第3問

Twenty-one girls およびtwenty-one boys took part におけるa mathematical contest. Each contestant solved でmost six problems. Fまたは各girl および各boy, でleast one problem was solved によりboth のthem. 証明せよ there was a problem solved によりでleast three girls およびでleast three boys.

ステップ 5/5: Contradict count

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ざっくり言うと

Every cell belongs へone のtwo classes.

441>210+210

詳しい解説

Every labelled cell has a problem を伴うでmost two girls またはでmost two boys, so $441\le N_G+N_B\le420$ , a contradiction. よって some problem has でleast three girls およびでleast three boys.