Solution to July's puzzle: Calculating the Arithmetic Maximum
As a reminder, last month's puzzle was: Given two input values m and n, calculate the greater of the two using a mathematical expression (no programmatic flow/case elements). The solution formula looks like this: (m+n)/2 + abs(m-n)/2. If you think about it, the greater of two values is their average plus half their difference. The average of two values is equal to the smaller value plus half the difference between the two. So, the average plus half the difference is equal to the smaller plus two times half the difference, which of course is the greater of the two.
August's puzzle: Covering a Chessboard with Domino Tiles
You have a chessboard with two missing corners as Figure A shows (red squares represent the missing corners). You have 32 domino tiles, each with a size of exactly two squares. Can you cover all the remaining 62 squares of the chessboard with domino tiles without covering the missing corners? If the answer is yes, suggest an arrangement of the domino tiles. If the answer is no, logically prove that it's impossible.