MathLabs

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 4/5 步：估计 labels 满足few boys
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通俗地说

Exchange girls 且boys.

NB≤21⋅10=210N_B\le21\cdot10=210
详细分析

The same argument 满足girls 且boys exchanged gives NB≤210 N_B\le210.