The diagram shows a restricted chess board with three black knights and three white knights. Your goal is to move the pieces so that the same squares are occupied but the colors are reversed. Your first move must use a black piece.

Pieces may move only as a normal chess knight, from one corner of a 2×3 rectangle to the opposite corner. No more than one piece may occupy a single square at a time. No piece may move onto a darkened square. No other rules of chess apply.

One turn is a sequence of moves made by a single piece. Find a solution with the minimum number of turns.

Redraw the board as a large X.

<pre>

6       7
 \     /
  2   3
   \ /
    1
   / \
  4   5
 /     \
8       9
</pre>

These numbers represent the squares from the board like this:

<pre>

XX  2 XX XX XX
XX  8 XX  6  3
XX XX  1 XX XX
 4  9 XX  7 XX
XX XX XX  5 XX
</pre>

We can see that the black knights are at positions 2, 4, and 9, and the white knights are at positions 3, 5, and 6.

The folowing sequence of moves (one piece's turn per line) solves the puzzle (Turn number: starting position-intermediate positions-ending position):

1: 4-8
2: 2-1-4
3: 3-7
4: 6-2-1-3
5: 4-1-2-6
6: 5-1-2
7: 9-5-1-4
8: 3-1-5-9
9: 7-3-1-5
10: 4-1-3-7
11: 8-4-1-3
12: 5-1-4
13: 3-1-5
14: 7-3

That should do it.

Posted by Erik O. on 2004-12-10 21:29:06