Because of this, we need to choose 15 integers in such a way that we can ensure that when they are divided by 14, at least two of them will provide the same residual.
In order to be sure that at least two of them have the same remainder when divided by 14.
Generally, If you divide a number by 14, the result is a fraction. There are 14 remainders that might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and, 13.
So if we pick a number and divide it by 14, the remainder can be one of 14 (0 memory 13). So if we select 14 numbers, we have the option to select 14 unique memories ranging from 0 to 13.
Finally, if we choose another integer, we will have the same reminders according to the drawer principle, because there are only 14 reminders and 15 > 14.
Therefore, we should choose the number of 15 so that at least two numbers have the same remainder when divided by 14.
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