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all of you have probably seen the moving number/picture puzzle. The one where you have numbers from 1 to 15 in a 4x4 grid, and are trying to get them from random starting position to 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 My girlfriend or some of my non-programmer friends can solve this with some mumbo-jumbo magic, that they can't explain to me. I can't solve the puzzle. The most promising approach I have found out is to solve first row, then I'd get 1 2 3 4 X X X X X X X X X X X then first column without touching solved cells 1 2 3 4 5 X X X 9 X X X 13 X X then second row to 1 2 3 4 5 6 7 8 9 X X X 13 X X then second column 1 2 3 4 5 6 7 8 9 10 X X 13 14 X the problem is, that remaining X (random) tiles are sometimes in unsolvable position and this is where my solution fails. But I feel as if I'm on the right path. My program does the solving of specified row/column by trying to get number X to specified position without messing up the correct cells, if possible. But it can't do the last 3 tiles on 2x2 grid. What am I missing?

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