By Philip Hamilton Williams, Evening News and Post, 1895. White to mate in two moves.
Mount Everest rises 29,029 feet above sea level, and Ecuador’s volcano Chimborazo rises only 20,702 feet. But because Earth bulges at the equator, Chimborazo is actually farther from the center of the planet. If we could connect the two peaks with a water pipe, in which direction would the water flow?
Imagine two concentric roulette wheels, each divided into 100 sectors. Choose 50 sectors at random on each wheel, paint them black, and paint the rest white. Prove that we can now position the wheels so that at least 50 of the aligned sectors match.
A carnival worker is asked to paint the deck of a carousel. Because the center of the carousel is occupied by machinery, he can’t measure its diameter or even its radius. The best he can do is to take the measurement shown in green, which is 42 feet.
He’s explaining this apologetically when his supervisor stops him. “That’s all the information we need,” he says. “That’s enough to tell us how much paint to buy.”
How did they go about it?
Alice gets a rocket-powered pogo stick for her birthday. She jumps 1 foot on the first hop, 2 feet on the second, then 4, 8, and so on. This gets alarming. By judicious hopping, can she arrange to return to her starting point?
You’re alone on a desert island and want to lay out a course for some snail races. Unfortunately, you have only an 8.5 x 11 inch sheet of paper. How can you use it to measure exactly 3 inches?
You and a friend are playing a game. Between you is a pile of 15 pennies. You’ll take turns removing pennies from the pile — each of you, on his turn, can choose to remove 1, 2, or 3 pennies. The loser is the one who removes the last penny.
You go first. How should you play?
I release a fish at the edge of a circular pool. It swims 80 feet in a straight line and bumps into the wall. It turns 90 degrees, swims another 60 feet, and hits the wall again. How wide is the pool?
Fifty-five chameleons live on a tropical island. Thirteen are green, 19 are brown, and 23 are gray. Whenever two chameleons of different colors meet, both change to the third color. Is it possible that all 55 chameleons might eventually be the same color?
Fourteen ladders stand in a row. At the foot of each ladder is a monkey; at the top is a banana. Festooning the ladders are an arbitrary number of ropes. Each rope connects a rung on one ladder to a rung on another, but no rung receives more than one rope.
At a signal all 14 monkeys begin climbing. If a monkey encounters a rope it climbs along it to the other end and then continues climbing upward. Show that every monkey gets a banana.
You have 13 reels of magnetic tape, one empty reel, and a machine that will wind tape from a full reel to an empty one, reversing its direction. You need all 13 tapes reversed on their original reels. Show how this can be done, or prove that it’s impossible.
By H. Van Beek, Chemnitzer Wochenschach, 1926 (special prize). White to mate in two moves.
A tank of water has two holes of equal area, one at top and one at bottom. The top one leads to a downspout, so that both holes discharge their water at the same level. Ignoring friction, which hole produces the faster flow of water?
You actually don’t need to know the physics in order to solve this — it yields to an insight.
Foaled in 1773, this thoroughbred racehorse bore the unlikely name of Potoooooooo.
How was it pronounced?
A shoelace is lying on the floor, and I’m too nearsighted to see how the lace crosses itself at points A, B, and C. If I pull on the ends, what’s the probability that it will produce a knot?
In 1908, two years before drawing against Emanuel Lasker for the world chess championship, Carl Schlechter published this problem in the Allgemeine Sportzeitung. White to mate in two moves:
What location on this line segment has the smallest sum of distances to the labeled points?