Yes, that's the same logic I used to force the one. Nice C code. Your critique of that Excel code is right on the money as well.
This has multiple answers I suppose
One which I got ....
( 9/36) + (7/28) + (5/10) = 1
One with java program
9/12+5/34+7/68 = 1
You added a zero to the problem for the first solution. Can you post your code?