Well, I understood the argument in question to be: was it possible for the model to be fooled by this question, not was it possible to prompt engineer it into failure.

The parameter space I was exploring, then, was the different decoding parameters available during the invocation of the model, with the thesis that if were possible to for the model to generate an incorrect answer to the question, I would be able to replicate it by tweaking the decoding parameters to be more "loose" while increasing sample size. By jacking up temperature while lowering Top-p, we see the biggest variation of responses and if there were an incorrect response to be found, I would have expected to see in the few hundred times I ran during my parameter search.

If you think you can fool it by slight variations on the wording of the problem, I would encourage you to perform a similar experiment as mine and prove me wrong =P