Duncan found a set of positive integers less than $50$ such that no two of them sum to a multiple of $7$. What is the largest number of integers in Duncan's collection?

[1, 2, 3, 7, 8, 9, 10, 15, 16, 17, 22, 23, 24, 29, 30, 31, 36, 37, 38, 43, 44, 45]==22 such integers

They are ALL < 50

No two of them sum up to a multiple of 7

They form: 22 C 2 ==231 sums and non of them is a multiple of 7.