(In reply to
Proving uniqueness by Steve Herman)
Steve,
"2 10 12 11 < odd number not largest, so no more possibilities starting with 2" should have been "2 8 10 11 < fail, prime"
2+10+12+11 = 35, which fails conditions (i), (iii) and  with the assumed definition that "the middle two" refers to the two numbers in the sequence of the four positive integers ascending (or descending)  (iv).
4 8 10 9 and 6 8 10 7 are easily discarded from consideration as are the sets of integers summing to 31 where three of the numbers are odd andor where the difference between the two middle numbers is not two.

Posted by Dej Mar
on 20150318 22:52:37 