## Minimize Product

Consider the following game. In front of you is a stack of 10 cards printed with the numbers 0 through 9, one per card. The stack is shuffled and, sight unseen, you draw a number from the top. You look at the number and place it somewhere in the multiplication equation below. You then draw another number, look at it, and place it somewhere else in the equation. You do that two more times, until all four slots are filled. Once a digit is placed, it can’t be moved, and it can’t be drawn again because it’s no longer in the stack. Your goal is to build a multiplication equation with the lowest possible product. What is the optimal strategy? And how much of this game is luck and how much is skill? In other words, how much does the expected product under the optimal strategy differ from simply placing the cards randomly? [Solution]

## Picnic Chances

On a lovely spring day, you and I agree to meet for a lunch picnic at the fountain in the center of our favorite park. We agree that we’ll each arrive sometime from noon and 1 p.m., and that whoever arrives first will wait up to 15 minutes for the other. If the other person doesn’t show by then, the first person will abandon the plans and spend the day with a more punctual friend. If we both arrive at the fountain at an independently random time between noon and 1, what are the chances our picnic actually happens? [Solution]