Truel

A truel is a three-way duel. The three participants take turns firing one shot at whichever opponent they choose, until only one is remaining. Allison, Ben, and Chase are in a truel, and have varying degrees of accuracy: Allison has…

Reroll the Die

Suppose there is a game in which you roll a fair, 6-sided die and win dollars equal to the outcome of the roll. How much would you expect to win on average? Suppose, if you don’t like the outcome of…

Inscribed Squares

Above are two identical isosceles right triangles containing two inscribed squares. In one, a perfect square has been inscribed such that two sides line up with the two legs of the right triangle. In the other, a perfect square has…