Minimum Participant

A test consisting of 20 questions. if the answer is correct then +2, if the answer is left empty then 0 and if the answer is wrong then -1. how many minimum participants must participate to guarantee so that there are three equal scores.

125 127 121 123 None of these

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2 solutions

Achmad Damanhuri
Apr 2, 2019

Min Score = -20, Max Score = 40. Except for score (39). So there are (1+40-(-20))-1=60 holes and there must be 121 pigeons to guarantee there are three equal score.

Why is 1 also added to get 60 holes?

Mr. India - 2 years, 2 months ago

+1 for the score 0. The total distinct integer from -20 to 40 is 40-(-20)+1 isn’t it. Try to count distinct integer from -5 to 5.

Achmad Damanhuri - 2 years, 2 months ago

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Understood, thank you!

Mr. India - 2 years, 2 months ago
Kyle T
Apr 3, 2019

Our answer is going to be in the form (2 * (# of distinct scores)) + 1
This is using the pigeonhole principal
There are 60 distinct final scores (-20 through 40, except 39), meaning our answer is ((2 * 60)+1) = 121

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