SOLUTION: Numbers are drawn from 100 integers 1 to 100. At least how many numbers is/are drawn at random to ensure that there are two numbers whose sum is 30?

Question 1146387: Numbers are drawn from 100 integers 1 to 100. At least how many numbers is/are drawn at random to ensure that there are two numbers whose sum is 30?
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

For the sum of two different positive integers to be 30, the largest possible value for the smaller of the two is 14.

So the worst case is to draw all the numbers from 15 to 100 before drawing any number less than 15.

That's 86 numbers, from 15 to 100 inclusive, without having a sum of 30 with two of them.

Then the 87th number will be less than 15; it will match up with a number already drawn to make a sum of 30.

ANSWER: 87 numbers need to be drawn to assure that two of them have a sum of 30.
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