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.
Every labelled cell has a problem 满足在most two girls 或在most two boys, so 441≤NG+NB≤420, a contradiction. 故 some problem has 在least three girls 且在least three boys.