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2. Introduction to Puzzles & Games
Robert Snapprsnapp@uvm.edu
Department of Computer ScienceUniversity of Vermont
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 1 / 44
1 Origins of puzzles & games
2 Johan Huizinga’s Homo Ludens
3 Roger Caillois’s Man, Play and Games
4 A survey of puzzlesWord puzzlesLogic puzzlesChessboard puzzlesMechanical puzzles
5 A survey of games
6 Bibliography
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 2 / 44
Origins of puzzles & games
Pieter Bruegel the Elder, Kinderspiele, oil on wood, 1560, Kunsthistorisches Museum, Vienna.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 3 / 44
Origins of puzzles & games
Les Evans, Children’s Games. Poster commissioned by Play Wales (www.playwales.org.uk)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 4 / 44
Johan Huizinga’s Homo Ludens
Play is older than culture, for culture, however inadequately defined, alwayspresupposes human society, and animals have not waited for man to teachthem their playing : : :
Here we have at once a very important point: even in its simplest forms onthe animal level, play is more than a mere physiological phenomenon or apsychological reflex. It goes beyond the confines of purely physical orpurely biological activity. It is a significant function — that is to say, there issome sense to it. In play there is something “at play” which transcends theimmediate needs of life and imparts meaning to the action. All play meanssomething.
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 5 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.
Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), or
I A representation of something (e.g., playing make believe, dance, or a dramaticperformance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The nature of play (Huizinga)
Play is fun. (Fun is an aesthetic quality, like beauty that resists logical analysis.)
Play is a voluntary activity: it expresses freedom.
Play is not “ordinary” or “real” life, but has a disposition all its own.
Play requires repetition.
Play involves tension (uncertainty) that is resolved in solution. (This includespuzzles and solitaire games.)
Play has rules.
Play can build and define social communities: e.g., bridge clubs.
Play is often serious.Two categories of play:
I A contest for something, (e.g., a competitive game or puzzle), orI A representation of something (e.g., playing make believe, dance, or a dramatic
performance)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 6 / 44
The language of play (Huizinga)
Ancient Greece:
the suffix -inda denotes a child’s game:
I sphairinda: a ball game,I helkustinda: tug-of-war,I streptinda: a throwing game,I basilinda: king of the castle.
paidia: “light-hearted” (or child-like) play
agôn: competitive play (e.g., the Olympics)
Ancient India (Sanskrit):
krı̄dati: play.
divyati: gambling.
Ancient China:
wan: a children’s game.
chen: a game of skill.
sai: a tournament.
Ancient America (Blackfoot):
koani: a children’s games.
kachtsi: a game with rules (chance orskill).
skets or skits: to win a game.
Play is universal!
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 7 / 44
The language of play (Huizinga)
Ancient Greece:
the suffix -inda denotes a child’s game:
I sphairinda: a ball game,I helkustinda: tug-of-war,I streptinda: a throwing game,I basilinda: king of the castle.
paidia: “light-hearted” (or child-like) play
agôn: competitive play (e.g., the Olympics)
Ancient India (Sanskrit):
krı̄dati: play.
divyati: gambling.
Ancient China:
wan: a children’s game.
chen: a game of skill.
sai: a tournament.
Ancient America (Blackfoot):
koani: a children’s games.
kachtsi: a game with rules (chance orskill).
skets or skits: to win a game.
Play is universal!
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 7 / 44
The language of play (Huizinga)
Ancient Greece:
the suffix -inda denotes a child’s game:
I sphairinda: a ball game,I helkustinda: tug-of-war,I streptinda: a throwing game,I basilinda: king of the castle.
paidia: “light-hearted” (or child-like) play
agôn: competitive play (e.g., the Olympics)
Ancient India (Sanskrit):
krı̄dati: play.
divyati: gambling.
Ancient China:
wan: a children’s game.
chen: a game of skill.
sai: a tournament.
