All sessions have the same list of solutions, but each session has a differently RNG'ed determination of which will and won't work.
Reminder: While characters do not exactly know ICly that the marked methods won't work, they have at least a slight worry or suspicion that these methods are riskier or less reliable. It's not a strong enough suspicion to not bother trying them at all, but it could very well inform how they approach distributing them.
When you offer a solution to another character and they accept it: describe what happens with whatever cool description/justification you like, and then specify whether it succeeds or fails at resolving the problem.
SOLUTIONS
Reminder: While characters do not exactly know ICly that the marked methods won't work, they have at least a slight worry or suspicion that these methods are riskier or less reliable. It's not a strong enough suspicion to not bother trying them at all, but it could very well inform how they approach distributing them.
When you offer a solution to another character and they accept it: describe what happens with whatever cool description/justification you like, and then specify whether it succeeds or fails at resolving the problem.