You are given a board 5x5 and 24 square pieces (1x1), one of them with a cross (+) and all the others 23 with a straight line on it (25 such pieces would cover the entire board).

                   (1)              (23) 
                +-------+         +-------+  
                |  _|_  |         | _____ |
                |   |   |         |       |
                +-------+         +-------+

Place the cross-piece in the upper left corner of the board.

Your task is to find "how to put the others 23 pieces," leaving the bottom right corner free, so that once this is made, by only sliding the pieces, you can bring the cross-piece from the upper left corner to the right bottom corner (that is "free" initially).

"How to put the other 23 pieces" means what must be the orientation of the line on each one, horizontal or vertical, since those placed with the line horizontal-oriented can only slide horizontally - to the right and to the left,- and those placed with the line vertical-oriented can only slide vertically - up and down. Obviously, sliding is limited by the edges of the board.

The cross-piece is the only one that can slide horizontally and vertically.

I basically played around with a program I found a while ago called SBPSolver.  You can make a sliding block puzzle and the program will check for solvability.

I assumed some obvious pattern would work, but my solution has none. 

H=horizontal mover, V=vertical mover:

+HHHV
HVVVV
VHVHV
VVHVH
VVVH

The program finds a 49 move solution.

Posted by Jer on 2005-09-30 19:27:34