# Solvability of Turing Machines

I'm preparing for an exam, and on a sample one provided (without solutions), we have this question: Is the following solvable or non-solvable: Given a turing machine $T$, does it accept a word of even length? - Given a deterministic 1-tape turing machine $T$, does $T$ ever read the contents of the 10th cell?

Thanks! -

• I think that they're both unsolvable by rice's theorem... but I am not sure if I can apply the theorem in both cases. What do you think? Would both of these constitute as "non-trivial properties"? What would be an example of a trivial property then? – user4734 Dec 7 '12 at 22:11
• Is the tape one side infinite, or two sided? In seems hard to avoid reading the 10th cell of a one sided infinite tape. – Hendrik Jan Dec 7 '12 at 22:23
• It does not specify... Does it actually matter? – user4734 Dec 7 '12 at 22:24
• It does matter: see the comment by Steve to the answer. Singe sided: then you have only a finite number of cells available, otherwise it is Turingcomplete if you avoid the 10th cell. Refer to the standard model you have been using in your lectures. Good luck with the exam... – Hendrik Jan Dec 8 '12 at 1:03
• @HendrikJan: Also one has to be precise, what "reads the content of a cell" means. – A.Schulz Dec 8 '12 at 5:55