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 \(S\)?
+128406 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
