Cut off the 4 corner squares of the 3x4 rectangular grid.
Now place the digits 1 to 8 in the remaining 8 squares in a way.
such that no adjacent numbers are in adjacent squares (horizontally, vertically, or diagonally).
How many different solutions exist?
The stars, above, mark the positions for digits.
The middle two positions are each adjacent to all but one of the other available positions, so only 1 and 8 can go there, as each has only one other number to be isolated from.
The 2 then has to go in the only position isolated from the 1, next to the 8, and the 7 has to go opposite that, next to the 1.
The 3 then can go in either of two positions: either above or below the 1. Likewise the 6 must go above or below the 8.
If the 6 and the 3 were to be placed either both above or both below, that would mean the 4 and 5 would also be together in the other two remaining places, so whichever is chosen for the 3 (up or down), the 6 must be placed down or up respectively. This solves the puzzle, as shown in Jer's post.
Posted by Charlie
on 2013-01-31 19:37:53