
- Beverage:water and Hobby:reading have the same parity positions
- Hobby:writing is not to the left of Music-Genre:salsa
- Sport:skiing != Music-Genre:salsa
- Music-Genre:indie and Beverage:mirinda have the same parity positions
- Hobby:writing == Sport:skiing or Hobby:writing == Transport:bike or both
- Beverage:hot-chocolate == Music-Genre:classical or Sport:basketball == Beverage:hot-chocolate or both
- Hobby:fishing is somewhere between Beverage:7up and Music-Genre:gospel
- Sport:basketball is not to the left of Hobby:hiking
- Transport:bus is not to the left of Beverage:mirinda
- Transport:helicopter is somewhere to the right of Music-Genre:classical

Answer the following question:

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

Answer: fishing


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, Beverage, Sport, Transport.
The attributes have the following possible values:
- Job: accountant, designer, dressmaker, engineer, fisherman, social-worker
- Hobby: gardening, magic-tricks, sudoku, video-games, woodworking, writing
- Beverage: almond-milk, coffee, fanta, juice, mirinda, water
- Sport: baseball, basketball, climbing, cycling, skateboarding, weightlifting
- Transport: airplane, bike, bus, scooter, skateboard, subway

Given the following premises about the line of people:
- Hobby:magic-tricks and Transport:airplane have the same parity positions
- Beverage:fanta and Hobby:magic-tricks have different parity positions
- Beverage:mirinda is not to the left of Sport:weightlifting
- Job:designer != Beverage:juice
- Sport:climbing != Hobby:gardening or Sport:climbing != Beverage:mirinda or both
- Transport:bus != Beverage:coffee or Beverage:coffee != Sport:cycling or both
- Beverage:mirinda is somewhere to the right of Transport:skateboard
- Job:fisherman is in an odd position
- Sport:climbing and Beverage:mirinda have different parity positions
- Beverage:coffee != Job:accountant or Beverage:coffee != Hobby:gardening or both
- Sport:skateboarding == Transport:airplane or Hobby:woodworking == Sport:skateboarding, but not both
- Transport:bus and Job:designer have different parity positions
- Job:dressmaker is somewhere between Sport:skateboarding and Beverage:coffee
- Sport:basketball is not to the left of Transport:bus
- Hobby:gardening is not to the right of Beverage:coffee
- Transport:skateboard is somewhere between Beverage:mirinda and Hobby:video-games
- Job:engineer is not to the left of Transport:scooter
- Transport:subway is not to the left of Sport:baseball
- Sport:climbing is somewhere to the left of Hobby:sudoku
- Job:fisherman != Beverage:fanta
- Hobby:gardening != Job:engineer
- Sport:basketball is not to the left of Beverage:almond-milk
- Transport:airplane and Beverage:juice have the same parity positions
- Job:dressmaker is somewhere between Sport:weightlifting and Sport:basketball
- Sport:cycling and Hobby:writing have different parity positions
- Transport:scooter and Beverage:juice have different parity positions
- Transport:bus is not to the right of Sport:weightlifting
- Beverage:fanta is somewhere to the left of Hobby:magic-tricks
- Hobby:writing != Job:designer
- Sport:baseball != Transport:subway
- Transport:subway == Beverage:juice or Beverage:juice == Job:fisherman, but not both
- Job:dressmaker is not to the right of Job:fisherman
- Job:fisherman == Sport:climbing or Sport:climbing == Beverage:mirinda, but not both
- Hobby:video-games is not to the right of Beverage:fanta
- Sport:basketball is somewhere to the left of Hobby:magic-tricks
- Sport:weightlifting != Transport:subway or Transport:subway != Beverage:almond-milk or both
- Job:social-worker is not to the left of Sport:weightlifting
- Job:accountant is not to the left of Sport:cycling
- Job:accountant is somewhere to the left of Transport:subway
- Beverage:fanta and Hobby:gardening have different parity positions
- Job:designer == Transport:bike or Job:designer == Sport:weightlifting, but not both
- Beverage:fanta is not to the left of Job:dressmaker
- Beverage:water is not to the left of Beverage:almond-milk
- Transport:bike != Beverage:coffee or Transport:bike != Job:designer or both
- Beverage:juice != Sport:cycling
- Transport:subway is not to the left of Job:fisherman
- Sport:basketball is somewhere between Transport:scooter and Hobby:gardening
- Sport:climbing != Transport:scooter or Sport:climbing != Hobby:video-games or both

Answer the following question:

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

Answer: skateboarding


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: australian, indian, indonesian, japanese
- Food: broccoli, garlic, peas, spinach
- Hobby: cooking, dancing, gardening, hiking
- Beverage: cola, fanta, mirinda, soy-milk
- Pet: cat, ferret, guinea-pig, turtle
- Transport: quad-bike, subway, tram, van

Given the following premises about the line of people:
- Pet:guinea-pig is not to the right of Food:broccoli
- Pet:turtle and Transport:van have the same parity positions
- Hobby:hiking is not to the right of Hobby:gardening
- Transport:tram != Food:spinach
- Food:garlic == Beverage:soy-milk or Beverage:soy-milk == Pet:turtle, but not both
- Nationality:indian is somewhere to the left of Beverage:fanta
- Pet:guinea-pig is not to the right of Food:peas
- Beverage:mirinda is not to the left of Hobby:dancing
- Beverage:soy-milk is somewhere to the right of Nationality:japanese
- Hobby:cooking is somewhere to the left of Hobby:dancing
- Food:peas != Beverage:mirinda or Food:peas != Transport:subway or both
- Hobby:gardening is somewhere to the left of Pet:guinea-pig
- Beverage:soy-milk is not to the left of Transport:tram
- Pet:ferret == Transport:subway or Pet:ferret == Hobby:hiking, but not both
- Nationality:australian is in an odd position
- Pet:cat and Nationality:indian have different parity positions

Answer the following question:

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

Answer: turtle


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, Pet.
The attributes have the following possible values:
- Job: architect, dancer, dressmaker, journalist, police-officer, scientist
- Hobby: baking, card-games, fishing, gardening, photography, traveling
- Movie-Genre: animation, comedy, musical, sports, spy, time-travel
- Music-Genre: blues, indie, jazz, r&b, salsa, soul
- Pet: bird, fish, frog, goldfish, mouse, rat

Given the following premises about the line of people:
- Music-Genre:soul and Job:police-officer have different parity positions
- Music-Genre:salsa is not to the left of Job:architect
- Hobby:photography is somewhere to the left of Pet:bird
- Movie-Genre:sports == Music-Genre:r&b or Movie-Genre:sports == Pet:bird or both
- Job:journalist is not to the right of Pet:frog
- Music-Genre:indie is somewhere between Pet:fish and Movie-Genre:spy
- Movie-Genre:sports != Hobby:card-games
- Pet:rat and Music-Genre:jazz have different parity positions
- Music-Genre:blues is not to the left of Hobby:traveling
- Hobby:baking is not to the right of Job:dressmaker
- Job:scientist != Music-Genre:r&b or Music-Genre:r&b != Movie-Genre:animation or both
- Pet:frog is somewhere to the left of Pet:mouse
- Job:scientist is somewhere to the right of Job:journalist
- Hobby:baking is somewhere to the right of Music-Genre:indie
- Job:scientist is somewhere to the left of Hobby:fishing
- Hobby:gardening is somewhere to the left of Hobby:card-games
- Movie-Genre:time-travel is not to the right of Hobby:baking
- Hobby:traveling != Movie-Genre:animation or Hobby:traveling != Music-Genre:indie or both
- Job:journalist is somewhere between Music-Genre:salsa and Pet:frog
- Pet:rat is somewhere between Music-Genre:indie and Movie-Genre:animation
- Movie-Genre:animation == Job:journalist or Movie-Genre:animation == Hobby:gardening or both
- Pet:fish is somewhere between Music-Genre:jazz and Music-Genre:soul
- Music-Genre:salsa is not to the right of Movie-Genre:animation
- Job:journalist and Movie-Genre:time-travel have the same parity positions
- Hobby:gardening and Job:dressmaker have different parity positions
- Hobby:gardening and Pet:rat have different parity positions
- Movie-Genre:time-travel is somewhere to the right of Music-Genre:salsa
- Pet:goldfish == Hobby:gardening or Music-Genre:salsa == Pet:goldfish, but not both
- Movie-Genre:animation is somewhere to the left of Pet:rat
- Movie-Genre:musical == Job:architect or Movie-Genre:musical == Hobby:card-games or both
- Music-Genre:r&b is somewhere to the left of Music-Genre:jazz

Answer the following question:

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

Answer: traveling


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, Music-Genre, Sport, Transport.
The attributes have the following possible values:
- Job: bartender, chef, coach, doctor, mechanic
- Food: apricot, lime, plum, potato, watermelon
- Beverage: 7up, fanta, lemonade, mirinda, tea
- Music-Genre: d&b, dubstep, folk, indie, salsa
- Sport: basketball, handball, lacrosse, soccer, tennis
- Transport: bike, car, ship, train, tram

