[malisper]

if the three numbers are a, b, and c, then either a+b=c, a+c=b, or b+c=a

[bena]

And they must all be positive integers.

So A + B = C and A + C = B. But we know that A + B = C, so we can replace C with (A + B). So we know that A + A + B = B.

So 2A + B = B. Or 2A = 0.

And this holds any way you slice it.

Even if you were to try and brute force it.

A = 1

B = 2

Then C = 3. But A + C has to equal B. That's 1 + 3 = 2? That's not true.

I don't see a case where you can add to the sum of two numbers one of the numbers and get the other number.

I'm guessing that's a misreading of the problem. Because it looks like the third number is the sum of the first two.

[refulgentis]

One of the cases has to be true, not all 3. (as you show, they're mutually exclusive for positive integers) i.e. "either" is important in the parent comment.