Motorola M500 User Manual download pdf (Page 14)

Page 12 M500 180

Solution 178.6 – Ten blocks

Ten pieces of various sizes slide round a board in the obvious

manner. Move the large square from the middle-left of the array

to the middle-right.

Dick Boardman

Denote the pieces by letters, as above, and divide

the board into 20 numbered squares, opposite.

Piece A originally covers squares 1, 2, 5, 6 and the

object of the puzzle is to move it to the position

that occupies squares 13, 14, 17, 18.

0 4 8 12 16

1 5 9 13 17

2 6 10 14 18

3 7 11 15 19

Initially, the method used was a breadth-ﬁrst search in which all the new

positions resulting from a given position were placed on a stack. Positions

which occurred before, positions which are symmetrical to previous positions

and positions in which pieces of similar shape are swapped were rejected.

This method found a solution in 106 moves after processing about 12000

positions.

Later versions of this program use a ‘best-ﬁrst’ search method in which

the stack is searched for the node with the highest value and the next posi-

tions are generated from that. Positions with the same value are processed

sequentially. This reduces the number of processed positions to about 5000.

The value of a position is taken as the number of the ﬁrst column containing

piece A.

1 2 ... 9 10 11 12 13 14 15 16 17 18 19 ... 31 32

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Motorola M500 User Manual Page 14