If \(S\) is a subset of \(\{1, 2, \ldots, 100\}\) with the property that no two distinct elements of \(S\) sum to 120, what is the largest possible value of the sum of the elements of \(S\)?

Guest Jul 26, 2018

#1**+1 **

I'm not sure about this, but here's my take

Note that any two elements drawn from the set { 60, 61, 62, 63,......,98, 99, 100} will always have a sum > 120

And the set {1, 2, 3,.....,17, 18, 19} can be combined with the first set such that no two elements drawn from this "combined" set will have a sum of 120

So...the sum of the elements of this set will be :

(19)(20) / 2 + [100 + 61] * 40/2 + 60

190 + 161* 20 + 60 =

190 + 3220 + 60 =

3470

CPhill
Jul 26, 2018