how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 11?

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09-12-2022
Mathematics

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how many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 11?

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sydney0783 sydney0783 · Answer 1 · 2022-12-19T07:27:41-05:00

We need to start by choosing some 10 integers so that we can ensure that when they are divided by 11, at least two of the integers will give the same remainder.

The following is the explanation:

If you divide a number by 11, the answer will be a fraction. There are 11 remainders which might occur, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

If for example we choose one number and divide it by 11, there is a chance that the remainder may be any of the 11 (0 reminders 1). Therefore, if we choose 10 numbers, we will have the opportunity to pick 10 unique remainders, ranging from 0 to 10.

In conclusion, if we select one more integer, that is we pick 10 integers, then at least two of them would have the same remainder since there are only 10 remainders.

Because of this, we need to choose 10 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 11.

Please click the link below to learn more about integers:

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