Question 1058085: 120 students take an exam which is marked out of a 100 (with no fractional marks). No 3 students are awarded the same mark. What is the smallest possible number of pairs of students what are awarded the same mark?
Answer by LinnW(1048)   (Show Source):
You can put this solution on YOUR website! Each of 101 students receive a score of 0,1,2 ... 100
Each of the remaining 19 students receives a score that is the same score
as one other students.
For example, we could have scores in descending order of
100,100,99,99,98,98,97,97,96,96,95,95,94,94,93,93,92,92,91,91,
90,90,89,89,88,88,87,87,86,86,85,85,84,84,83,83,82,82
81,80,... 0
Notice that if we do not have 19 students with the same score
we will have less than a total of 120 students.
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