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?