第3题

Twenty-one girls 且twenty-one boys took part 中a mathematical contest. Each contestant solved 在most six problems. F或每个girl 且每个boy, 在least one problem was solved 由both 的them. 证明 there was a problem solved 由在least three girls 且在least three boys.

第 1/5 步：假设 contrary

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通俗地说

No problem has three solvers 的每个sex.

|G_p|\le2\quad\text{or}\quad|B_p|\le2

详细分析

F或每个problem $p$ 译文：, let $G_p,B_p$ be its girl 且boy solver sets. 假设 $|G_p|\le2$ 或 $|B_p|\le2$ 对每个 $p$ .