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9 January, 22:16

There are six professors teaching the introductory discrete mathematics class at someuniversity. The same final exam is given by all five professors. The exam score is aninteger between 0 and 100 (inclusive, that is, both 0 and 100 are possible). How manystudents must there be to guarantee that there are two students with the same professorwho earned the same final examination score?

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  1. 9 January, 23:42
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    607 students to guarantee that there are two students with the same professorwho earned the same final examination score.

    Step-by-step explanation:

    This problem is an example of the Pigenhole principle.

    The first step is finding the number of boxes and objects:

    For each score, we have a box which contains the student who got that score.

    If there were only one professor grading, there would need to be 101+1 = 102 students to ensure that that there are two students with the same professorwho earned the same final examination score.

    However, for each student, there are a combination of six to five = 6 possible combinations for a score.

    So there should be at least 6*101+1 = 607 students to guarantee that there are two students with the same professorwho earned the same final examination score.
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