SlidingBlock Puzzles

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Sliding-Block Puzzles

• MAA Online Math Games
• Ed Pegg Jr., December 13, 2004

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What is a Sliding-Block Puzzle?

• a set of shapes which are placed inside a frame.
  Within that frame the shapes can be moved around
  only by sliding, with NO turning, lifting or
  jumping allowed

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Finding the hardest possible simple
sliding-block puzzle?
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Making really hard sliding-block puzzles with
just a few pieces

• Oskar van Deventer James Stephens
• ConSlide Puzzle
• Bulbous Blob Puzzle

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making a prototype of the puzzle
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Taniguchi solver
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4x5 rectangle old style sliding block puzzle

• Dad's puzzle
• the Century puzzle by John Conway

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Quzzle, the simplest complex puzzle?
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Making more difficult puzzles!!

• Supercompo 123 moves
• Super-Century 138 moves
• Century and a Half 150 moves
• HiFi 200 moves
• Pentomino Mosaics

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In February 1964, Martin Gardner Mathematical
Games column

• "These puzzles are very much in want of a theory.
  Short of trial and error, no-one knows how to
  determine if a given state is obtainable from
  another given state, and if it is obtainable,
  no-one knows how to find the minimum chain of
  moves for achieving the desired state."

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sliding-block puzzles are PSPACE-complete !!!
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Nob Yoshigahara Puzzle Design Competition !!
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References

• http//www.maa.org/editorial/mathgames/mathgames_1
  2_13_04.html
• http//www.swiss.ai.mit.edu/7Ebob/sliding-blocks.
  pdf