Ancient America (Blackfoot):
koani: a children’s games.
kachtsi: a game with rules (chance orskill).
skets or skits: to win a game.
Play is universal!
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 7 / 44
The language of play (Huizinga)
Ancient Greece:
the suffix -inda denotes a child’s game:
I sphairinda: a ball game,I helkustinda: tug-of-war,I streptinda: a throwing game,I basilinda: king of the castle.
paidia: “light-hearted” (or child-like) play
agôn: competitive play (e.g., the Olympics)
Ancient India (Sanskrit):
krı̄dati: play.
divyati: gambling.
Ancient China:
wan: a children’s game.
chen: a game of skill.
sai: a tournament.
Ancient America (Blackfoot):
koani: a children’s games.
kachtsi: a game with rules (chance orskill).
skets or skits: to win a game.
Play is universal!
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 7 / 44
“Culture arises in the form of play.”
Real civilization cannot exist in the absence of a certain play-element, forcivilization presupposes limitation and mastery of the self, the ability not toconfuse its own tendencies with the ultimate and highest goal, but tounderstand that it is enclosed with certain bounds freely accepted.Civilization will, in a sense, always be played according to certain rules,and true civilization will always demand fair play : : :
True play knows no propaganda; its aim is in itself, and its familiar spirit ishappy inspiration.
From Johan Huizinga, 1950 [4].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 8 / 44
Roger Caillois’s Classification of Games
AGÔN ALEA MIMICRY ILINX(Competition) (Chance) (Simulation) (Vertigo)
PAIDIA Racing Counting-out Make believe “whirling”
Wrestling rhymes Magic HorsebackTumult Etc. Heads or tails Tag, Arms riding
Agitiation Athletics Costumes SwingingLaughter Waltzing
Kite-flying Boxing, Betting VoladorSolitaire Billiards Roulette CarnivalsPatience Fencing Skiing
Crossword Chess Simple, complex Theater Mountainpuzzles Contests and continuing climbing
Sports lotteries Spectacles TightropeLUDUS in general in general walking
From Roger Caillois, 1961 [2].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 9 / 44
A survey of puzzlesWord puzzles
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.Q: “What is the difference between a flea and an elephant?”
I palindromes:“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]
I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.Q: “What is the difference between a flea and an elephant?”A: “An elephant can have fleas, but a flea can’t have elephants.”
I palindromes:“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]
I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]
I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]I puns
I tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]I punsI tongue twisters
I crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)
I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
A survey of puzzlesWord puzzles
I riddles.I palindromes:
“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]I punsI tongue twistersI crossword puzzles (December 21, 1913 issue of The New York World.)I cryptograms
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 10 / 44
Word Puzzles: gmasran! anagrams
Bill Amend, The Burlington Free Press, July 3, 2005.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 11 / 44
“The Zebra Puzzle,” (Life International, 1962)
1 There are five houses.2 The Englishman lives in the red house.3 The Spaniard owns the dog.4 Coffee is drunk in the green house.5 The Ukrainian drinks tea.6 The green house is immediately to the right of the ivory house.7 The Old Gold smoker owns snails.8 Kools are smoked in the yellow house.9 Milk is drunk in the middle house.10 The Norwegian lives in the first house.11 The man who smokes Chesterfields lives in the house next to the man with the fox.12 Kools are smoked in the house next to the house where the horse is kept.13 The Lucky Strike smoker drinks orange juice.14 The Japanese smokes Parliaments.15 The Norwegian lives next to the blue house.
Now, who drinks water? Who owns the zebra?
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 12 / 44
Sudoku logic puzzles
2 3 9 71
4 7 2 85 2 9
1 8 74 3
6 7 17
9 3 2 6 5
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 13 / 44
A survey of puzzlesWord puzzles
Logic puzzles
Route finding puzzles
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 14 / 44
Route finding puzzles: Mazes
The Great Vermont Corn Maze, North Danville, VT, 2005.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 15 / 44
Route finding puzzles: Mazes
The Great Vermont Corn Maze, North Danville, VT, 2006.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 16 / 44
A survey of puzzlesWord puzzles
Logic puzzles
Route finding puzzles
Chessboard puzzles
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 17 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0Z0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0Z0Z0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0Z0Z0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0Z0Z0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0™Xq0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another?
