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?
