# The Logical Puzzle - 19 Aug 2005

### Solution to August's Puzzle: Covering a Chessboard with Domino Tiles

In last month's puzzle, there was a chessboard with two missing corners that had been black. Using 32 domino tiles, each with a size of exactly two squares, you were asked whether it's possible to cover all the remaining 62 squares of the chessboard with domino tiles, without covering the missing corners. To solve this puzzle, you need to consider that because the two missing corners had been the same color (i.e., black), you have 32 white squares and 30 black squares left. Each domino tile covers exactly two squares—one black and one white. Any layout that you come up with will cover the same number of squares from each color. Therefore, it's impossible to completely cover all 62 remaining squares of the chessboard with domino tiles.

### September's Puzzle: The Missing Buck

Three people arrive at a hotel and ask to share a room. The charge is \$30, so each person chips in \$10. Later on, the hotel receptionist finds out that he overcharged them by \$5. Realizing that he can't evenly split \$5 between the three guests, he pockets \$2 and gives each guest \$1 back. However, the receptionist finds it hard to sleep that night because the numbers don't seem to add up. Each guest eventually paid \$9, and \$9 x 3 + \$2 = \$29. Where's the missing buck?

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