When I'm setting obstacles in front of my players in game I don't always plan how they're going to overcome them. I figure out how the obstacle, or problem, is going to be introduced. I figure out what it does and how it can interact and - well, obstruct - the players. But I don't write down how it is overcome. It works out pretty well, and today I want to talk about why.
The Danger of a Set Solution
There's a danger in having a set solution. The danger is that when you plan a solution your brain may take it as the only solution. This then makes the problem not of making a solution, but of finding what solution the GM has planned and executing it. The only thing is, sometimes players don't catch on to that. Your clues don't work because the players are taking them wrong. Why? Because unlike you they don't have the whole picture. Now your minor obstacle is a major hurdle, or worse, it just killed someone, and your game is on halt.
Now, things can get even worse when the PCs start to get frustrated. Maybe they come up with other, viable solutions except you won't accept them because you planned a way out. For example, say someone is trapped in a box and is going to be drowned. The solution you have is a hidden switch in a nearby bookcase another player can hit. Only, the players don't check the book case. Someone tries to freeze the water source, someone tries to dimension door the trapped PC out, someone tries to break the door open with an axe of rending. None of these have a chance of working though, because you made a solution and that's it.
This often doesn't happen intentionally either. Removed from the game the GMs who stick to the prepared solution may see how those other plans could and should work - or at least make things different. In the moment though? It's hard to do.
Free To Assess
On the other hand, if you don't have a prepared solution then you have to assess solutions as the players give them to you and see if they'd work. This doesn't mean you make the trap less dangerous, but it does mean you don't have a pre-set notion for how to solve it. Now when a player says "I search the room for a hidden switch" it doesn't turn into a game of figuringout where the PC is searching, but instead just a dice roll and maybe they get it. On the other hand, attempts to stop the water via freezing, breaking the cage open, or otherwise working around the problem can be explored without the fear of them running up, against, or into, the prepared solution.
The best way to employ this is with balance. If an enemy took the time to set up a death trap with one specific way out, that can be honored. The idea here isn't to leave you more open to spare PCs, but to prevent you from getting hyper-focused on the available solution that you discount other ones.
Be open to the players' creativity, but be realistic about what those solutions are. It's unlikely someone with a strength lower than 20 can rip open a metal box without tools to help, but that doesn't mean she can't help the trapped rogue get out of the box by bending it some.
Make them work for it, but if an idea should work, let it work.