Given the following premises about the line of people:
- Music-Genre:salsa and Sport:handball have different parity positions
- Sport:soccer and Beverage:lemonade have different parity positions
- Job:bartender == Transport:ship or Job:bartender == Beverage:lemonade or both
- Sport:basketball and Job:coach have the same parity positions
- Food:potato is somewhere to the left of Beverage:tea
- Transport:train is not to the left of Beverage:7up
- Sport:lacrosse == Music-Genre:indie or Music-Genre:indie == Food:lime or both
- Job:bartender is not to the right of Food:watermelon
- Beverage:tea is on the left or right of Beverage:fanta
- Music-Genre:salsa is somewhere to the left of Food:lime
- Music-Genre:salsa is not to the left of Sport:soccer
- Sport:handball is not to the left of Music-Genre:folk
- Music-Genre:d&b is somewhere between Food:plum and Sport:basketball
- Transport:bike is somewhere to the left of Beverage:mirinda
- Job:chef is in an even position
- Sport:soccer is not to the left of Beverage:fanta
- Transport:ship and Beverage:tea have different parity positions
- Food:plum == Job:coach or Job:coach == Beverage:fanta or both
- Job:chef != Food:plum
- Transport:ship is not to the left of Food:lime
- Sport:lacrosse == Job:mechanic or Job:mechanic == Music-Genre:folk, but not both
- Sport:handball is in an odd position
- Transport:ship is not to the right of Transport:train
- Music-Genre:folk is on the left or right of Job:bartender
- Sport:lacrosse is somewhere to the right of Sport:tennis
- Beverage:mirinda == Transport:ship or Beverage:mirinda == Job:bartender or both
- Transport:tram is somewhere to the left of Food:apricot
- Music-Genre:indie is on the left or right of Sport:lacrosse

Answer the following question:

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

Answer: tennis


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, Music-Genre, Pet, Sport.
The attributes have the following possible values:
- Food: cherry, peas, radish, spinach
- Music-Genre: disco, funk, house, jazz
- Pet: guinea-pig, horse, mouse, rabbit
- Sport: cycling, handball, tennis, volleyball

Given the following premises about the line of people:
- Food:peas is on the left or right of Sport:tennis
- Food:peas is somewhere to the left of Music-Genre:jazz
- Music-Genre:jazz is somewhere to the right of Pet:horse
- Music-Genre:house is on the left or right of Music-Genre:disco
- Food:radish is on the right of Sport:cycling
- Food:cherry is on the left of Food:spinach
- Sport:volleyball is on the far right
- Music-Genre:disco is on the far left or far right
- Music-Genre:house == Pet:mouse
- Pet:guinea-pig is somewhere to the left of Pet:horse
- Food:peas is somewhere to the right of Music-Genre:disco

Answer the following question:

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

Answer: funk


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, Pet, Sport, Transport.
The attributes have the following possible values:
- Job: designer, manager, police-officer, project-manager
- Beverage: 7up, hot-chocolate, iced-tea, milk
- Pet: cat, hamster, rabbit, rat
- Sport: baseball, basketball, biathlon, rowing
- Transport: boat, car, quad-bike, scooter

Given the following premises about the line of people:
- Pet:hamster and Job:police-officer have the same parity positions
- Transport:boat and Sport:baseball have the same parity positions
- Beverage:iced-tea != Transport:scooter or Beverage:iced-tea != Job:designer or both
- Pet:rabbit is somewhere to the right of Beverage:7up
- Transport:boat is somewhere to the left of Transport:scooter
- Sport:baseball is somewhere to the right of Job:manager
- Pet:hamster is somewhere to the left of Sport:rowing
- Beverage:milk is somewhere to the left of Transport:boat
- Sport:rowing is on the left or right of Beverage:hot-chocolate
- Transport:car is somewhere to the right of Sport:baseball
- Pet:cat == Transport:scooter or Pet:cat == Job:project-manager, but not both
- Job:project-manager is somewhere to the left of Pet:hamster
- Beverage:hot-chocolate is somewhere to the right of Sport:biathlon

Answer the following question:

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

Answer: manager


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, Pet, Transport.
The attributes have the following possible values:
- Job: doctor, dressmaker, manager, pilot, scientist, security-guard
- Hobby: board-games, collecting, dancing, filmmaking, singing, video-games
- Movie-Genre: adventure, crime, disaster, family, martial-arts, sports
- Music-Genre: d&b, disco, folk, funk, gospel, punk
- Pet: bird, chinchilla, goldfish, pony, rabbit, rat
- Transport: airplane, boat, ship, snowmobile, taxi, van

Given the following premises about the line of people:
- Hobby:board-games is somewhere to the right of Pet:chinchilla
- Movie-Genre:adventure is on the left of Music-Genre:disco
- Movie-Genre:family is on the far left
- Pet:goldfish is somewhere to the left of Hobby:video-games
- Pet:rabbit is not to the right of Transport:van
- Music-Genre:folk is on the right of Transport:taxi
- Job:pilot is somewhere to the left of Transport:boat
- Music-Genre:disco is on the right of Pet:bird
- Transport:boat is on the left of Job:dressmaker
- Transport:boat is on the right of Movie-Genre:disaster
- Job:security-guard is somewhere to the left of Hobby:collecting
- Hobby:singing is somewhere to the left of Hobby:filmmaking
- Transport:airplane is somewhere to the right of Transport:boat
- Job:scientist is on the left of Movie-Genre:adventure
- Pet:rabbit is somewhere to the right of Pet:rat
- Movie-Genre:crime is on the right of Hobby:video-games
- Hobby:video-games is somewhere to the right of Hobby:dancing
- Music-Genre:gospel is in an odd position
- Music-Genre:gospel != Pet:goldfish
- Movie-Genre:adventure is somewhere to the right of Movie-Genre:martial-arts
- Music-Genre:d&b is on the left or right of Movie-Genre:adventure
- Transport:ship is on the left of Pet:rat
- Hobby:board-games is somewhere to the right of Movie-Genre:crime
- Music-Genre:funk is somewhere to the right of Job:scientist
- Hobby:dancing is on the left or right of Transport:van
- Hobby:collecting is somewhere to the left of Job:doctor
- Job:manager is somewhere to the left of Job:pilot

Answer the following question:

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

Answer: rabbit


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, Hobby, Pet, Sport, Transport.
The attributes have the following possible values:
- Nationality: japanese, mexican, nigerian, russian, turkish
- Movie-Genre: action, crime, documentary, thriller, zombie
- Hobby: baking, dancing, gardening, reading, woodworking
- Pet: chinchilla, ferret, guinea-pig, horse, rat
- Sport: golf, rowing, skateboarding, snowboarding, weightlifting
- Transport: roller, snowmobile, subway, taxi, trike

Given the following premises about the line of people:
- Hobby:dancing is somewhere to the right of Pet:rat
- Transport:subway is on the left of Hobby:reading
- Pet:guinea-pig == Sport:golf
- Sport:weightlifting == Transport:subway or Sport:weightlifting == Nationality:russian, but not both
- Hobby:dancing is somewhere between Hobby:baking and Nationality:mexican
- Nationality:mexican is on the right of Hobby:dancing
- Nationality:mexican == Transport:trike or Hobby:gardening == Nationality:mexican, but not both
- Hobby:reading and Movie-Genre:zombie have the same parity positions
- Hobby:gardening is somewhere to the left of Transport:taxi
- Pet:guinea-pig is somewhere to the left of Pet:horse
- Nationality:mexican is somewhere to the left of Nationality:nigerian
- Pet:ferret is on the right of Hobby:dancing
- Transport:taxi and Sport:weightlifting have different parity positions
- Pet:chinchilla is not to the left of Hobby:reading
- Nationality:japanese is not to the right of Transport:snowmobile
- Transport:subway is on the left of Sport:rowing
- Transport:snowmobile is not to the right of Pet:guinea-pig
- Movie-Genre:documentary is on the left or right of Movie-Genre:thriller
- Movie-Genre:thriller is somewhere between Hobby:dancing and Transport:snowmobile
- Hobby:gardening is in an odd position
- Sport:snowboarding and Hobby:gardening have different parity positions
- Movie-Genre:crime is in the middle

Answer the following question:

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

Answer: guinea-pig


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, Food, Hobby, Music-Genre, Sport, Transport.
The attributes have the following possible values:
- Beverage: cola, fanta, lemonade, sprite
- Food: broccoli, eggplant, grapefruit, pumpkin
- Hobby: camping, chess, dancing, photography
- Music-Genre: folk, rock, soul, techno
- Sport: biathlon, skiing, soccer, water-polo
- Transport: airplane, jet-ski, quad-bike, trike

Given the following premises about the line of people:
- Hobby:dancing is on the left or right of Transport:airplane
- Music-Genre:soul is on the right of Hobby:chess
- Hobby:dancing == Food:eggplant
- Music-Genre:folk is on the left or right of Music-Genre:rock
- Transport:trike is somewhere to the left of Beverage:fanta
- Hobby:photography is somewhere to the left of Transport:quad-bike
- Hobby:camping == Beverage:sprite
- Transport:airplane is on the far left
- Sport:biathlon is on the left of Beverage:lemonade
- Sport:skiing is not to the right of Food:grapefruit
- Food:grapefruit is on the left of Food:broccoli
- Hobby:chess is on the left or right of Transport:jet-ski
- Sport:biathlon is on the left or right of Sport:soccer
- Music-Genre:folk is on the left of Sport:soccer

