There are some students who participate in the Math Olympiad. Each of them has to do 10 math problems. The points are as follows: the contestants get 2 points for each correct answer, 1 point for each blank answer, and 0 points for each wrong answer. At least how many students are there to ensure that two of them get the same score?
Math Olympiad question
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mmm4444bot
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Can you share any thoughts?
Have you finished your last exercise? Good suggestions/comments there.
Dr.Peterson
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It doesn't say in the problem.
Steven G
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Can you score exactly 0 points? (yes, answer all 10 questions and get them all wrong)
Can you score exactly 1 point? (yes, answer 9 which are all wrong and leave 1 problem blank)
Can you score exactly 2 points?
Can you score exactly 3 points?
Can you score exactly 4 points?
...
Can you score exactly 20 points?
Can you score exactly 21 points?
Can you score exactly 22 points?
...
Can you score exactly 1 point? (yes, answer 9 which are all wrong and leave 1 problem blank)
Can you score exactly 2 points?
Can you score exactly 3 points?
Can you score exactly 4 points?
...
Can you score exactly 20 points?
Can you score exactly 21 points?
Can you score exactly 22 points?
...