Let a = {1, 2, 3, 4, 5, 6, 7, 8, 9}. n distinct integers will be chosen from a. how big does n have to be
to ensure that the sum of two of the chosen integers is 9?

Partition the set A into 4 subsets: {1, 8}, {2, 7}, {3, 6}, and {4, 5}, each consisting of two integers whose sum is 9. If 5 integers are selected from A, then by the Pigeonhole Principle at least two must be from the same subset. But then the sum of these two integers is 9.

No solution : there is no number of boxes that she bought

I’m pretty sure the answer is a