verbs - Meaning/Breakdown of 答えの出しようのない疑問

I saw this sentence in a book:

そんな答えの出しようのない疑問を、おそらくこの場に集められたプレーヤー全員が考えたのだろう。

The fan translation I had reads:

Most players who had been forced here would have been asking this answer-less question.

I am somewhat confused by the 出しよう part, what is this formed from? I have a guess. I found a discussion about this in German on a forum. Someone said:

力の出しようがない＝力を出せない:
One is unable to bring their strength to bear (man kann seine Kraft nicht aufbieten)

That example made the expression しょうがない come to mind which I understand to mean literally "there is no way of doing it".

If xしよう is "way of doing x", is x出しよう "way of 出すing x"? Or for the phrase in the question title: "question for which there is no way of exposing the answer".

Does verb stem + よう generally mean "way of doing [verb stem]?" It seems like that's where this is headed but I'm not having much luck finding any explanations to that effect on the web.

Answer

You're on the right track. A dictionary specifically defines this usage of よう as:

６ 実現の可能性の意を表す。「あの男がそんな悪いことをしようはずがない」

It's usually used in the form of masu-stem + よう + が + ある or masu-stem + よう + が + ない, which mean "there's a way of ～ing" or "there's no way of ～ing", respectively.

So, yes, 答えの出しようのない疑問 literally means "question for which there is no way of giving the answer". Simply put, an unanswerable question.

Other examples:

• 言いようのない不安 indescribable anxiety


• 忘れようのない事件 incident I can never forget


• 信じようがない説明 explanation I can never believe

There is another adjective しょうがない (≒there's no use ～ing), occasionally also written as しようがない, but that's a different thing. 答えを出してもしょうがない疑問 would mean "a question which is not worth solving".

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EDIT: I said しょうがない is different, but etymologically, the i-adjective しょうがない (of no use, meaningless; can't be helped, nothing can't be done) is from し + よう + が + ない (no way of doing anything). It won't be directly preceded by another verb.