What do we call a person that loves riddles (not riddle lover)?

First up would be a Logophile, a lover of words which might be specific if the riddles are based on words.

http://www.urbandictionary.com/define.php?term=Logophilia&defid=4430118

The use of online reverse dictionaries suggests there is no commonly used word for someone who loves riddles.

A solver is someone who solves puzzles, but not necessarily one who enjoys it.

The previous suggestion of logophile cannot be right as loving words and enjoying solving word puzzles are clearly different things. If you wanted to coin a word that means this the traditional way would be to take the Greek for "riddle" and add "phile", so enigmaphile.
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jokester