Use the third conditional to express a circumstance of condition. This form of conditional is also used to describe a situation that can be imagined or could be considered not real.
Compare
If I see John, I will say hello. (First conditional)
If I had seen John, I would have said hello. (Third Conditional)
The third conditional didn’t happen.
If clause + consequence clause. (possible in the interrogative and negative)
If clause (past perfect) + consequence (would have) (possible in the interrogative and negative)
Exception: It is possible to skip the if preposition by using the participle had only.
If we had not gone it would have been difficult. (with if)
Had we not gone it would have been difficult. (without if)
If I had taken the time, I would have come to visit. (also "Had I taken the time…")
I would have come to visit if I had taken the time.
If I had not seen John, I would not (wouldn't) have know about the project. (also "Had I not seen John…")
I would not (wouldn't) have know about the project if I had not seen John?
If they had had the time, would you not have (wouldn't you have) decided to make an effort? (also "Had they had…")
Would you not have (Wouldn't you have) decided to make an effort if they had had the time?
If they had not succeeded, would they not have (wouldn't they have) received the award? (also "Had they not succeeded…")
Would they not have (Wouldn't they have) received the award if they had not succeeded?