Answer the following question:

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

Answer: rock


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, Nationality, Sport, Transport.
The attributes have the following possible values:
- Job: accountant, dancer, electrician, fisherman, photographer, scientist
- Hobby: cooking, drawing, hiking, magic-tricks, sudoku, traveling
- Nationality: brazilian, chinese, dutch, malaysian, spanish, thai
- Sport: cycling, rowing, snowboarding, soccer, swimming, weightlifting
- Transport: airplane, bike, car, motorbike, scooter, skateboard

Given the following premises about the line of people:
- Nationality:chinese is on the left or right of Transport:car
- Nationality:spanish == Sport:rowing
- Sport:cycling is on the right of Nationality:chinese
- Job:scientist is on the left or right of Sport:weightlifting
- Hobby:hiking != Sport:weightlifting
- Transport:bike == Sport:weightlifting
- Transport:bike is on the right of Nationality:dutch
- Sport:rowing is on the left or right of Job:photographer
- Transport:skateboard is somewhere to the right of Hobby:hiking
- Job:scientist is somewhere to the right of Transport:car
- Hobby:cooking == Sport:soccer
- Nationality:chinese is between Nationality:dutch and Nationality:malaysian
- Sport:swimming is on the right of Job:dancer
- Transport:airplane is somewhere to the right of Sport:rowing
- Nationality:brazilian == Hobby:traveling
- Transport:scooter != Hobby:cooking
- Transport:bike is on the left or right of Sport:swimming
- Job:accountant is on the left of Transport:skateboard
- Sport:snowboarding is on the right of Nationality:thai
- Hobby:magic-tricks is on the right of Hobby:sudoku
- Hobby:hiking == Job:electrician
- Transport:car != Job:fisherman
- Transport:motorbike is on the far left or far right

Answer the following question:

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

Answer: hiking


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, Nationality, Transport.
The attributes have the following possible values:
- Job: analyst, dressmaker, musician, nurse
- Food: avocado, cherry, cranberry, onion
- Nationality: australian, egyptian, russian, turkish
- Transport: car, ship, skateboard, van

Given the following premises about the line of people:
- Food:avocado is on the left or right of Nationality:australian
- Job:dressmaker != Transport:car
- Nationality:egyptian and Job:dressmaker have different parity positions
- Food:cranberry != Job:analyst
- Nationality:turkish == Transport:skateboard
- Nationality:australian is somewhere to the right of Job:musician
- Transport:ship is somewhere to the right of Transport:skateboard
- Transport:van is on the left or right of Food:onion
- Nationality:russian is on the left of Job:analyst
- Food:cranberry is not to the left of Transport:ship
- Transport:car is somewhere between Transport:van and Transport:skateboard
- Food:avocado is somewhere to the left of Food:cherry

Answer the following question:

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

Answer: onion


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, Pet, Sport.
The attributes have the following possible values:
- Beverage: fanta, juice, mirinda, tea, water
- Food: grapefruit, grapes, lime, papaya, peas
- Movie-Genre: adventure, documentary, superhero, thriller, time-travel
- Pet: fish, frog, goldfish, guinea-pig, hedgehog
- Sport: cycling, parkour, sailing, skiing, water-polo

Given the following premises about the line of people:
- Sport:parkour == Beverage:tea or Sport:parkour == Food:lime or both
- Beverage:water and Pet:fish have different parity positions
- Pet:frog is somewhere between Pet:guinea-pig and Beverage:juice
- Beverage:water is not to the left of Food:papaya
- Beverage:juice is somewhere to the left of Movie-Genre:superhero
- Movie-Genre:documentary and Sport:skiing have different parity positions
- Food:lime is somewhere to the right of Sport:parkour
- Pet:fish is somewhere to the right of Movie-Genre:superhero
- Food:grapefruit is not to the right of Movie-Genre:documentary
- Food:lime == Pet:guinea-pig or Food:lime == Sport:cycling, but not both
- Pet:guinea-pig is somewhere between Pet:hedgehog and Sport:parkour
- Beverage:fanta is somewhere to the right of Beverage:mirinda
- Sport:cycling is somewhere to the left of Movie-Genre:documentary
- Food:grapes == Beverage:water or Beverage:water == Pet:hedgehog or both
- Beverage:tea and Food:grapefruit have the same parity positions
- Pet:hedgehog == Beverage:juice or Movie-Genre:time-travel == Pet:hedgehog or both
- Pet:hedgehog and Beverage:fanta have the same parity positions
- Movie-Genre:documentary != Food:lime
- Movie-Genre:adventure is not to the left of Sport:water-polo
- Sport:parkour != Food:grapefruit or Movie-Genre:documentary != Sport:parkour or both
- Food:papaya != Movie-Genre:thriller

Answer the following question:

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

Answer: time-travel


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, Nationality, Pet, Sport, Transport.
The attributes have the following possible values:
- Job: librarian, paramedic, police-officer, videographer
- Food: eggplant, mango, orange, pepper
- Nationality: german, japanese, malaysian, polish
- Pet: bird, lizard, mouse, pony
- Sport: baseball, rowing, soccer, volleyball
- Transport: airplane, bike, bus, scooter

Given the following premises about the line of people:
- Food:orange is not to the left of Transport:airplane
- Job:paramedic == Pet:pony or Food:mango == Job:paramedic or both
- Pet:pony is somewhere to the right of Transport:scooter
- Sport:soccer and Pet:lizard have the same parity positions
- Food:eggplant is in an even position
- Pet:lizard is on the left or right of Pet:bird
- Job:paramedic is on the left or right of Job:librarian
- Food:pepper is not to the left of Job:police-officer
- Food:eggplant is not to the right of Sport:soccer
- Nationality:malaysian != Job:librarian
- Sport:volleyball is not to the left of Sport:baseball
- Nationality:malaysian is somewhere to the left of Food:eggplant
- Transport:bus != Pet:pony or Transport:bus != Nationality:malaysian or both
- Nationality:japanese and Food:eggplant have the same parity positions
- Pet:bird != Food:mango
- Transport:bike is not to the left of Job:videographer
- Sport:baseball is in an even position
- Sport:rowing is not to the left of Nationality:german
- Food:mango is not to the right of Food:pepper
- Sport:soccer != Pet:pony
- Food:orange is on the left or right of Transport:bike

Answer the following question:

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

Answer: pony


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, Movie-Genre, Food, Transport.
The attributes have the following possible values:
- Nationality: colombian, indian, malaysian, mexican
- Movie-Genre: disaster, epic, musical, scientific
- Food: avocado, cauliflower, lemon, strawberry
- Transport: airplane, helicopter, scooter, van

Given the following premises about the line of people:
- Food:lemon is on the right of Movie-Genre:disaster
- Transport:airplane != Nationality:colombian
- Transport:van != Nationality:malaysian
- Transport:van is somewhere to the right of Nationality:mexican
- Movie-Genre:musical is on the left or right of Movie-Genre:disaster
- Movie-Genre:epic is somewhere to the left of Food:avocado
- Food:lemon is on the right of Nationality:malaysian
- Movie-Genre:scientific is on the left or right of Nationality:malaysian
- Transport:airplane is on the left of Nationality:mexican
- Food:strawberry == Nationality:mexican
- Movie-Genre:scientific is somewhere to the left of Transport:scooter

Answer the following question:

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

Answer: scientific


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`
 - Everyone has a unique favorite cigar: `prince`, `pall mall`, `blue master`, `dunhill`
 - Each person has a unique favorite drink: `milk`, `coffee`, `water`, `tea`
 - People have unique hair colors: `blonde`, `black`, `red`, `brown`

## Clues:
1. The person who has brown hair is not in the fourth house.
2. The person who likes milk is the person who has brown hair.
3. The person partial to Pall Mall is somewhere to the right of the person who has black hair.
4. Peter is somewhere to the left of the Dunhill smoker.
5. The person who smokes Blue Master is directly left of Alice.
6. The tea drinker is Peter.
7. Eric is the person who has brown hair.
8. Eric is not in the third house.
9. Alice is the Dunhill smoker.
10. The person who has blonde hair is the Prince smoker.
11. The one who only drinks water is not in the fourth house.
 What is the value of attribute Drink for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: tea


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

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

Answer: google pixel 6


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Peter`, `Alice`, `Eric`, `Arnold`
 - People use unique phone models: `iphone 13`, `samsung galaxy s21`, `google pixel 6`, `oneplus 9`, `huawei p50`
 - Each person has a unique hobby: `knitting`, `photography`, `painting`, `cooking`, `gardening`
 - Everyone has a unique favorite cigar: `pall mall`, `blends`, `blue master`, `dunhill`, `prince`
 - People have unique favorite sports: `swimming`, `baseball`, `tennis`, `basketball`, `soccer`
 - Everyone has a favorite smoothie: `cherry`, `desert`, `lime`, `watermelon`, `dragonfruit`

