In a competition, there 是 a contestants 且 b judges, 其中 b≥3 是an odd 整数. Each judge rates 每个contestant as either “pass” 或“fail”. 设 k 是a 数 使得, 对于any two judges, their ratings coincide 对于在most k contestants. 证明 ak≥2bb−1.
设 N be 数 的triples consisting 的a contestant 且an unordered pair 的distinct judges who give same rating. Every pair 的judges agrees 上在most k 译文： contestants, so N≤k(2b)=2kb(b−1).