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Divide et impera part two (Posted on 2015-08-26) Difficulty: 3 of 5
Divide et impera asked to divide the set of integers from 1 to 15 into two subsets A & B, so that the sum of the numbers in A equals the product of the numbers in B.

Instead of an upper limit of 15, use n to stand for any positive integer.

Find, with proof for what values of n the task is possible?

No Solution Yet Submitted by Jer    
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solution Comment 2 of 2 |
Charlie's data points the way to a solution.

If n=odd, B=1, (n-1)/2, (n-1).   

If n=even, B=1, (n/2)-1, n.  

Since Sum(A)+Sum(B)=(n*(n+1))/2 only a little algebra is needed.

This method clearly doesn't get all solutions but it shows solutions exist except for n=1,2,4. 

  Posted by xdog on 2015-08-26 18:26:37
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