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.
Fix a boy. At least one 的h是在most six problems 是solved 由在least three girls, 由于 6⋅2<21. 故 在most five 的h是problems have 在most two girl solvers, contributing 在most 5⋅2=10 cells. 因此 NG≤210.