MathLabs

第4题

A magician has one hundred cards 数ed 11 到 100100. 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 5/5 步:计数
A,B,C are residue classes modulo 3or{1},{100},{2,…,99}.A,B,C\text{ are residue classes modulo }3\quad\text{or}\quad\{1\},\{100\},\{2,\dots,99\}.
详细分析

End点 和s rule out other progressi上differences 且force singlet上cards.