Yeah I think this one is just semantics/being at least a bit politically aware. "There is no solution" is for most shorthand for "I can give you 20 solutions,

Yeah I think this one is just semantics/being at least a bit politically aware. "There is no solution" is for most shorthand for "I can give you 20 solutions, but I don't think any of them are good enough to be effective for this case. Would you like to hear the 3 best ones I've thought of?" It's a bad kind of shorthand to use. Stating that "these are the best solutions I know of right now, and I've exhausted my current ideas" is better than saying there's no solution - it avoids it seeming like you're just not interested. Everything has a best solution after all, even if that solution may not be good enough.