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A math contest is made up of 52 multiple choice questions each worth either 0 (if wrong or no answer) or 1 (if right). How many students must write the test to be sure that at least 39 have the same final score?

 Jun 22, 2020
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There are 53 different scores that a student can get:  0, 1, 2, 3, ..., 51, 52.

 

So, it will take 53(1) + 1 students to guarantee that 2 students have the same score.

Likewise, it will take 53(2) + 1 students to guarantee that 3 students have the same score.

And, it will take 53(3) + 1 students to guarantee that 4 students have the same score.

 

To guarantee that at least 39 students to have the same score:  53(38) + 1  =  2015.

 Jun 22, 2020

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