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Boxes galore (Posted on 2016-02-11) Difficulty: 2 of 5
For a positive integer n, what is the largest k such that the numbers 1,2, ... ,n can be put into k boxes so that the sum of the numbers in each box is the same?

No Solution Yet Submitted by Ady TZIDON    
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Solution Possible solution | Comment 1 of 2
If k is even they can be put in k=n/2 boxes with 2 in each box:
{1,n}{2,n-1}...{n/2,1+n/2}

If k is odd they can be put into k=(n+1)/2 boxes:
solution as for the next smaller even number but put the largest number in its own box.



 


Edited on February 11, 2016, 12:16 pm
  Posted by Jer on 2016-02-11 09:20:44

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