Finally: An Analogy
(that works)

I’ve often found it hard to explain what is Olympiad type Maths to people.

Not anymore; I think the analogy below explains it well:

Olympiad Maths can be likened to Magic.
Its questions are like magical tricks.
And, solving it is like decoding a magician’s trick.

For example, a professor of Physics went to a magic show. There were many magicians who displayed a variety of magical illusions which were original to them.

Now, the professor knows that most (if not all) of these tricks employ some sort of ‘physics’ when manipulated (either physically or by perspective), it can cause one to be ‘tricked’.

However, figuring out what exactly happens in a magic trick often proves difficult even for this professor.

But almost certainly, if the magician discloses the modus operandi for these tricks (from his perspective – revealing the solution), the professor of physics would be able to understand it.

Likewise, a Math Olympiad problem is often difficult due to the same reason of having to figure out what ‘trick’ the problem-creator has hidden within it in order to solve it.