As always in a good story, I'd say it depends.
Is the riddle itself relevant to the story? Or, is the method of solving it relevant to the story? If so, I think it's fair to show the reader how the protagonist solves the riddle, even if it ends up boiling down only to something like he thought about it for a moment before it dawned on him that these astronomically centered people probably meant circles around the sun, making it obvious that they were somehow referring to leap years.
If the riddle or method of solution isn't relevant to the story, then I'd leave it out altogether. The protagonist encounters some undecipherable (by him/her) symbols, which there is no need to explain further, next to a lock, and he starts thinking through what he knows of the people who left it or even just tries combinations at random. Exactly what works then would depend on the established backstory - obviously it can't be completely indecipherable if he is the established expert on the people or culture, for example.
Bottom line, the reader is probably reading the story for entertainment, not to be quizzed at puzzles. So whether you decide to outline the process of solving the riddle in excruciating detail, or just do a little bit of hand-waving, don't simply dismiss the obstacle you introduced for your character. There are few things more jarring (and breaking suspension of disbelief) than bits of story which are introduced and then left completely unexplained to the reader. If you aren't willing to explain it (the lock in this case), don't introduce it at all (leave the door unlocked).