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=n^{2} 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.
(In reply to
A very tricky problem (spoiler) by Steve Herman)
shouldn't 404814.25 be 4048143.75? The former is smaller than one million, let alone 4,046,133.

Posted by Charlie
on 20120529 15:00:38 