## Clues:
1. Peter is in the first house.
2. The person who loves soccer is the person who paints as a hobby.
3. The person partial to Pall Mall is the person who enjoys knitting.
4. The person who uses a Google Pixel 6 is not in the fifth house.
5. The person who enjoys knitting is somewhere to the left of Alice.
6. Peter is directly left of the person who smokes Blue Master.
7. The Prince smoker is the person who uses a OnePlus 9.
8. The person who loves basketball is directly left of the photography enthusiast.
9. The Dunhill smoker is somewhere to the left of the photography enthusiast.
10. There is one house between the person who drinks Lime smoothies and the person who loves basketball.
11. The person who enjoys gardening is somewhere to the right of the person who enjoys knitting.
12. The Dragonfruit smoothie lover is in the third house.
13. The person who loves baseball is the person partial to Pall Mall.
14. Eric is the person who loves tennis.
15. The person who uses a OnePlus 9 is Peter.
16. The Dunhill smoker is the person who uses a Huawei P50.
17. The Desert smoothie lover is the person who loves soccer.
18. The person who uses a Samsung Galaxy S21 is directly left of Arnold.
19. The person who loves tennis is somewhere to the right of the Watermelon smoothie lover.
 What is the value of attribute Name for the person whose attribute PhoneModel is oneplus 9? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Alice`
 - People have unique favorite music genres: `pop`, `classical`, `jazz`, `rock`
 - Each person has a unique hobby: `cooking`, `gardening`, `painting`, `photography`
 - Each person has a unique level of education: `master`, `associate`, `high school`, `bachelor`
 - Each person has a unique type of pet: `fish`, `bird`, `dog`, `cat`

## Clues:
1. The person who loves classical music is not in the fourth house.
2. Arnold is the person with a master's degree.
3. Alice is the person who owns a dog.
4. The person who enjoys gardening is not in the third house.
5. The person with a bachelor's degree is Alice.
6. Alice is the photography enthusiast.
7. Arnold is directly left of the person who loves pop music.
8. The person with an associate's degree is directly left of the photography enthusiast.
9. The person who loves rock music is the person who loves cooking.
10. The person with an associate's degree is Eric.
11. The person who has a cat is the person who loves jazz music.
12. Arnold is somewhere to the right of the person with an aquarium of fish.
 What is the value of attribute Hobby for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: photography


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Bob`, `Alice`, `Carol`
 - The people keep unique animals: `rabbit`, `dog`, `fish`, `bird`, `cat`, `horse`
 - Each person has a unique hobby: `cooking`, `knitting`, `painting`, `woodworking`, `photography`, `gardening`
 - People have unique favorite sports: `basketball`, `soccer`, `swimming`, `tennis`, `baseball`, `volleyball`
 - Each person prefers a unique type of vacation: `cruise`, `cultural`, `city`, `camping`, `mountain`, `beach`
 - Each person has a unique favorite drink: `water`, `root beer`, `boba tea`, `tea`, `milk`, `coffee`

## Clues:
1. The person who enjoys camping trips is the person who loves cooking.
2. The person who loves baseball is the photography enthusiast.
3. The person who loves volleyball is somewhere to the left of the person who prefers city breaks.
4. Carol is the person who loves tennis.
5. The dog owner is the person who loves swimming.
6. The photography enthusiast is the tea drinker.
7. The person who loves baseball is directly left of the person who goes on cultural tours.
8. Peter is the person who enjoys camping trips.
9. The person who enjoys knitting is the person who keeps horses.
10. The coffee drinker is directly left of the person who loves soccer.
11. The person who enjoys mountain retreats is the person who loves soccer.
12. The boba tea drinker is not in the fourth house.
13. The cat lover is somewhere to the left of the dog owner.
14. The person who loves beach vacations is Bob.
15. The coffee drinker is somewhere to the right of Alice.
16. The tea drinker is the fish enthusiast.
17. The person who likes milk is Carol.
18. There is one house between the rabbit owner and the woodworking hobbyist.
19. The person who loves cooking is not in the third house.
20. The person who loves tennis is the rabbit owner.
21. The dog owner is directly left of the person who likes going on cruises.
22. The woodworking hobbyist is the dog owner.
23. There are two houses between the person who paints as a hobby and the person who keeps horses.
24. Arnold is the root beer lover.
 What is the value of attribute Hobby for the person whose attribute Drink is tea? Please reason step by step, and put your final answer within \boxed{}

Answer: photography


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Arnold`, `Carol`, `Alice`, `Peter`, `Eric`
 - The mothers' names in different houses are unique: `Sarah`, `Janelle`, `Aniya`, `Kailyn`, `Holly`, `Penny`
 - Each mother is accompanied by their child: `Fred`, `Samantha`, `Bella`, `Meredith`, `Alice`, `Timothy`
 - Each person prefers a unique type of vacation: `city`, `mountain`, `camping`, `beach`, `cruise`, `cultural`
 - People have unique favorite book genres: `romance`, `mystery`, `historical fiction`, `science fiction`, `biography`, `fantasy`

## Clues:
1. The person who loves beach vacations is not in the second house.
2. The person who loves fantasy books is somewhere to the left of Peter.
3. The person whose mother's name is Sarah is the person who prefers city breaks.
4. The person who enjoys camping trips is somewhere to the right of Peter.
5. The person who likes going on cruises is the person's child is named Meredith.
6. There is one house between the person who is the mother of Timothy and Eric.
7. The person whose mother's name is Janelle is not in the second house.
8. The person's child is named Fred is somewhere to the left of Eric.
9. The person who goes on cultural tours is in the fourth house.
10. The person whose mother's name is Janelle is not in the first house.
11. The person whose mother's name is Holly is somewhere to the right of the person who loves historical fiction books.
12. The person's child is named Bella is somewhere to the left of Alice.
13. Arnold is somewhere to the right of the person who loves fantasy books.
14. The person who loves mystery books is in the fourth house.
15. The person's child is named Alice is the person who enjoys camping trips.
16. The person whose mother's name is Kailyn is the person who likes going on cruises.
17. There are two houses between the person who loves fantasy books and The person whose mother's name is Aniya.
18. The person who loves fantasy books is Carol.
19. The person who likes going on cruises is the person who loves biography books.
20. The person who loves fantasy books is in the third house.
21. The person whose mother's name is Aniya is the person who loves romance books.
22. The person whose mother's name is Janelle is not in the fourth house.
23. The person's child is named Fred is not in the fourth house.
24. The person who loves biography books is not in the second house.
25. There are two houses between The person whose mother's name is Holly and Eric.
 What is the value of attribute Vacation for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: mountain


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Arnold`, `Alice`
 - Each person has an occupation: `doctor`, `teacher`, `artist`, `engineer`
 - Each person has a unique type of pet: `fish`, `dog`, `bird`, `cat`
 - People have unique heights: `short`, `average`, `tall`, `very short`
 - People have unique favorite book genres: `fantasy`, `science fiction`, `romance`, `mystery`

## Clues:
1. The person who has a cat is directly left of the person who is a teacher.
2. Alice and the person who has an average height are next to each other.
3. The person who is tall is somewhere to the right of Arnold.
4. The person who keeps a pet bird is not in the third house.
5. The person who loves science fiction books is the person who is tall.
6. The person who is a doctor is not in the third house.
7. The person who loves fantasy books is the person with an aquarium of fish.
8. Eric is the person who is very short.
9. The person who is a teacher is directly left of Alice.
10. The person with an aquarium of fish is somewhere to the right of the person who is an engineer.
11. The person who loves fantasy books is Eric.
12. The person who loves romance books and the person with an aquarium of fish are next to each other.
 What is the value of attribute House for the person whose attribute Pet is dog? Please reason step by step, and put your final answer within \boxed{}

Answer: 3


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Peter`, `Alice`, `Arnold`, `Bob`, `Carol`
 - Each person has a unique hobby: `cooking`, `knitting`, `painting`, `gardening`, `woodworking`, `photography`
 - Everyone has a favorite smoothie: `lime`, `cherry`, `desert`, `blueberry`, `watermelon`, `dragonfruit`
 - The people are of nationalities: `chinese`, `dane`, `german`, `norwegian`, `swede`, `brit`
 - People have unique favorite music genres: `hip hop`, `country`, `rock`, `jazz`, `classical`, `pop`

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

Answer: 1


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Alice`, `Peter`
 - People have unique heights: `tall`, `short`, `average`, `very short`

## Clues:
1. Alice is somewhere to the left of the person who is very short.
2. The person who is tall is somewhere to the right of the person who has an average height.
3. The person who has an average height is Eric.
4. Peter is not in the fourth house.
5. There is one house between the person who is short and Peter.
6. The person who is very short is not in the third house.
 What is the value of attribute House for the person whose attribute Name is Arnold? Please reason step by step, and put your final answer within \boxed{}

Answer: 4


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Carol`, `Peter`, `Eric`, `Bob`
 - Each person has a unique type of pet: `cat`, `bird`, `fish`, `dog`, `hamster`, `rabbit`
 - People have unique heights: `super tall`, `average`, `tall`, `very short`, `very tall`, `short`
 - People have unique favorite sports: `baseball`, `tennis`, `soccer`, `swimming`, `basketball`, `volleyball`

