Can you give an example of a complex math problem that is easy to solve? I am working on a project presentation and would like to illustrate that it is often difficult or impossible to estimate how long a task would take. I’d like to make the point by presenting three math problems (proofs, probably) that on the surface look equally challenging.  But…


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*One is simple to solve (or prove)

*One is complex to solve (or prove) 

*And one is impossible


So if a mathematician can’t simply look at a problem and say, “I can solve that in a day, or a week, or a month, how can anyone else that is truly solving a problem? The very nature of problem solving is that we don’t know where the solutions lies and therefore we don’t know how long it will take to get there.
Any input or suggestions would be greatly appreciated.

One set that (I think) meets your requirements and for which the statements are accessible to many:


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*Prove that $\sqrt{2}$ is irrational

*Prove that $e$ is irrational

*Prove that $e+\pi$ is irrational

