random – Steve Miller's Math Riddles

Is this Seat Taken?

100 people are waiting to board a plane. The first person’s ticket says Seat 1; the second person in line has a ticket that says Seat 2, and so on until the 100th person, whose ticket says Seat 100. The first person ignores the fact that his ticket says Seat 1, and randomly chooses one…

How to Pick Up the Bucks

You have 2N coins of varying denominations (each is a non-negative real number) in a line. Players A and B take turns choosing one coin from either end. Prove A always has a strategy that ensures he end up with at least as much as B. Communicated by A. Roy

FRUITful Problem

There are three boxes. One has apples, one has oranges and the other has apples and oranges. The boxes are labeled wrong so that no label is correct. Sue opens just one box, and without looking in the box, takes out one piece of fruit. She looks at the fruit and immediately labels all the…

Don’t Flip Out, Square!

A square has a quarter in each corner. You are blindfolded and must get all quarters to be heads up or all to be tails up. You will be told when you have done this. You may flip however many you want, then ask if you are done (this constitutes a turn). The square is…

Chess Problem

Consider a 5×5 chess board. Is it possible to place five queens on the board such that three pawns can safely be placed on the board? In other words, by carefully choosing where to place the five queens, can you arrange it so that there are three squares on the board that none of the…

Bridge Over Troubled Students

There are four men who want to cross a bridge. They all begin on the same side. You have 17 minutes to get all of them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either one or…

What’s My Card?

A student is given five random cards from a standard deck of 52 cards. He must choose four cards to reveal to his professor and the order in which to reveal them; his goal is to reveal four cards in such a way that the professor knows what the fifth hidden card is. How does…