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    All I see in the second is a deduction. If someone asks "Why did you do it?" you cannot reply "I had to have done it". Commented Jan 11 at 13:59
  • What do you mean by It couldn't have been done by anybody but him? That could be interpreted two ways - "He is the only person who could have done it" (a deduction about the past) or "He was the only person able to do it" (a statement about a situation in the past). Otherwise, I agree with Stuart's answer. Commented Jan 11 at 13:59
  • @KateBunting, I meant "He is the only person who could have done it" (a deduction about the past). This is what I learnt from the readings I have made about the issue. I didn't know it could be interpreted two ways. Commented Jan 11 at 14:01
  • @TimR, Very interesting and helpful approach, which I have never encountered in any of my readings on that so far. Thanks I appreciate it. Commented Jan 11 at 14:12
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    TLDR: "He had to do it" assumes that he did do it, and it asserts that he could not have chosen to do any differently. "He must have done it" sounds like an accusation, and it sounds as if it's based on deduction: These are the facts,... Someone did it, and the only way we can explain the facts is if he was the one who did it. Commented Jan 12 at 3:06