2. introduction to puzzles & games - uvmrsnapp/puzzles/lectures/introduction.pdf · johan...

2. Introduction to Puzzles & Games

Robert [email protected]

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


Origins of puzzles & games

Pieter Bruegel the Elder, Kinderspiele, oil on wood, 1560, Kunsthistorisches Museum, Vienna.


Origins of puzzles & games

Les Evans, Children’s Games. Poster commissioned by Play Wales (www.playwales.org.uk)


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].


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)








Play has rules.


Play is often serious.

Two categories of play:


performance)








Play has rules.




performance)








Play has rules.



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)








Play has rules.




performance)


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!



“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.



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].


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



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 riddles.I palindromes:

“Doc, note. I dissent. A fast never prevents a fatness. I diet on cod.” [1]





“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




“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




“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




“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


Word Puzzles: gmasran! anagrams

Bill Amend, The Burlington Free Press, July 3, 2005.


“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?


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



Logic puzzles

Route finding puzzles


Route finding puzzles: Mazes

The Great Vermont Corn Maze, North Danville, VT, 2005.


Route finding puzzles: Mazes

The Great Vermont Corn Maze, North Danville, VT, 2006.



Logic puzzles


Chessboard puzzles


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



8 XqZ0Z0Z0Z7 Z0Z0Z0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0Z0Z0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0

a b c d e f g h



8 XqZ0Z0Z0Z7 Z0Z0Z0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0

a b c d e f g h



8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0

a b c d e f g h



8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0™Xq0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0Z0Z0

a b c d e f g h



8 XqZ0Z0Z0Z7 Z0ZXqZ0Z06 0™Xq0Z0Z0Z5 Z0Z0Z0Z04 0ZXqZ0Z0Z3 Z0Z0Z0Z02 0Z0Z0Z0Z1 Z0Z0™Xq0Z0

a b c d e f g h


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


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


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


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 b c d e f g h


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]


a b c d e f g h



Logic puzzles


Chessboard puzzles

Planar arrangements


Planar arrangements: Tangrams

A Chinese ivory tangram puzzle, 19th century. (Jerry Slocum, 2003 [7]).



Logic puzzles


Chessboard puzzles

Planar arrangements

Mechanical puzzles


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


Dexterity Puzzle (c. 2500 BCE)

From http://puzzlemuseum.com/faqs/oldestpz.htm(Image Copyright ©1996/2000 James Dalgety.)


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]).


Sliding Block Puzzles




Chessboard puzzles

Planar arrangements

Mechanical puzzles

“Impossible objects”


Impossible object 1

Author: Gary Foshee, from Slocum and Botermans, 1986 [8].


Impossible object 2

Author: Gary Foshee, from Slocum and Botermans, 1986 [8].


Types of GamesWord games

Games of chance

Combinatorial games

Games of decision


Types of GamesWord games

I Scrabble

Games of chance

Combinatorial games

Games of decision


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


Royal game of Ur (c. 2500 BCE)

British Museum, London.


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


Dice games

Two women playing with “knucklebones” (tali or astragals). Hellenistic, 330 BCE. (British Museum, London)


Card games

Georges de la Tour, The Cheat with the Ace of Diamonds, late 1620s. Louvre, Paris, (Photo: Giraudon).


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.


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


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


Go or Wei Chi

Oldest known go board. From Arther M. Sackler Gallery, 2004 [6].


Mancala

From Jean-Marie L’Hôte 1994 [3].


Boardgames from World War II

From www.bbc.uk.co

From www.dailymail.co.uk


Types of gamesWord games

Games of chance

Combinatorial gamesGames of decision

I Rock, paper, scissorsI Prisoner’s dilemmaI Russian roulette


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.


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