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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?

 Sep 17, 2022
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[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.

 Sep 17, 2022

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