1) A fly lands in a room that measures 30 feet (length) by 12 (width) by 12 (height). When his IQ rises, he finds himself on the end wall, 1 foot from the ceiling, 6 feet from each side. He spots a female fly on the opposite end wall, 1 foot from the floor and 6 feet from each side. To impress the lady, he wants to walk to her by the shortest path. How far must he walk?
2) Take a chessboard and remove two squares from opposite corners. Divide the rest of the board into oblongs that are 2 squares long and one wide. Or can you?
The answers to August’s puzzles were supplied in the August issue.
Here are the answers to this month’s puzzles:
1) Picture the scene in 2 dimensions. We have 4 rectangles, each immediately above the other, and each 30 by 12. To the left of the second from the top, is a square that is 12 by 12. To the right of the bottom rectangle is another square the same size, ie 12 by 12. This is the room reduced to 2 dimensions. We can now draw the straight line which the fly must walk. We can also construct the right-angled sides of which the straight line is the hypotenuse. The triangle’s sides turn out to be 24 by 32 by 40, which is the familiar 3-4-5 right-angled triangle. Therefore, 40 feet.
2) The board’s 64 squares alternate white and black. This means that opposite corners are the same colour. When you remove two white or two black squares, you leave an unbalanced set of pairs behind. Oblongs (2 squares by 1) always contain two colours and therefore there will always be two white or two black squares left over, the opposite colour from the one you took.