## Clues:
1. There is one house between the person who has an average height and the person who is short.
2. The person with an aquarium of fish is in the fifth house.
3. The person who has a cat is the person who is tall.
4. The person who is very tall is the person who loves soccer.
5. Peter is in the first house.
6. The person who loves tennis is in the sixth house.
7. Carol is somewhere to the right of the person who is very tall.
8. The person who loves volleyball is directly left of the person who loves soccer.
9. The person who loves baseball is directly left of the person who is super tall.
10. Carol and Bob are next to each other.
11. The person who is super tall is not in the sixth house.
12. The person who is short is not in the fourth house.
13. There is one house between the person who loves swimming and Bob.
14. The person who loves basketball is somewhere to the left of the person who owns a dog.
15. The person who owns a rabbit is somewhere to the left of the person who is short.
16. The person who keeps a pet bird is the person who is short.
17. Arnold is not in the second house.
18. Bob is directly left of Eric.
19. The person who owns a rabbit and the person who is very tall are next to each other.
 What is the value of attribute Name for the person whose attribute Height is average? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Eric`, `Arnold`, `Bob`, `Peter`, `Alice`
 - Everyone has a unique favorite cigar: `dunhill`, `blue master`, `blends`, `pall mall`, `prince`
 - Each person has an occupation: `lawyer`, `artist`, `engineer`, `doctor`, `teacher`
 - People own unique car models: `ford f150`, `toyota camry`, `honda civic`, `bmw 3 series`, `tesla model 3`
 - Everyone has a favorite smoothie: `watermelon`, `cherry`, `dragonfruit`, `desert`, `lime`
 - Everyone has something unique for lunch: `stew`, `spaghetti`, `grilled cheese`, `pizza`, `stir fry`

## Clues:
1. There are two houses between the person who owns a BMW 3 Series and the person who owns a Tesla Model 3.
2. The person who is an artist is Bob.
3. The person who owns a Ford F-150 is the person who smokes Blue Master.
4. The person who loves the spaghetti eater is in the second house.
5. The person who is an engineer is the Watermelon smoothie lover.
6. Alice is the person who drinks Lime smoothies.
7. The person who is an artist is the Dunhill smoker.
8. The person who likes Cherry smoothies is not in the fifth house.
9. Peter is not in the fourth house.
10. The Desert smoothie lover is the person who loves stir fry.
11. The person who likes Cherry smoothies is somewhere to the right of the person who smokes many unique blends.
12. The person who is a teacher is the person who loves eating grilled cheese.
13. Arnold is the person who is a lawyer.
14. The Dragonfruit smoothie lover is the person who owns a Honda Civic.
15. Peter is somewhere to the right of the Desert smoothie lover.
16. The Prince smoker is the Watermelon smoothie lover.
17. There is one house between the person who owns a Honda Civic and the person who loves the stew.
18. The person who owns a Tesla Model 3 is the person who likes Cherry smoothies.
19. The person who owns a Ford F-150 is directly left of the person who is a doctor.
20. The person who is an artist is the Desert smoothie lover.
 What is the value of attribute Food for the person whose attribute House is 4? Please reason step by step, and put your final answer within \boxed{}

Answer: stew


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`
 - Each person has a unique birthday month: `feb`, `jan`, `april`, `sept`
 - People have unique hair colors: `black`, `blonde`, `brown`, `red`
 - Each person lives in a unique style of house: `colonial`, `ranch`, `victorian`, `craftsman`
 - Each person has an occupation: `engineer`, `artist`, `doctor`, `teacher`
 - Everyone has a favorite smoothie: `cherry`, `dragonfruit`, `desert`, `watermelon`

## Clues:
1. The person who is an engineer is the person whose birthday is in February.
2. The person who likes Cherry smoothies is somewhere to the left of the person who has red hair.
3. The person who is a doctor is the person who has blonde hair.
4. The person whose birthday is in January is the person living in a colonial-style house.
5. Alice is the person residing in a Victorian house.
6. Peter is the Desert smoothie lover.
7. Peter is the person whose birthday is in September.
8. The Dragonfruit smoothie lover is the person who is a teacher.
9. The Watermelon smoothie lover is the person residing in a Victorian house.
10. The person living in a colonial-style house is directly left of the person who has black hair.
11. The person whose birthday is in February is in the fourth house.
12. The person who has black hair is not in the third house.
13. Eric is the person in a ranch-style home.
14. The person who has blonde hair is directly left of the person who likes Cherry smoothies.
 What is the value of attribute Smoothie for the person whose attribute Name is Alice? Please reason step by step, and put your final answer within \boxed{}

Answer: watermelon


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

## Clues:
1. The person partial to Pall Mall is the person with an associate's degree.
2. The person who loves white is the Prince smoker.
3. The person with a high school diploma is not in the fourth house.
4. The person with a master's degree is not in the second house.
5. Arnold is not in the fourth house.
6. The person whose favorite color is red is not in the third house.
7. The person whose favorite color is red is somewhere to the left of Eric.
8. The person who loves cooking is somewhere to the right of Peter.
9. The person who loves a bouquet of daffodils is somewhere to the left of the person who paints as a hobby.
10. The person who loves white is the person who loves the boquet of lilies.
11. Alice is the photography enthusiast.
12. Arnold is somewhere to the right of the person partial to Pall Mall.
13. The person who loves white is in the second house.
14. The person whose favorite color is green is directly left of the person who enjoys gardening.
15. The Dunhill smoker is the person with a high school diploma.
16. The person who loves the rose bouquet is somewhere to the right of the person whose favorite color is green.
 What is the value of attribute Education for the person whose attribute Flower is roses? Please reason step by step, and put your final answer within \boxed{}

Answer: master


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Alice`, `Arnold`
 - Each mother is accompanied by their child: `Bella`, `Fred`, `Meredith`, `Samantha`
 - People have unique hair colors: `red`, `brown`, `black`, `blonde`
 - They all have a unique favorite flower: `carnations`, `roses`, `daffodils`, `lilies`
 - The people keep unique animals: `cat`, `bird`, `fish`, `horse`

## Clues:
1. Alice is somewhere to the right of the person who has red hair.
2. The person who loves a bouquet of daffodils is directly left of Arnold.
3. The fish enthusiast is the person's child is named Samantha.
4. Alice is directly left of the bird keeper.
5. The cat lover is the person who loves the rose bouquet.
6. The person who loves a carnations arrangement is somewhere to the right of the person who has brown hair.
7. The person who loves a bouquet of daffodils is directly left of the bird keeper.
8. Eric is the person's child is named Meredith.
9. There are two houses between the person who has red hair and the person who has black hair.
10. Eric is in the fourth house.
11. The person's child is named Bella is the person who loves a bouquet of daffodils.
 What is the value of attribute Name for the person whose attribute Flower is lilies? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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

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

Answer: green


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Bob`, `Arnold`, `Eric`, `Peter`
 - People have unique favorite book genres: `romance`, `mystery`, `biography`, `fantasy`, `science fiction`
 - Each person has a unique birthday month: `sept`, `feb`, `jan`, `mar`, `april`
 - Each person prefers a unique type of vacation: `mountain`, `beach`, `city`, `camping`, `cruise`
 - The people keep unique animals: `horse`, `bird`, `fish`, `dog`, `cat`

## Clues:
1. The person whose birthday is in April is the person who loves mystery books.
2. The person whose birthday is in March is somewhere to the left of the person who loves mystery books.
3. The person who loves beach vacations is Arnold.
4. The person who loves beach vacations is the person whose birthday is in January.
5. The bird keeper is directly left of Peter.
6. The person who loves science fiction books is somewhere to the left of the person whose birthday is in February.
7. The fish enthusiast is somewhere to the right of Bob.
8. The fish enthusiast is Eric.
9. The fish enthusiast is the person who loves fantasy books.
10. The person who enjoys mountain retreats is directly left of the person whose birthday is in April.
11. The person whose birthday is in April is the person who enjoys camping trips.
12. The person whose birthday is in September is the person who loves science fiction books.
13. The cat lover is the person who prefers city breaks.
14. The person who loves romance books is somewhere to the right of the person who loves science fiction books.
15. The cat lover is the person whose birthday is in February.
16. The person who keeps horses is Peter.
 What is the value of attribute House for the person whose attribute BookGenre is biography? Please reason step by step, and put your final answer within \boxed{}

Answer: 1


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Alice`, `Bob`, `Eric`, `Arnold`
 - The people are of nationalities: `norwegian`, `german`, `dane`, `brit`, `swede`
 - People have unique favorite book genres: `fantasy`, `biography`, `romance`, `mystery`, `science fiction`
 - Everyone has something unique for lunch: `stir fry`, `grilled cheese`, `pizza`, `spaghetti`, `stew`
 - Each person has a favorite color: `red`, `green`, `blue`, `yellow`, `white`
 - The people keep unique animals: `bird`, `dog`, `cat`, `horse`, `fish`

## Clues:
1. The person who loves fantasy books is the Norwegian.
2. The cat lover and the person who loves biography books are next to each other.
3. The German is Bob.
4. The person who loves yellow is Bob.
5. The person whose favorite color is green is Peter.
6. There is one house between the Dane and the person who is a pizza lover.
7. The person who loves blue is somewhere to the left of the Dane.
8. The person who loves eating grilled cheese is somewhere to the left of the Norwegian.
9. The person who loves the spaghetti eater is Peter.
10. The person who keeps horses is Alice.
11. The fish enthusiast is directly left of the person who loves science fiction books.
12. There is one house between the Norwegian and Arnold.
13. The person who loves romance books is the British person.
14. There are two houses between the Norwegian and Alice.
15. The bird keeper is the person whose favorite color is red.
16. The dog owner is directly left of the fish enthusiast.
17. The person who loves the stew is the Norwegian.
 What is the value of attribute Food for the person whose attribute Color is blue? Please reason step by step, and put your final answer within \boxed{}

