puzzled? - is a ``fun'' talk in beamer possible? · puzzled? is a “fun” talk in...
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Puzzled?Is a “fun” talk in Beamer possible?
Sho Uemura
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Here’s a useless outline
Some cute puzzlesSome tricky puzzlesFour equivalent boring puzzlesSome annoying puzzlesAn infinite unsolvable puzzle
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Puzzle boxes
200 years old (Japan)
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Art puzzles
Inspired by puzzle boxes but with a much wider variety of designelementsAnnual competitions:http://www.puzzleworld.org/designcompetition/
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Six-piece burrs
200 years oldDemo: http://www.research.ibm.com/BurrPuzzles/B6JM9.html
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DisentanglementSpatial reasoning puzzlesThese pictures are boring
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Chinese rings
2000 years old (China)Design enforces these rules:
I Can only manipulate rings up to the first ring on the handle, or theone after it
I Cannot manipulate a ring if the previous ring is off the handle
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Equivalent puzzles
Equivalent to staircase puzzle and Spinout; similar to Tower ofHanoi
I Spinout demo: http://www.puzzles.com/products/SpinOut/PlayOnline.htm
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Recursion and Gray codesPuzzle is recursive (to solve the n-ringpuzzle, first solve the n − 1-ring puzzle)Gray codes: sequences of binary numberswhere successive numbers differ by one bit
I Usually generated recursively:coincidentally this means Gray codescorrespond to solutions of Chinese ringspuzzle
Relationship between Chinese rings andbinary numbers discovered by ÉdouardLucas (inventor of Tower of Hanoi)
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Jigsaw puzzlesTraditional jigsaws are O(n2) search problems (each edge has aunique match)
I Boring unless you’re the government (DARPA Shredder Challenge)Tetravex is hard (many matches→ nonlocal) — NP-complete
I “Eternity II” puzzle (16x16 Tetravex puzzle, rotations allowed)remains unsolved (despite $2M prize July 2007—end of 2010)
“Tetravex tiles” were originally called Wang tiles in formal logicTiling problem: given an finite set of Wang tiles and infinite supplyof each can you tile an infinite plane?
I Undecidable: equivalent to halting problem for a Turing machine
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Aperiodic tiling
This implies there must exist “aperiodic tile sets” that can tile theplane, but can’t form periodic patterns (otherwise you couldsearch for periodic tilings)Below: aperiodic Wang tiles, Penrose tiles2011 Nobel in chemistry awarded for discovery of quasicrystals
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Links
http://www.research.ibm.com/BurrPuzzles
http://www.johnrausch.com/PuzzlingWorld/
http://visualiseur.bnf.fr/CadresFenetre?O=NUMM-3943&I=188&M=tdm
http://www.tavernpuzzle.com/
http://www.puzzleworld.org/PuzzleWorld/
http://www.puzzles.com/products/spinout.htm
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