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Could you tell me if I have to use how couldn't I or how couldn't have I in the sense of criticizing oneself for failure to do something in the past? For example:

The problem turns out to be so easy. How couldn't I figure it out/how couldn't have I figured it out.

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Neither "how couldn't I" nor "How couldn't have I" are standard, common phrases for this situation, or indeed for any situation I can think of. I suspect that are actually grammatically incorrect. The concept could be expressed as:

  • How could i have failed to figure it out.

  • Why didn't I figure it out.

  • I don't understand why I didn't figure it out.

  • Surely anyone could have figured it out, but I didn't.

There are many other possible and correct variants on this theme.

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The problem turns out to be so easy. How couldn't I figure it out/how couldn't have I figured it out.

I would say both of your suggestions are wrong. The correct one would be:

The problem turns out to be so easy. How couldn't I have figured it out?

Also,

The problem turns out to be so easy. Why couldn't I have figured it out?

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