I see no point in having a puzzle which has no clues given and which therefore can only be brute-forced by trying all combinations sequentially.
What do you mean? If you're talking about the claw puzzle then boy do I have bad news for you...
If you're talking about the animal totems you spin around, there's definitely hints towards it.
If you're referring to the totem puzzle, there is a solution in-game. There are two small rooms, one on each side of the throne; one room has totems you can't move and the other has the totem puzzle. All you have to do is make the moveable totems line up with the immobile versions and pull the chain.
There are clues...and they are already so easy that you can't call them puzzles.
In all fairness though, unless a person looks up Skyrim stuff a lot or actively goes looking for hints/cheats, the chances of finding out that..
Bleak Falls Barrow, one of the first locations you're most likely to visit (whether you're sent by balgruuf or lucan), or atleast find a dragon claw, explains the solution in Arvel's journal.