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I've only just started to study a degree in Mathematics and I find it extremely satisfying to have a seemingly easy question that is incredibly difficulty or tricky to work out. I've looked into heaps of competition exams (although they aren't really what I'm looking for - seeing that they don't usually seem easy). A good example are the so called 'Coffin Problems' (you can find some here).

I'm reaching out here to hear any original problems that fit into this category. Here's an example of mine:

If $\sin \theta + \cos \theta + \tan \theta = -1$, find the values of $\sin \theta + \cos \theta - \tan \theta$ for $\theta$ not being a multiple of $\pi$.

From memory, one of the answers I got for that problem was $\sqrt{2}-1$, although I know that there are plenty of other answers.

Also, I appologise if this question does not belong on this site. This was the only site I thought of to ask a question like this. Thanks!

LogicAndTruth
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There are some questions that are easy to comprehend, but for which we have no solution yet, period. I don't know if that is what you're looking for, or if you only want problems that do have a solution, but that hard to find, but here are some problems of the first kind:

Goldbach Conjecture: Every even number greater than $2$ is the sum of two prime numbers

E.g. $4=2+2; 6=3+3; 8=5+3$, etc.

We can comprehend this question immediately ... but no one knows the answer. We suspect it's true, but there is no proof yet.

https://en.wikipedia.org/wiki/Goldbach%27s_conjecture

Collatz Conjecture: Take any whole positive number. If ity is even, divide by $2$. If odd, multiply by $3$ and add $1$. Keep doing this. The Collatz Conjecture is that if you keep doing this, you'll always at some point end up with 1.

Example: $7\to 22\to11\to34\to17\to52\to26\to13\to40\to20\to10\to5\to16\to8\to4\to2\to1$

Again, easy to comprehend, but no one knows if it's true or not.

https://en.wikipedia.org/wiki/Collatz_conjecture

Bram28
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