a Encryption how to problem i have

[Trac3y]

I have a need to offer a secure way to prove that the answer to a question was predetermined.

Example (My idea how)

I encrypt a answer and offer a private key?(a way to check the answer ,maybe after a time limit)

I ask the question.

When the right answer is found i  show encrypted answer .

My problem is that if have private key , i can supposedly in this argument change the original answer.

How can i do this with users confidence of nobody changed answer? Is encryption and private key even the best plan im not sure.

Best would be if a script give answer after timer runs out and somehow i could not provably change it ,also then user can check somehow what the original answer was and be sure it was un-tampered (time-stamped maybe)