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Comment by Torkel | Hacker News Reader

I have a similar memory! I read about the problem in the book and worked on it for days, trying to solve it. I was in junior high at the time, and my math teacher spotted what I was doing. The teacher figured out quite quickly that it was impossible to solve. And I felt sort of dumb for not figuring out it was impossible and having a teacher prooving it :)

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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.

I wouldn't feel dumb about it. People often look at very difficult problems for a very long time before they conclude a solution is impossible and later to be disproven. I would expect this one to be any different. Yes, there are currently no known solutions, but that doesn't preclude a brilliant mind coming in down the road with a solution.

In this case, there is provably no solution. A brilliant mind can’t fight that, any more than it can prove that 2+2=5. :-)

(Yes, using the traditional definitions of all those symbols.)

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