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A Modern Treatment of the 15 Puzzle Aaron F. Archer

Summary: A Modern Treatment of the 15 Puzzle
Aaron F. Archer
1 Introduction
In the 1870's the impish puzzlemaker Sam Loyd caused quite a stir in the
United States, Britain, and Europe with his now­famous 15­puzzle. In its
original form, the puzzle consists of fifteen square blocks numbered 1 through
15 but otherwise identical and a square tray large enough to accommodate
16 blocks. The 15 blocks are placed in the tray as shown in Figure 1, with
the lower right corner left empty. A legal move consists of sliding a block
adjacent to the empty space into the empty space. Thus, from the starting
placement, block 12 or 15 may be slid into the empty space. The object of
the puzzle is to use a sequence of legal moves to switch the positions of blocks
14 and 15 while returning all other blocks to their original positions.
Loyd writes of how he ``drove the entire world crazy'', and that ``A prize
of $1,000, offered for the first correct solution to the problem, has never been
claimed, although there are thousands of persons who say they performed
the required feat.'' He continues,
People became infatuated with the puzzle and ludicrous tales are
told of shopkeepers who neglected to open their stores; of a dis­
tinguished clergyman who stood under a street lamp all through


Source: Archer, Aaron - Algorithms and Optimization Group, AT&T Labs-Research


Collections: Computer Technologies and Information Sciences