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 3/5 步:译文:Force equality
∣A+B∣+∣B+C∣+∣C+A∣≤197.|A+B|+|B+C|+|C+A|\le197.
详细分析

All three 和sets lie 中整数s 从3 through 199, so 每个bound 是sharp.