What is the most complex chess problem? There are many chess problems and studies that are very nuanced and can take ages to properly figure out. 

What is the chess puzzle/problem with the longest (proven) solution?
If you're looking for the puzzle with the longest forced sequence, it would be this position ,which contains a win for white in 549 moves.
[FEN &quot;1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - - 0 1&quot;]

It was found by computers from the generation of 7-man endgame tablebases, and there are several similar positions with the same distance to mate.
If that seems a little extreme, then the longest mate puzzle made by a human was Otto Blathy's 'monster', which is a mate in 292 moves but contains an illegal starting position (i.e. it could never occur in a real game).
If you won't accept that, then here are the current record-holders for the longest puzzles created by a person from legal positions - A mate in 271 with 'obtrusive units' (legal, but must have come about through piece promotion, such as having two dark-squared bishops) and a mate in 267 without those. And, surprisingly, both of those were created by the same person.
As for the &quot;most variations that don't work&quot; as you stated, it's probably also the mate in 549 listed above, with the number of moves that would let the other player slip out or otherwise prolong the sequence even more.