8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0™Xq0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another? Can it be done?
8 0Z0Z0Z0Z7 Z0ZXq™Xq0Z06 0ZXqZ0™Xq0Z5 Z0™Xq0ZXqZ04 0Z0ZXqZ0Z3 Z0Z0™Xq0Z02 0Z0Z0Z0Z1 Z0Z0•Tk0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: the eight-queensCan one place eight queens on a standard chessboard so that no pair of piecesattack one another? Yes. Here is one of the 92 solutions.
8 XqZ0Z0Z0Z7 Z0Z0™Xq0Z06 0Z0Z0Z0™Xq5 Z0Z0ZXqZ04 0ZXqZ0Z0Z3 Z0Z0Z0™Xq02 0™Xq0Z0Z0Z1 Z0ZXqZ0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 18 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves? A knight has at most eight legal moves.
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves?
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
Chessboard puzzle: knight’s tourIs it possible for a single knight to visit every square of the board, and return to itsoriginal location in exactly 64 moves? One of the 13,267,364,410,532 (closed &undirected) knight’s tours. [5]
8 0Z0Z0Z0Z7 Z0Z0Z0Z06 0Z0Z0Z0Z5 Z0Z0Z0Z04 0Z0–UN0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0
a b c d e f g h
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 19 / 44
A survey of puzzlesWord puzzles
Logic puzzles
Route finding puzzles
Chessboard puzzles
Planar arrangements
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 20 / 44
Planar arrangements: Tangrams
A Chinese ivory tangram puzzle, 19th century. (Jerry Slocum, 2003 [7]).
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 21 / 44
A survey of puzzlesWord puzzles
Logic puzzles
Route finding puzzles
Chessboard puzzles
Planar arrangements
Mechanical puzzles
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 22 / 44
Mechanical PuzzlesClassification Scheme of Slocum and Botermans (1986) [8]:
Dexterity Puzzles: Rolling marble (or ball bearing) puzzles, Labyrinth puzzle.
Put-together puzzles: e.g., pentominoes, teaser puzzle, tangrams, eight queens, magicsquares, soma cube, 3d-jigsaw puzzles, puzzle rings.
Take-apart puzzles: Chinese puzzle balls, torpedo puzzle, japanese trick boxes,
Interlocking solid puzzles: wooden burr puzzles, Altekruse puzzle, Stuart Coffin’s puzzles.
Disentanglement puzzles: Chinese Rings, Torpedo Puzzle.
Sequential movement puzzles: peg solitaire, Tower of Hanoi, shunting puzzles, slidingblock puzzles, Rubik’s cube, etc.
Puzzle Vessels:
Vanishing Puzzles: Geometric dissctions.
Impossible Objects
Folding Puzzles: hexaflexagons
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 23 / 44
Dexterity Puzzle (c. 2500 BCE)
From http://puzzlemuseum.com/faqs/oldestpz.htm(Image Copyright ©1996/2000 James Dalgety.)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 24 / 44
An interlocking solid puzzle: the Altekruse Puzzle
W. Altekruse invented a 12 piece puzzle in 1890. Stewart Coffin discoverd 14, 36, and 38 piece variations.(Slocum and Botermans, 1986 [8]).
