conundrum
A very tricky problem or puzzle that’s hard to solve.
A conundrum is a confusing and difficult problem that seems to have no good solution, or a puzzle that's surprisingly hard to figure out. The word suggests being genuinely stuck, where you can't see a clear way forward.
Imagine you want to earn money for a new bike by mowing lawns, but you need a working lawnmower first, which costs money you don't have. That's a conundrum: you need money to make money. Or consider a school assignment where you're told to write about your favorite book, but you have three favorites and can only choose one. Each choice feels wrong somehow. That's a conundrum too.
The word has a slightly playful feel, even when the problem is serious. Scientists face conundrums when their experimental results don't match their theories. Mathematicians tackle conundrums that have stumped people for centuries.
A conundrum differs from an ordinary problem because it seems to trap you: every solution creates a new problem, or the question itself seems impossible to answer fairly. When your dad says, “Here's a conundrum,” before describing a tricky situation, he's signaling that finding a good answer will take some serious thinking, and maybe even then there won't be a perfect solution.