That suffers from the same problem if a and b are pointers to the same thing (which was the issue in my code, since I indexed the same cell of the array).

Note that the problem is not that a and b have the same value, or even that one of them is 0, it's that a and b alias to the same memory location, effectively being two handles to the same variable.

Hmm, swaps the zero problem for a overflow/underflow one?

If you stick to multiplication and addition then the beauty of modular arithmetic ensures that over and underflow are only a problem if your final result under/overflows.

In particular you can solve the problem in this article by just subtracting the numbers from 1+2+...+n-1+n. The remainder will be your missing number (though be careful with the 1+2+...+n-1+n = n(n-1)/2 formula; division by 2 is very much not compatible with arithmetic modulo a power of 2, so divide first then multiply, or keep a running total if you want to be flexible).

Worse. The zero problem does not exist if the two variables are at different memory locations. The overflow problem of this solution always exists. Plus, if a and b are at the same memory location, it suffers from the same zero problem.

Uh,

  def swap(a, b):
      return b, a

?

Or since this is presumably python, just inline it without a function:

  (a, b) = (b, a)