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 videothis video Launay givegave an example, namely :A non-terminating game of Beggar-My-Neighbor https://www.youtube.com/watch?v=knyQyV4aXrA(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?