A word for something impossible or near impossible to do but fun to try

Question

A word that describes something impossible or near impossible to do but fun to try. One example I can think of is trying to lick one's elbow. A contortionist can do it but not everyone else. We sure give it a try despite knowing we can't do it.

Gonja · Answer

Perhaps the word is not specific enough, but I'd simply suggest challenging.

Something challenging is demanding, so perhaps it doesn't quite stretch to being "near impossible", however a challenge suggests something which is "fun to try". I suppose it depends whether you are looking for an obscure or common word. HTH

Shashi Kumar Raja · Answer

You can use Conundrum or Enigma to refer to difficult but interesting problems.
As per google-

conundrum- confusing and difficult problem or question.
a question asked for amusement, typically one with a pun in its answer; a riddle.

user254495 · Answer

Your endeavors are futile. Such a word simply does not exist.

Carmine Bokesch · Answer

If referencing Sisyphusical, the word origin coming out of Sisyphus. The defining should be roughly, though most accurately with the following: 
  An impossible task to accomplish, yet repeatedly attempted as that of a challenge, with demanding physical exertion. Mostly that as being damned to repeat attempting for an eternity.

A word for something impossible or near impossible to do but fun to try

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