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