Should I admit to cheating when it appears I cheated but I did not? One of my TAs is accusing me of cheating. 

The professor had shared a 2-question quiz through our online portal (Google Meet). One of the questions contained a 9-digit sequence. Somehow, I misread this sequence and ended up solving the problem using a different 9-digit sequence. My incorrect sequence exactly matched the sequence used on a different version of the quiz, which had been administered to a different section of the class several days before. I do not know how similar the two sequences were; I assume they were very different.

I understand how bad this looks, but I actually did not cheat. I am baffled as to how this could have happened given how careful I normally am about reading the question. I have no history of cheating in other classes.

I don't understand how I can prove that I did not cheat. The other question of the quiz was, of course, exactly as given on my quiz, so I'm thinking I may argue along the lines of "if I were to cheat why would I do it on only 1 question", although this seems slightly weak to me. 

One complication is that the professor said that anyone suspected of cheating will be required to take an incomplete on the class and do the exam whenever university resumes. This is not ideal, as I am bound to forget a lot of material. On top of this, the classes I am taking next semester require this one as a prereq and this will derail by entire class schedule. I don't think there are any classes I can take for my major without this prerequisite filled.

The professor is offering that I can admit to cheating and then he'll give me a warning for the final and get a 0 on the quiz. Assuming the warning for the final does not come with the above requisite of webcam, should I falsely admit to cheating? 

While I am normally against false admissions, I need to resolve this quickly, as the final is the day after tomorrow. Also, given how bad this looks, if I don't accept this and am found guilty, then I will probably fail this class and have to retake it anyways.

Update: For anyone who finds this later, I requested the Prof to let me take the exam without a webcam, given that it may be dropped later. He agreed and also stated there would be no need to drop it later. After the exam, I laid out many of the points given below, which the Prof said he would take into consideration and look into overturning the decision. I had an easy out, where I could take the 0 on the quiz and still get an A in the class, but there is a lot of good advice below for those who are still stuck.
I'm panicking right now, as I was supposed to be studying for finals


If you did not cheat, you do not need to be panicking.  

I recommend these steps:


Tell the professor that you did not cheat.
Tell them that right now you need to focus on studying for your exams.
Tell them that you look forward to straightening the matter out after the exams.
Request to take the exam at the normal time.  Point out that the professor can always require you to take the in-person exam later, so it is possible to resolve the accusation later.
Go back to studying.


After you have taken your exams, then learn and follow your university's procedure for resolving these disputes.  Keep it calm and logical.

If you are still feeling panicky when you need to study, talk to your university's counseling service.