Decidability of a language of Turing Machine descriptions
Given a Turing Machine M (with its finite number of tape symbols,
finite number of states, etc...), how hard is it to prove that there
is an input on which it will run for more than 10 steps? How much of
the input will be read in 10 steps at most? How many different
computations have to be checked to see whether one takes more than 10
steps?

added later: I was editing this when the reference to question Is the set of Turing machines which stop in at most 50 steps on all inputs, decideable? was given as comment.