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Let's begin this lesson with a look at

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a common single player game called eight
puzzle.

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Eight puzzle is a sliding tile game.

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The game board is a three by three square,

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with number tiles in all but one of the
cells.

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The state of the game is modified by
sliding

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number tiles into the empty space from
adjacent cells.

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Thus moving the empty space to a new
location.

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there are four possible moves in, at most
four possible moves.

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Moving empty space up, down, left or
right.

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Obviously not all these moves are possible
on all states.

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States shown on the left and right here
illustrate

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the possible moves from the state shown in
the center.

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The tile could be moved down.

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The emp, I'm sorry, the empty cell can be
moved

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down, the empty cell can be moved to the
right.

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The ultimate objective of the game is to
place the tiles in order,

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and position the empty square in the lower
right cell, as shown here.

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the game terminates after 8 moves or when
all of

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the tiles are in their right positions,
whichever comes first.

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In some versions of the game, partial
credit

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is given for states that approximate the
ultimate goal.

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With ten points being allocated for each
numbered tile in the correct position,

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and 20 points being allocated for having
the empty tile in the correct position.

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For example, the first state shown here is
worth 40 points, since

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four of the cells, the ones colored green
are in their correct positions.

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And the second stage on here is worth a
hundred points since all of the tiles

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are in their correct positions, and the
empty

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cell is in the lower right hand corner.

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Now as with other games, it is possible to
describe eight puzzle in GDL.

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Here are the rules for three puzzle, its a
version of

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eight puzzle in a two by two board without
partial credit.

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Rules for eight puzzle with partial credit
are, are very much the same,

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except they're a little more verbose, and
wouldn't easily fit on a page.

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We won't go through the details of either
rule set in

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this lesson, but it may be worth your
while to pause and

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look over the rules and be sure you
understand them.

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