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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
avatar+87537 
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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

 

 

cool cool cool

CPhill  Jul 26, 2018

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