6+19+30 = 55 appears to be the minimum value that satisifies the conditions.
6+19 = 25
6+30 = 36
I understand this combination, but how did you find this from the beginning?
well I used software but if I had to do it by hand
a) I'd be angry because this stuff tests nothing
b) I'd start by looking at perfect squares. We can quickly rule out (1,4,9)
(4,9,16) through (16,25,36) will take a bit more work to rule out
then you'll arrive at (25,36,49) which has a solution