These should give your brain a work out. First correct answers e-mailed to me wins you a Humboldt Mud at Old Town Coffee and Chocolates -- with me along for company. (Be still, my heart!)
Four Triangles: Arrange six wooden matches, without breaking, so they form four triangles, each side of which is equal to the length of a match. (Hints at end of column.)
Part 1: Here's a regular chess board except that its opposite corners are missing. Can you cover the board with 31 rectangular blocks, each the size of two squares? [SEE FIGURE A]
Part 2: And here's a 5 x 5 chessboard. Starting on the square marked with a dot, can an ant walk through each square once and only once (no diagonal moves, no leaving the board)? [SEE FIGURE B]
Chain Reaction: A jeweler charges $1 to cut a link and reweld it. You have four chains, each of three links. What's the least it will it cost to make them into a closed loop of 12 links? [SEE FIGURE C]
Hole in the Sphere: What's the volume remaining in a sphere that has a 2-inch-long hole drilled through its center? You may be thinking that I haven't given you sufficient information. Trust me, I have -- which could save you a lot of calculation. (The volume of a sphere is 4/3 r^3)
Largest Number: What's the largest number you can express with three integers?
Water and Wine: You have two glasses, one of which contains 10 ounces of water, the other 10 ounces of wine. Pour one ounce of water into the wine, mix thoroughly, then pour one ounce of the wine-water mixture into the water. Is there now more water in the wine or wine in the water?
Tennis Tourney: The local tennis club had 125 entrants for its annual singles elimination tournament. In the first round, 62 games were played to eliminate about half the contestants (the odd man had a bye); in the second round a further quarter were eliminated, and so on until the winner emerged. How many matches were played?
Barry Evans (firstname.lastname@example.org) is puzzling about what to write for next week's column. The collection of his first 80 Field Notes columns is available directly from him or from Eureka Books.
Four Triangles: Think "dimensions." Chess Board: Think "parity." How many of each black and white squares need to be covered? And what color will the ant end on? Chain Reaction: Suppose instead the task was to create a 12-link chain out of three chains of three links each plus three loose links? Hole in the Sphere: If you do trust me, then there must be a unique answer, no matter what the size of the hole. So why not make life easy and assume the hole's diameter is zero? Largest Number: (1) Three 9's might be a good place to start. (2) You can do better than 9 x 9 x 9: don't forget powers, e.g. 9^9 (9 x 9 x 9 x 9 x 9 x 9 x 9 x 9 x 9). (3) Which is larger, 99^9 or 9^99? Water and Wine: Imagine instead you have two equal piles of marbles, one containing ten red marbles, the other ten black. Mix them up and divide again so you've now got two mixed piles of ten marbles each. Suppose three black marbles have "contaminated" the red pile, how many red marbles are now in the black pile? Tennis Tourney: How many players were eliminated?