The Best Problems by Martin Gardner Martin Gardner's 100th Birthday is just about to come and I am a huge fan of his books and games. I personally loved his puzzles, like the beautiful topological puzzle Reversed Trousers:

Each end of a 10-foot length of rope is tied securely to a man’s ankles. Without cutting or untying the rope, is it possible to remove his trousers, turn them inside out on the rope and put them back on correctly?

Which are some of the best of Martin Gardner's puzzles or games?
 A: According to his son Jim, the favorite puzzle of Martin Gardner was The monkey and the coconuts:

Five men and a monkey were shipwrecked on a desert island, and they spent the first day gathering coconuts for food. Piled them all up together and then went to sleep for the night.

But when they were all asleep one man woke up, and he thought there might be a row about dividing the coconuts in the morning, so he decided to take his share. So he divided the coconuts into five piles. He had one coconut left over, and gave it to the monkey, and he hid his pile and put the rest back together.
By and by, the next man woke up and did the same thing. And he had one left over and he gave it to the monkey. And all five of the men did the same thing, one after the other; each one taking the fifth of the coconuts in the pile when he woke up, and each one having one left over for the monkey. And in the morning they divided what coconuts were left, and they came out in five equal shares. Of course each one must have known that there were coconuts missing; but each one was guilty as the others, so they didn’t say anything. How many coconuts were there in the beginning?

A: I personally like The Flight Around the World, which appeared as problem 19 in his book My Best Mathematical and Logic Puzzles:

A group of airplanes is based on a small island. The tank of each plane holds just enough fuel to take it halfway around the world. Any desired amount of fuel can be transferred from the tank of one plane to the tank of another while the planes are in flight. The only source of fuel is on the island, and for the purpose of the problem it is assumed that there is no time lost in refueling either in the air or on the ground. What is the smallest number of planes that will ensure the flight of one plane around the world on a great circle, assuming that the planes have the same constant ground speed and rate of fuel consumption and that all planes return safely to their island base?

I like to give this question to pre-calculus students because it (typically) gives them good motivation to play with fractions.
