Which is correct:
I (had / have had) no idea you were such a good chess player.
The book said that 'had' is correct, but why? Why the present perfect is not correct?
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It would seem to me to be because it doesn't necessarily relate directly to the present.
For instance, you could say:
I had no idea you were such a good chess player until you won the tournament.
But it would make no sense to say:
I have had no idea you were such a good chess player until you won the tournament.
We also know it doesn't relate directly to the present because the statement tells us that the person is now aware of the other person being a good chess player, so that awareness must have arisen already (int the past).
The present perfect tense refers to an action or state that either occurred at an indefinite time in the past (e.g., we have talked before) or began in the past and continued to the present time (e.g., he has grown impatient over the last hour).
Per my above explanation, we know that the second part is not true (the person having "no idea" is not still true in the present).
As for "an action or state that either occurred at an indefinite time in the past", having no idea is a continuous state, and therefore we cannot say that it occurred "at a time" (definite or indefinite).