第4题

A magician has one hundred cards 数ed

1

到

100

. He puts them in到three boxes, red, white 且blue, 每个nonempty. A member selects two boxes, chooses one card 从each, 且announces their 和. Given th是和, magician identifies box 从which no card was chosen. How many assignments 的cards 到three boxes make th是always possible?

第 1/5 步：Encode condition

上一步下一步

A+B,\quad B+C,\quad C+A\text{ pairwise disjoint}.

详细分析

A repeated 和 would give two possible omitted boxes.