Answer: stew


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Bob`, `Alice`, `Eric`, `Arnold`
 - People use unique phone models: `oneplus 9`, `google pixel 6`, `samsung galaxy s21`, `iphone 13`, `huawei p50`
 - Each person has an occupation: `lawyer`, `engineer`, `teacher`, `artist`, `doctor`

## Clues:
1. The person who uses a Samsung Galaxy S21 is directly left of Eric.
2. There are two houses between Alice and the person who is an artist.
3. The person who uses an iPhone 13 is directly left of Bob.
4. The person who is a lawyer is in the third house.
5. The person who is a doctor is Arnold.
6. The person who is an engineer is directly left of the person who is an artist.
7. The person who uses a OnePlus 9 is somewhere to the right of Eric.
8. The person who uses a Google Pixel 6 is Peter.
 What is the value of attribute House for the person whose attribute Occupation is doctor? 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`, `Bob`, `Peter`, `Eric`, `Carol`, `Alice`
 - Each person lives in a unique style of house: `craftsman`, `colonial`, `mediterranean`, `modern`, `victorian`, `ranch`
 - Each person has an occupation: `nurse`, `doctor`, `artist`, `engineer`, `lawyer`, `teacher`
 - People have unique favorite sports: `swimming`, `basketball`, `baseball`, `tennis`, `soccer`, `volleyball`

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

Answer: 5


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 Name for the person whose attribute Occupation is doctor? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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

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

Answer: 1


There are 3 houses, numbered 1 to 3 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Arnold`, `Eric`, `Peter`
 - People have unique favorite music genres: `pop`, `rock`, `classical`
 - Each mother is accompanied by their child: `Fred`, `Meredith`, `Bella`
 - People have unique favorite book genres: `mystery`, `romance`, `science fiction`

## Clues:
1. The person's child is named Fred is directly left of the person who loves mystery books.
2. Peter is in the first house.
3. The person who loves mystery books is the person who loves classical music.
4. The person who loves science fiction books is the person's child is named Meredith.
5. Eric is the person who loves mystery books.
6. The person who loves rock music is somewhere to the right of the person who loves romance books.
 What is the value of attribute Name for the person whose attribute MusicGenre is pop? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


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

## Clues:
1. The person whose favorite color is green is the person who uses a Google Pixel 6.
2. The person who uses a Xiaomi Mi 11 is somewhere to the right of the person who uses a Huawei P50.
3. There are two houses between Peter and the person whose favorite color is red.
4. Eric is somewhere to the right of the person whose favorite color is green.
5. Carol is the person who uses an iPhone 13.
6. The person who loves blue is not in the second house.
7. The person who uses a Samsung Galaxy S21 is somewhere to the left of the person who loves yellow.
8. The person who loves blue is somewhere to the left of the person who loves white.
9. Carol and the person whose favorite color is red are next to each other.
10. The person who uses a Google Pixel 6 is Bob.
11. Alice is the person who uses a Xiaomi Mi 11.
12. The person whose favorite color is green is not in the second house.
13. The person who loves purple is directly left of Carol.
14. Alice is the person who loves purple.
 What is the value of attribute Name for the person whose attribute PhoneModel is huawei p50? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


Triangle $ABC$ has no obtuse angles. On side $AC$ of this triangle, a point $D$ is taken such that $AD = \frac{3}{4}AC$. Find angle $A$, given that line $BD$ divides triangle $ABC$ into two similar triangles.

Answer: 30


Let $[x]$ denote the greatest integer not exceeding $x$, e.g. $[5.6]=5$ and $[3]=3$. How many different integers are there in the sequence $\left[\frac{1^{2}}{2006}\right], \left[\frac{2^{2}}{2006}\right], \left[\frac{3^{2}}{2006}\right], \ldots, \left[\frac{2006^{2}}{2006}\right]$?

Answer: 1505


A positive integer is called lucky if it is divisible by 7, and the sum of its digits is also divisible by 7. Fix a positive integer \( n \). Show that there exists some lucky integer \( \ell \) such that \( |n - \ell| \leq 70 \).

Answer: 70


In a certain math competition, there are 6 questions, each worth 7 points (the final score for each question is an integer, with a minimum of 0 points and a maximum of 7 points). The total score of each participant is the product of their scores on the 6 questions. If two participants have the same score, then the sum of the 6 questions' scores is calculated to determine their ranking. If these are also the same, the participants are tied. In this competition, there are $8^{6}=262144$ participants with no ties. What is the total score of the participant ranked $7^{6}=117649$?

Answer: 1


From the ten-digit number 2946835107, 5 digits were removed. What is the largest possible number that could result from this?

Answer: 98517


The amount in rubles transferred by one of the enterprises to the Peace Fund is represented by the largest even five-digit number, where the first three digits form a number that is a perfect square, and the last three digits form a number that is a perfect cube. What amount was transferred to the Peace Fund by the enterprise?

Answer: 62512


In the diagram, there is a karting track layout. Start and finish are at point $A$, but the go-kart driver can return to point $A$ any number of times and resume the lap.

The path from $A$ to $B$ and vice versa takes one minute. The loop also takes one minute to complete. The loop can only be traversed counterclockwise (the arrows indicate the possible direction of travel). The driver does not turn back halfway and does not stop. The racing duration is 10 minutes. Find the number of possible different routes (sequences of segments traversed).

Answer: 34


Let \( P \) be a polyhedron where every face is a regular polygon, and every edge has length 1. Each vertex of \( P \) is incident to two regular hexagons and one square. Choose a vertex \( V \) of the polyhedron. Find the volume of the set of all points contained in \( P \) that are closer to \( V \) than to any other vertex.

Answer: \frac{\sqrt{2}}{3}


In a circle with center \( O \), the chord \( AB \) intersects the radius \( OC \) at point \( D \), with \( \angle CDA = 120^{\circ} \). Find the radius of the circle that is tangent to the segments \( AD \), \( DC \), and the arc \( AC \), given that \( OC = 2 \) and \( OD = \sqrt{3} \).

Answer: 2\sqrt{21}-9


We color certain squares of an $8 \times 8$ chessboard in gray. How many squares can be colored at most if we want no $3 \times 1$ gray trimino?

Answer: 43


In the diagram, \(ABCD\) is a rectangle with points \(P\) and \(Q\) on \(AD\) such that \(AB = AP = PQ = QD\). Also, point \(R\) is on \(DC\) with \(DR = RC\). If \(BC = 24\), what is the area of \(\triangle PQR\)?

Answer: 16


The structure shown in the figure is in equilibrium. It is known that the length of the uniform rod is $l = 50 \text{ cm}$, and its mass is $m_{2} = 2$ kg. The distance between the attachment points of the left thread to the rod is $S = 10$ cm. Determine the mass $m_{1}$ of the load. All threads are weightless and inextensible. The blocks are weightless.

Answer: 10


(1) Given that \( a > 0 \) and \( b > 0 \), and \( a + b = 1 \), find the minimum value of \(\left(a + \frac{1}{a^{2}}\right)^{2} + \left(b + \frac{1}{b^{2}}\right)^{2}\). Also, find the maximum value of \(\left(a + \frac{1}{a}\right)\left(b + \frac{1}{b}\right)\).

(2) Given that \( a > 0 \), \( b > 0 \), and \( c > 0 \), and \( a + b + c = 1 \), find the minimum value of \( u = \left(a + \frac{1}{a}\right)^{3} + \left(b + \frac{1}{b}\right)^{3} + \left(c + \frac{1}{c}\right)^{3} \).

Answer: \frac{1000}{9}


9. A circle of radius 1 is inscribed in triangle $A B C$, where $\cos \widehat{A B C}=0.8$. This circle touches the midline of triangle $A B C$, parallel to side $A C$. Find the length of side $A C$.

Answer: 3


5. A certain meeting has 30 participants, each of whom knows at most five others; among any five people, at least two are not acquaintances. Find the largest positive integer $k$, such that in any group of 30 people satisfying the above conditions, there always exists a group of $k$ people, none of whom are acquaintances.
(Cold Gangsong, Contributed)

Answer: 6


Example 1. On the three sides of $\triangle A B C$, there are $l, m, n$ points respectively. Lines are drawn from each vertex to the points on its opposite side. If no three of these lines intersect at the same point, how many regions do they divide $\triangle A B C$ into?

Answer: 1 + l + m + n + lm + ln + mn


12. (12 points) A row of 2012 balls, colored red, yellow, and blue, are arranged in a line, with a distance of 1 centimeter between each adjacent pair of balls. In every set of 4 adjacent balls, there is 1 red ball, 1 yellow ball, and 2 blue balls. The distance between the 100th red ball from the left and the 100th yellow ball from the right is 1213 centimeters. The distance between the 100th blue ball from the left and the 100th blue ball from the right is $\qquad$ centimeters.

