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Produce More (Posted on 2012-05-29) Difficulty: 2 of 5
Among pairs of numbers whose sum is 16, 8*8=64 is the greatest possible product. However, if we allow for a sum of 17 then there are 3 distinct ways of achieving a higher product with two positive integers: 9*8, 10*7, and 11*6 are all greater than 64.

Among pairs of numbers whose sum is 2n, n*n=n2 is the greatest possible product. However, if we allow for a sum of 2n+1 then there are 2012 distinct ways of achieving a higher product with two positive integers.

Find the minimum value of n.

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): A very tricky problem (spoiler) | Comment 4 of 5 |
(In reply to re: A very tricky problem (spoiler) by Charlie)

Charlie:


Thanks for catching this.  I missed a digit in my multiplicand.  Or maybe it was my multiplier.  This is now fixed in my original post.

Actually, I also had a more serious error.  I had missed the first pair for non-integral n, namely (n + .5) * (n+ .5).  This changed my calculations, and now I have the minimum n as a non-integer (different solution from Broll's) and the maximum n as an integer.

A much more interesting problem than I expected.  Thanks, Jer.

Steve

Edited on May 29, 2012, 3:54 pm
  Posted by Steve Herman on 2012-05-29 15:34:49

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