Can you actually solve puzzles and explore while in hiding?

By Richard U. Pickman, in Mansions of Madness

as the topic says...

the rules say nothing about it not being possible. how do you guys interpret the rules.

Assuming that the puzzle in question is an obstacle and not a lock card, yes.

One could also use non-combat spells, a variety of equipment, and so on.

Though evasion rules would apply.