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 3/5: 翻訳:Force equality
∣A+B∣+∣B+C∣+∣C+A∣≤197.|A+B|+|B+C|+|C+A|\le197.
詳しい解説

All three 和sets lie における整数s から3 through 199, so すべてのbound はsharp.