I think the miner can cheat in step 3. After you submit your private key as a transaction, the miner can delay it to be included in the blockchain for arbitrary time. During which, the miner can use your private key to decrypt your answer submit in step 2. And resubmit their version of the answer.
That won't help him much, since my answer is already published in the blockchain when he will publish his answer.It is trivial to see that my answer was published first.
