Problem 4
A magician has one hundred cards numbered to . He puts them into three boxes, red, white and blue, each nonempty. A member selects two boxes, chooses one card from each, and announces their sum. Given this sum, the magician identifies the box from which no card was chosen. How many assignments of the cards to the three boxes make this always possible?
Step 5 of 5: Count
Detailed analysis
Endpoint sums rule out the other progression differences and force the singleton cards.