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 Crossing the board (Posted on 2005-09-30)
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.

 See The Solution Submitted by pcbouhid Rating: 3.8000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Minimum solution Comment 10 of 10 |
(In reply to Minimum solution by Tristan)

Indeed there are six solutions with 31-move paths. Three of them are

`+-???||-??-||-??-|-|??-|Odrurdrdrddluruldluruldluruldlur---------------------- +-???||-??-|-|??-|-|??|-Odrdrurdrddluruldluruldluruldlur---------------------- +-???|-|??-|-|??|--|??|-Odrdrdrurddluruldluruldluruldlur`

The other three are obtained by flipping each of these about the main diagonal, thereby mapping any horizontal at row r, column c, to a vertical at row c, column r, and similarly changing verticals to horizontals in the move.  The paths then change by changing d, r, u and l to r, d, l and u respectively.

 Posted by Charlie on 2005-10-03 20:50:56

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