Conjugated word + んだ vs nonconjugated word + conjugated んだ

Question

Suppose I have a verb/adjective/noun, let's say 無理, and I add (な)んだ to it as an explanatory sentence-ending particle. What would be the difference in nuance between the following two conjugated constructions?

1. それは無理だったんだ。
2. それは無理なんだった。

More generally, what is the difference in meaning between conjugating a word before adding んだ (to any tense, such as past negative) and doing it the other way around? Please also provide examples where one would be more appropriate than the other for each of the two cases, and consider what would happen if ん were replaced by の.

Answer 1

無理だったんだ is straightforward, it's a combination of 無理だった ("was impossible") and the explanatory-の. "So it is that it was impossible", "Because it was not possible", "(I failed but) it was impossible (in the first place)", etc.

無理なんだった is usually interpreted as a combination of 無理なんだ ("it's that it's impossible"; present tense) and discovery-た. "(Ah, I've just recalled) it is impossible (and that fact explains something)", "(That reminds me,) this is not possible!" Note that this refers to something at present. For example, imagine you've been trying hard to open a treasure box with a key for an hour, and suddenly remembered you had heard from someone that the box actually required two keys to open. You may say "あっ、無理なんだった、鍵が2つ要るんだった!"

When のだった/んだった is used with an action verb, it also describes a regret, something that should have happened in the past.

• ボタンを押したんだ。
  (It is that) I pushed the button.
• ボタンを押すんだった。
  [regret] I should have pushed the button (but I didn't).
  [recall] (Oh, I've just recalled) I have to push the button (to open this door)!