At least in the first version of the game, the 'solutions' list was actually just a sequential list of what the answer would be for each given day. So, calling them 'possible solutions' on my part was actually a little misleading (sorry), there's no probability going on or anything like that. Not sure if NYT changed it.

The value is that we all get the same answer, so which makes it more fun to compare our results (this does mean that you can just cheat and look up the answer, and it might have been possible to obscure the list somehow, but probably getting into an escalating war with cheaters was not a priority for such a simple little free game).