I am very interested by problem in mathematics which are difficult (go at least 10 years without a resolution, say) but which have a solution that is short and elementary.

In this video Launay gave an example, namely A non-terminating game of Beggar-My-Neighbor (incorrectly claimed in Winning Ways to have been solved a long time ago).

Launay calls these problems "Pokémon problems": difficult to catch but once you catch them, they're in your pocket.

Question: What are other problems like this?