Too many balls! - 1
Joana has a box with 2017 balls numbered from 1 to 2017 inclusive. What is the minimum number of balls she must take out from the box to guarantee that there is at least one ball whose number is a multiple of 3 among the withdrawn balls?
Problem from OBMEP 2017
The answer is 1346.
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1 solution
First, we need to know how many numbers between 1 and 2017 are multiple of 3
Smallest number in the range which is multiple of three is 3 and the greatest one is 2016 If we divide both of them by 3, we can see how many numbers we have. (3 --- 2016) -> (1---672)
So, we have 672 of them. If Joana takes out at least 2017-672+1 balls, it is certain that at least one of them will be multiple of 3.