Markers can move forward one square, or can jump over a marker of either colour if there is an empty square to land on.
Markers are not removed from the board if jumped.
You DO NOT have to alternate moving black and white markers.
The x's move E or S and o's move N or W and the goal is to make the x's and o's change places in these two board positions and in the general case.

Easy:

+-+-+-+    N
|x|x|x|  W + E
+-+-+-+    S
|x| |o|
+-+-+-+
|o|o|o|
+-+-+-+


Medium:

+-+-+-+-+-+
|x|x|x|x|x|
+-+-+-+-+-+
|x|x|x|x|x|
+-+-+-+-+-+
|x|x| |o|o|
+-+-+-+-+-+
|o|o|o|o|o|
+-+-+-+-+-+
|o|o|o|o|o|
+-+-+-+-+-+

Consider the medium case (the small is similar enough).

The center row is the key.  It looks just like the 1D version of this problem.  If this row were all blanks, the five columns would also be 1D versions. 

Think of solving the center row as usual except the first time each of the squares is a blank use the opportunity to solve that column.

It wasn't asked, but the total number of moves would just be 6 times the number required for a simple xx_oo problem.  (The easy would take 4 times the number required for x_o 4*3=12)

Posted by Jer on 2006-06-07 11:57:32