10 30 points 9 1 26 points 9 1 28 points 8 2 22 points 8 1 1 24 points 8 2 26 points ... There is no need to list them one by one. There are *** 16 possible results, so at least 33 people must take the exam in order to make the scores of at least 3 people the same. (33 people because the worst case scenario is that the top 32 people have two scores in each category, so no matter what the score of the 33rd person is, there will be three people with the same score. )
I wonder if there is an easier way.