Answer: 1615


# 5. Place the signs $\times$ and : instead of the squares in the expression

$$
1 \square 3 \square 3^{2} \square 3^{4} \square 3^{8} \square 3^{16} \square 3^{32} \square 3^{64}=3^{99}
$$

such that the value of the expression becomes $3^{99}$.

Answer: 1 \times 3 : 3^{2} : 3^{4} : 3^{8} \times 3^{16} \times 3^{32} \times 3^{64} = 3^{99}


1. Provide an example of a natural number that is divisible by 2019, and the sum of its digits is also divisible by 2019. Don't forget to show that your example meets the condition.

Answer: 20192019\ldots2019


50. One day, from 8 a.m. to 6 p.m., the hour hand and the minute hand overlap $\qquad$ times.

Answer: 10


# 7.

1) $\angle A P B=\angle B A C, \angle A P B=\angle A K C, \angle A K C=\angle B A C, \angle K A C=\angle A B C$.

Segment $A C$ is a tangent segment to the circle.

$\triangle A B C \approx \triangle A K C \Rightarrow$

$\frac{A B}{A K}=\frac{A C}{K C}=\frac{B C}{A C} \Rightarrow \frac{A B}{4}=\frac{A C}{3}=\frac{12}{A C} \Rightarrow A C=6, \quad A B=8$.
2) $C D$ is a median $\Rightarrow$ by the cosine theorem for triangles $A D C$ and $B D C$ we have:

$A C^{2}=A D^{2}+C D^{2}-2 A D \cdot C D \cos \angle A D C, \quad B C^{2}=B D^{2}+C D^{2}+2 B D \cdot C D \cos \angle A D C$.

Since $A D=B D$, then $A C^{2}+B C^{2}=2 A D^{2}+2 C D^{2}$,

$C D^{2}=\frac{1}{2}\left(A C^{2}+B C^{2}\right)-A D^{2}=\frac{1}{2}(36+144)-16=74, C D=\sqrt{74}$.

3) Let $D P=x, D N=y$ ( $N$ is the intersection point of line $C D$ with the circle, $N \neq P$ ).

Quadrilateral $A N B P$ is inscribed in the circle $\Rightarrow A D \cdot D B=P D \cdot B T, \quad 16=x y$. By the properties of tangents and secants to the circle we have $C N \cdot C P=A C^{2},(C D-y) \cdot(C D+x)=A C^{2}$, $(\sqrt{74}-y) \cdot(\sqrt{74}+x)=36$

4) Solving the system of equations $16=x y, \quad(\sqrt{74}-y) \cdot(\sqrt{74}+x)=36 \Rightarrow y=\frac{22}{\sqrt{74}}+x \Rightarrow$ $x^{2}+\frac{22}{\sqrt{74}} x-16=0, x=\frac{-11+3 \sqrt{145}}{\sqrt{74}}, D P=\frac{-11+3 \sqrt{145}}{\sqrt{74}}$.

Answer: \dfrac{-11 + 3\sqrt{145}}{\sqrt{74}}


The warehouse has nails in boxes weighing 24, 23, 17, and 16 kg. Can the storekeeper release 100 kg of nails from the warehouse without opening the boxes?

Answer: Yes


4. The number $a_{n}$ is formed by writing down the first n consecutive natural numbers in sequence, for example, $a_{13}=12345678910111213$. Determine how many numbers divisible by 24 are among the numbers $a_{1}, a_{2}, \ldots, a_{10000}$.

Answer: 834


4. Given a circle of radius $R$. At a distance of $2 R$ from the center of the circle, a point $A$ is chosen. From this point, a tangent and a secant are drawn, and the secant is equidistant from the center of the circle and the point of tangency. Find the length of the segment of the secant enclosed within the circle.

Answer: \dfrac{2\sqrt{130}}{13} R


1. Buses from Moscow to Voronezh depart every hour, at 00 minutes. Buses from Voronezh to Moscow depart every hour, at 30 minutes. The trip between the cities takes 8 hours. How many buses from Voronezh will the bus that left from Moscow meet on its way?

Answer: 16


4. Charity. A generous person distributed the same amount of money equally among those who asked him for assistance every week. One day he noticed:

- If the number of petitioners is five less next week, each will receive two dollars more.

But, alas, after a week, the number of petitioners did not decrease but increased by four.

- This means,--the benefactor noted,--that each will receive one dollar less.

How much did each petitioner receive this last time?

Answer: 5


Through point \( M \), located on the diameter of a circle with radius 4 cm, a chord \( AB \) is drawn, forming a \( 30^{\circ} \) angle with the diameter. A chord \( BC \), perpendicular to this diameter, is drawn through point \( B \). Find the area of triangle \( ABC \), given that \( AM:MB = 2:3 \).

Answer: \dfrac{180\sqrt{3}}{19}


4. In a given circular cone, with height $H$ and base radius $R$, a cylinder with maximum volume is inscribed. In this cylinder, a cone is inscribed, and in that cone, another cylinder with maximum volume is inscribed, etc. (the bases of the cylinders and cones are in the same plane). Find the sum of the volumes of the inscribed cylinders.

Answer: \dfrac{4}{23} \pi R^2 H


4. Once, a team of Knights and a team of Liars met in the park and decided to ride the circular carousel, which can accommodate 40 people (the "Chain" carousel, where everyone sits one behind the other). When they sat down, each person saw two others, one in front of them and one behind them, and said: "At least one of the people sitting in front of me or behind me belongs to my team." One seat remained empty, and they invited another Liar. This Liar said: "Together with me, we can arrange ourselves on the carousel so that this rule is satisfied again." How many people were in the team of Knights? (A Knight always tells the truth, a Liar always lies.)

Answer: 26


On a plane, there are 2019 points. Drawing circles passing through these points, a drawing method is called "$k$-good" if and only if drawing $k$ circles divides the plane into several closed shapes, and there is no closed shape containing two points. Then, find the minimum value of $k$ , it ensures that no matter how these 2019 points are arranged, there always exists a $k$-good drawing method.

Answer: 1010


4. Given $f(x)=a \sin x+b \sqrt[3]{x}+c \ln \left(x+\sqrt{x^{2}+1}\right)+1003(a, b, c$ are real numbers $)$, and $f\left(\lg ^{2} 10\right)=1$, then $f(\lg \lg 3)=$ $\qquad$ .

Answer: 2005


Example 3: 10 people go to a bookstore to buy books. It is known that each person bought three types of books, and any two people have at least one book in common. Question: What is the maximum number of people who bought the most purchased book, at a minimum? (No. 8

Answer: 5


9. (16 points) Given

the ellipse $\Gamma: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$
with the left and right endpoints of the major axis being $A$ and $B$, and the left and right foci being $F_{1}$ and $F_{2}$. If there exists a point $P$ on the ellipse $\Gamma$ such that $P F_{1}$ and $P F_{2}$ trisect $\angle A P B$, among all ellipses $\Gamma$ that satisfy the above conditions, find the number of different eccentricities $e$.

Answer: 1


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Arnold`, `Bob`, `Alice`
 - Each person has a unique favorite drink: `milk`, `tea`, `root beer`, `water`, `coffee`
 - Each person has a favorite color: `blue`, `white`, `red`, `green`, `yellow`
 - Each mother is accompanied by their child: `Samantha`, `Meredith`, `Timothy`, `Bella`, `Fred`
 - Each person lives in a unique style of house: `modern`, `ranch`, `victorian`, `colonial`, `craftsman`
 - People use unique phone models: `samsung galaxy s21`, `iphone 13`, `huawei p50`, `oneplus 9`, `google pixel 6`

## Clues:
1. The person in a Craftsman-style house is directly left of the person living in a colonial-style house.
2. The person living in a colonial-style house is somewhere to the left of the person who uses a Samsung Galaxy S21.
3. The person who uses a Huawei P50 is the person in a Craftsman-style house.
4. The root beer lover is somewhere to the left of the person residing in a Victorian house.
5. There is one house between the person in a ranch-style home and the root beer lover.
6. The person who uses a OnePlus 9 is the person whose favorite color is red.
7. The tea drinker is not in the fourth house.
8. The person living in a colonial-style house and Peter are next to each other.
9. The person in a ranch-style home is directly left of the person whose favorite color is green.
10. The person who is the mother of Timothy and the person's child is named Meredith are next to each other.
11. The person who loves blue is the person residing in a Victorian house.
12. Bob is the person residing in a Victorian house.
13. The person's child is named Bella is the person who uses a Google Pixel 6.
14. The person who loves blue is the one who only drinks water.
15. The person who likes milk is the person who is the mother of Timothy.
16. The person who loves white is Arnold.
17. The root beer lover is directly left of the person who uses a Samsung Galaxy S21.
18. The person who likes milk is Alice.
19. The person who is the mother of Timothy is the person whose favorite color is green.
20. The person who loves white is not in the first house.
21. The person's child is named Samantha is the person whose favorite color is red.
 What is the value of attribute Color for the person whose attribute PhoneModel is oneplus 9? Please reason step by step, and put your final answer within \boxed{}

