[Normal_gaussian]

There are a whole class of problems that revolve around the incompatibility of operations based on the primes (in this case 2 and 3). When you attempt to solve, and fail to solve, any of them you are likely to gain an instinctive appreciation for all of them - the kind of appreciation that would lead a maths teacher to a proof to the contrary very fast.

It should be noted that if the teacher had had the foresight (often a big ask) to simply tell you they suspected there was no solution, which is often the case with such problems presented as they are, and that you should attempt a proof alone, you would likely not feel so bad about not spotting it immediately.