This is actually funny. I would argue the solution is invalid, except that due to mortality it actually works. The problem lies in the assumption about how Ali

This is actually funny. I would argue the solution is invalid, except that due to mortality it actually works. The problem lies in the assumption about how Alice thinks. The set of integers is countably infinite, so your probability to guess a specific number N is zero if the distribution is uniform (e.g. there isn't a higher likelihood of picking "smaller / closer to zero" numbers.) [1] But because it would take a lot of mortal time to describe arbitrarily large numbers, you MUST assume that because Alice is mortal, she'll pick a number she could describe in her lifetime. Therefore, the question is not valid. Alice does not truly have a domain over all the integers to choose from. She only has the ability to pick numbers she could write down on a slip of paper within her lifetime. Since the paper is limited in how much information it can contain anyway, it therefore cannot represent any arbitrary integer from the infinite set. So the question is re-written: Alice picks two integers from a finite pool.. [1] https://math.stackexchange.com/questions/30619/probability-of-picking-a-specific-value-from-a-countably-infinite-set https://math.stackexchange.com/questions/30619/probability-o...