Answer: red


There are 5 houses, numbered 1 to 5 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Alice`, `Arnold`, `Eric`, `Peter`, `Bob`
 - People have unique hair colors: `black`, `red`, `gray`, `blonde`, `brown`
 - The people are of nationalities: `dane`, `norwegian`, `swede`, `brit`, `german`
 - Each person lives in a unique style of house: `ranch`, `colonial`, `modern`, `craftsman`, `victorian`
 - Each person has a unique birthday month: `sept`, `jan`, `mar`, `april`, `feb`
 - Each person has an occupation: `engineer`, `doctor`, `lawyer`, `teacher`, `artist`

## Clues:
1. The person who has brown hair is the person whose birthday is in March.
2. The person who is a doctor is the Dane.
3. Eric is the person whose birthday is in March.
4. The person whose birthday is in February is directly left of the person who is an engineer.
5. There is one house between the person in a ranch-style home and the German.
6. Bob is the person whose birthday is in January.
7. The person who is an artist is the Swedish person.
8. The Swedish person is in the second house.
9. Peter is not in the fourth house.
10. The person who is an artist is somewhere to the left of the person who is a teacher.
11. The person who is an artist is directly left of the person who has gray hair.
12. Alice is the person who has red hair.
13. The person whose birthday is in September is not in the third house.
14. Arnold is somewhere to the left of the person living in a colonial-style house.
15. The person in a modern-style house is in the fifth house.
16. The person who has black hair is the Norwegian.
17. There are two houses between the person whose birthday is in January and the British person.
18. The person who has red hair is the person in a Craftsman-style house.
19. The person who is an engineer and the British person are next to each other.
20. There is one house between Arnold and the person who has red hair.
 What is the value of attribute Occupation for the person whose attribute House is 1? Please reason step by step, and put your final answer within \boxed{}

Answer: lawyer


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`, `Peter`, `Alice`
 - People have unique heights: `very short`, `short`, `tall`, `average`
 - Each person prefers a unique type of vacation: `cruise`, `beach`, `city`, `mountain`
 - Each person has a favorite color: `green`, `red`, `yellow`, `white`
 - Each mother is accompanied by their child: `Fred`, `Bella`, `Meredith`, `Samantha`

## Clues:
1. The person who loves beach vacations is the person who is very short.
2. The person who is very short is the person who loves white.
3. The person who has an average height is the person's child is named Bella.
4. The person who has an average height is the person whose favorite color is red.
5. Peter is the person's child is named Samantha.
6. The person whose favorite color is green is directly left of the person who loves white.
7. Alice is in the third house.
8. The person who likes going on cruises is the person's child is named Bella.
9. The person who is short is the person who loves yellow.
10. The person who is very short is the person's child is named Fred.
11. Eric is the person who loves yellow.
12. The person who prefers city breaks is Eric.
13. The person who is short is somewhere to the left of the person who is tall.
 What is the value of attribute Name for the person whose attribute Color is green? Please reason step by step, and put your final answer within \boxed{}

Answer: Peter


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Eric`, `Alice`, `Arnold`
 - Each person has a unique level of education: `bachelor`, `high school`, `associate`, `master`
 - People have unique favorite music genres: `jazz`, `rock`, `pop`, `classical`
 - Each person has a favorite color: `green`, `red`, `yellow`, `white`
 - They all have a unique favorite flower: `lilies`, `carnations`, `daffodils`, `roses`

## Clues:
1. The person with a bachelor's degree is the person who loves a bouquet of daffodils.
2. The person who loves a carnations arrangement is not in the first house.
3. The person with a master's degree is Alice.
4. The person with a master's degree is directly left of the person who loves classical music.
5. Eric is not in the second house.
6. Arnold is not in the third house.
7. The person who loves yellow is directly left of the person who loves the rose bouquet.
8. The person who loves pop music is in the second house.
9. The person with an associate's degree is not in the fourth house.
10. The person who loves a carnations arrangement is not in the fourth house.
11. The person whose favorite color is red is directly left of the person who loves white.
12. The person whose favorite color is red is the person who loves rock music.
13. Arnold is the person who loves yellow.
14. The person who loves a bouquet of daffodils is the person who loves yellow.
 What is the value of attribute Flower for the person whose attribute House is 2? Please reason step by step, and put your final answer within \boxed{}

Answer: roses


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`
 - They all have a unique favorite flower: `roses`, `carnations`, `daffodils`, `lilies`
 - Each person lives in a unique style of house: `victorian`, `craftsman`, `colonial`, `ranch`
 - Everyone has a unique favorite cigar: `prince`, `dunhill`, `blue master`, `pall mall`

## Clues:
1. The person in a ranch-style home is in the third house.
2. The person who smokes Blue Master is somewhere to the left of the person residing in a Victorian house.
3. There are two houses between Eric and the person who loves the rose bouquet.
4. The Prince smoker is Peter.
5. The person in a Craftsman-style house is the Dunhill smoker.
6. The Dunhill smoker is the person who loves a carnations arrangement.
7. Arnold is in the fourth house.
8. The Prince smoker is in the second house.
9. The person who loves the boquet of lilies is the person who smokes Blue Master.
 What is the value of attribute HouseStyle for the person whose attribute House is 3? Please reason step by step, and put your final answer within \boxed{}

Answer: ranch


There are 6 houses, numbered 1 to 6 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Bob`, `Eric`, `Arnold`, `Carol`, `Alice`, `Peter`
 - Each person has a unique hobby: `cooking`, `painting`, `knitting`, `photography`, `woodworking`, `gardening`
 - People have unique hair colors: `brown`, `auburn`, `black`, `red`, `gray`, `blonde`
 - People have unique favorite sports: `swimming`, `volleyball`, `basketball`, `baseball`, `tennis`, `soccer`
 - The mothers' names in different houses are unique: `Sarah`, `Holly`, `Penny`, `Janelle`, `Kailyn`, `Aniya`
 - Everyone has a unique favorite cigar: `dunhill`, `blends`, `pall mall`, `prince`, `yellow monster`, `blue master`

## Clues:
1. The person who has gray hair is directly left of The person whose mother's name is Janelle.
2. The person who loves soccer is in the sixth house.
3. Arnold is the person who has blonde hair.
4. The photography enthusiast is the person who smokes Yellow Monster.
5. There is one house between the Dunhill smoker and the person who loves cooking.
6. The person who paints as a hobby is the person who has blonde hair.
7. The Dunhill smoker is directly left of Alice.
8. The person who paints as a hobby is directly left of the person who loves volleyball.
9. The person who loves soccer is The person whose mother's name is Aniya.
10. The person partial to Pall Mall is somewhere to the left of Carol.
11. The person who enjoys knitting and the person who loves basketball are next to each other.
12. The person partial to Pall Mall is directly left of The person whose mother's name is Holly.
13. The person who loves soccer is the Prince smoker.
14. The person who loves swimming is The person whose mother's name is Penny.
15. The person whose mother's name is Kailyn is the person who loves volleyball.
16. The person who loves basketball is The person whose mother's name is Janelle.
17. The person who enjoys knitting is the person who loves volleyball.
18. The person who enjoys knitting is not in the third house.
19. The person who has auburn hair is somewhere to the left of the photography enthusiast.
20. The person whose mother's name is Sarah is not in the fifth house.
21. Bob is directly left of the person who has red hair.
22. The Dunhill smoker is the person who enjoys gardening.
23. The person who loves baseball is the person who has auburn hair.
24. Eric is the person who smokes many unique blends.
25. The person who has brown hair is somewhere to the right of The person whose mother's name is Penny.
 What is the value of attribute FavoriteSport for the person whose attribute Hobby is knitting? Please reason step by step, and put your final answer within \boxed{}

Answer: volleyball


There are 4 houses, numbered 1 to 4 from left to right, as seen from across the street. Each house is occupied by a different person. Each house has a unique attribute for each of the following characteristics:
 - Each person has a unique name: `Peter`, `Arnold`, `Alice`, `Eric`
 - They all have a unique favorite flower: `roses`, `daffodils`, `carnations`, `lilies`
 - Each person has a unique hobby: `photography`, `painting`, `cooking`, `gardening`
 - Each person has a unique type of pet: `dog`, `fish`, `bird`, `cat`
 - Each person has a favorite color: `red`, `yellow`, `green`, `white`
 - Each person lives in a unique style of house: `craftsman`, `colonial`, `ranch`, `victorian`

## Clues:
1. The person in a Craftsman-style house is Arnold.
2. The person who loves the rose bouquet is somewhere to the right of Peter.
3. The photography enthusiast is the person who owns a dog.
4. The person who loves a bouquet of daffodils is not in the fourth house.
5. The person who loves the rose bouquet is the person whose favorite color is red.
6. The person in a Craftsman-style house is in the second house.
7. Eric is the person residing in a Victorian house.
8. The person with an aquarium of fish is the person who loves white.
9. The person who loves cooking is somewhere to the right of the person whose favorite color is red.
10. The person who loves white is the person who loves a carnations arrangement.
11. The person who loves white is somewhere to the right of the person who enjoys gardening.
12. The person who loves a bouquet of daffodils is the person who loves yellow.
13. The person living in a colonial-style house is the person whose favorite color is red.
14. The person who has a cat is Eric.
 What is the value of attribute Hobby for the person whose attribute Flower is carnations? Please reason step by step, and put your final answer within \boxed{}

Answer: painting