Question 184
In an oral exam, there are 10 examiners and 1024 contestants. Each contestant will be asked by each examiner and receive a result of either “pass” or “fail”. It is given that for any two contestants, there is some examiner who will rate one passed and the other failed. Two contestants are said to be “separative” if they have different results by at least 3 examiners. Prove that it is possible to select 24 pairwise separative contestants.