perplexus.info :: General : Crossing the board

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.

Submitted by pcbouhid

Rating: 3.8000 (5 votes)

Solution: (Hide)

The best way to find a solution is to work backwards. One of many obtained by hand, since this problem is an original and I have no knowledge to program a computer to solve it (in minimum moves), is shown below with 12 pieces placed with the line horizontal-oriented and the remaining 11 with the line vertical-oriented, and that needs 39 moves. It is a little implementation after solving a 4x4 grid. The way it was found is not shown here, because the explanation would be too extensive:
+-----+-----+-----+-----+-----+ | _|_ | ___ | ___ | ___ | ___ | | | | | | | | +-----+-----+-----+-----+-----+ | | | ___ | | | ___ | | | | | | | | | | | | +-----+-----+-----+-----+-----+ | | | | | ___ | | | | | | | | | | | | | | | +-----+-----+-----+-----+-----+ | ___ | | | | | ___ | | | | | | | | | | | | +-----+-----+-----+-----+-----+ | ___ | ___ | | | ___ | XXX | | | | | | | XXX | +-----+-----+-----+-----+-----+
For minimum moves, read the computer-assisted solutions presented by Charlie and Tristan, that agreed with a minimum moves of 31.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Minimum solution	Charlie	2005-10-03 20:50:56
re: Solution	Charlie	2005-10-03 20:27:24
Minimum solution	Tristan	2005-10-03 05:27:22
Solution	Tristan	2005-10-03 05:09:01
re: solution	Ken Haley	2005-10-03 03:04:48
re: Spoiler	pcbouhid	2005-10-01 12:25:21
almost started	Percy	2005-09-30 23:41:46
solution	Josh70679	2005-09-30 22:08:24
solution -- computer assisted	Charlie	2005-09-30 21:08:44
Spoiler	Jer	2005-09-30 19:27:34

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