Unsolvable problem?

Question

What is the correct construction of "unsolvable problem"? Is it "解{と}けられない問題{もんだい}"？**(Question 1)** > Plain(intransitive): 解{と}ける "To be solved". > Potential form(of intransitive): 解けられる "can be solved". > Potential + Negated(of intransitive): 解けられない "cannot be solved" ----- > Plain(transitive) 解{と}く "(Some agent) solves". > Potential form(of transitive): 解ける "(Some agent) can solve".　 > Potential + Negated(of transitive): 解けない "(Some agent) cannot solve" ----- Does 解けられない問題 mean it intrinsically cannot be solved? **(Question 2)** Does the transitive version "解けない" implies that some agent is unable to solve, but does not mean it is absolutely unsolvable? **(Question 3)** *(Agent: one who initiates and/or completes an action or event)

Answer 1

Good news! 解けられない問題 is correct. You could also use 解決{かいけつ}できない問題{もんだい}, since 解決 sounds a bit more technical.