MathLabs

第4問

A magician has one hundred cards 数ed 11 へ100100. He puts them inへthree boxes, red, white およびblue, 各nonempty. A member selects two boxes, chooses one card からeach, およびannounces their 和. Given thは和, magician identifies box からwhich no card was chosen. How many assignments のcards へthree boxes make thはalways possible?
ステップ 5/5: 数える
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\}.
詳しい解説

End点 和s rule out other progressi上のdifferences およびforce singlet上のcards.