Clobber is played by two players, White and Black, on a rectangular nbym checkerboard. In the initial position, all squares are occupied by a stone, with white stones on the white squares and black stones on the black squares. A player moves by picking up one of their stones and clobbering an opponent's stone on an adjacent square (horizontally or vertically). The clobbered stone is removed from the board and replaced by the stone that was moved. The game ends when one player, on their turn, is unable to move, and then that player loses.
Note that all clobber positions are all small: Since White has a legal move if and only if Black does, non-zero numbers cannot appear as values. Hence, every clobber positions has a well-defined atomic weight.
It appears that most positions have a far simpler atomic weight than canonical value. For this reason, we strongly suspect that atomic weights are the key to understanding most positions which appear in practice. Using the toolkit, I have searched all positions which can fit onto a small board for new atomic weights. See this file for the results of this search; a position is outputed if it has a ``normalized'' atomic weight which has not been outputed yet.
The second prize of $500 was awarded to J.P. Grossman. His entryand solution is available in plain text.
XXXXXXX XOXXXXX XXXXXXXThe canonical form is shown using a larger clobber position in a file you can dowload in either postscript or pdf.