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 25 / 44
Sliding Block Puzzles
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 26 / 44
A survey of puzzlesWord puzzles
Route finding puzzles
Chessboard puzzles
Planar arrangements
Mechanical puzzles
“Impossible objects”
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 27 / 44
Impossible object 1
Author: Gary Foshee, from Slocum and Botermans, 1986 [8].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 28 / 44
Impossible object 2
Author: Gary Foshee, from Slocum and Botermans, 1986 [8].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 29 / 44
Types of GamesWord games
Games of chance
Combinatorial games
Games of decision
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 30 / 44
Types of GamesWord games
I Scrabble
Games of chance
Combinatorial games
Games of decision
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 31 / 44
Types of GamesWord gamesGames of chance
I Dicing (hazard, craps)I LotteriesI Bridge, hearts, spades, gin rummy, etc.I Poker, blackjack, rouletteI HorseracesI Royal game of Ur, senetI ParchisiI Backgammon
Combinatorial games
Games of decision
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 32 / 44
Royal game of Ur (c. 2500 BCE)
British Museum, London.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 33 / 44
Senet (c. 1250 BCE)
Queen Nefertari playing senet. Scene from the 17th Chapter of The Book of the Dead. Wallpainting, 19thDynasty c. 1290–1220 BC. Tomb of Nefertari, Valley of the Queens, Thebes, Egypt.
Photo Credit: Werner Forman / Art Resource, NY
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 34 / 44
Dice games
Two women playing with “knucklebones” (tali or astragals). Hellenistic, 330 BCE. (British Museum, London)
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 35 / 44
Card games
Georges de la Tour, The Cheat with the Ace of Diamonds, late 1620s. Louvre, Paris, (Photo: Giraudon).
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 36 / 44
Card games
Georges de la Tour, The Cheat with the Ace of Clubs, late 1620s. Kimbell Art Museum, Fort Worth, Texas.
This painting, together with its partner on the previous slide, represents what may bethe most valuable “Can you spot the difference?” puzzle on the planet.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 37 / 44
Types of gamesWord games
Games of chanceCombinatorial games
I tic tac toe, 2D, 3D, : : :I nim & hackenbushI dots and boxes, sproutsI mancala, baoI chess, chess variantsI checkers, draughtsI reversi othelloI hex, bridg-itI halma, chinese checkersI KensingtonI nine men’s morrisI go
Games of decision
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 38 / 44
Go or Wei Chi
Felice Beato (1820/25–1903/07) Playing Go. Hand-colored albumen print. Ca. 1870–1880. Museo diStoria della Fotografia Fratelli Alinari, Florence, Italy. Photo: Alinari/Art Resource, NY
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 39 / 44
Go or Wei Chi
Oldest known go board. From Arther M. Sackler Gallery, 2004 [6].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 40 / 44
Mancala
From Jean-Marie L’Hôte 1994 [3].
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 41 / 44
Boardgames from World War II
From www.bbc.uk.co
From www.dailymail.co.uk
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 42 / 44
Types of gamesWord games
Games of chance
Combinatorial gamesGames of decision
I Rock, paper, scissorsI Prisoner’s dilemmaI Russian roulette
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 43 / 44
Bibliography
[1] Tony Augarde, The Oxford Guide to Word Games, Oxford University Press,Oxford, 1986.
[2] Roger Caillois. Man, Play and Games, University of Illinois Press, Urbana, IL,1961.
[3] Jean-Marie L’Hôte, Histoire des Jeux en Société, Flammarion, Paris, 1994.
[4] Johan Huizinga, Homo Ludens, Routledge & Kegan Paul, Ltd., London, 1950.Reprinted by The Beacon Press, Boston, 1955.
[5] Brendan D. McKay, “Knight’s tours of an 8 � 8 chessboard,” Technical Report,TR–CS–97–03, Department of Computer Science, Australian National University,Canberra, 1997.
[6] Arther M. Sackler Gallery, Asian Games: The Art of Contest, Asia Society, NewYork, 2004.
[7] Jerry Slocum, The Tangram Book, Sterling Publishing, New York, 2003.
[8] Jerry Slocum and Jack Botermans, Puzzles Old & New: How to Make and SolveThem, University of Washington Press, Seattle, 1986.
Robert R. Snapp © 2010, 2014 2. Introduction to Puzzles & Games CS 32, Summer 2014 44 / 44
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