Prove there exists a recursive language which no TM accepts in n steps.

Question

There is a problem I can't solve: Assume n is an integer. Prove that there exists a recursive language such that there is no Turing Machine which accepts it and makes a maximum of n steps for every input. I'll be glad to receive hints. Thanks!

Answer 1

Hint: In $n$ steps, a Turing machine can read from at most the first $n$ cells. So any Turing machine with this property depends only on the contents of the first $n$ cells of the input tape.