You could choose to make a decision that is, in relevant aspects, equivalent to simularing Omega. This subjects Omega to the Halting Problem. If you make the Halting Problem irrelevant by limiting time, you’ve also limited Omega’s ability to perfectly simulate you, contradicting the conditions of the problem.
If there are certain algorithms that you just can’t execute due to your limitations, then there may be a logical answer which you are incapable of producing.
There is a time limit so I don’t think the halting problem is relevant here.
You could choose to make a decision that is, in relevant aspects, equivalent to simularing Omega. This subjects Omega to the Halting Problem. If you make the Halting Problem irrelevant by limiting time, you’ve also limited Omega’s ability to perfectly simulate you, contradicting the conditions of the problem.
Omega has more processing power than you
If there are certain algorithms that you just can’t execute due to your limitations, then there may be a logical answer which you are incapable of producing.