# Prove Undecidability: TM M enters each of its states on Input W?

Consider the following problem: given a Turing Machine $M$ and an input string $w$, does $M$ enter each of its states during its computation on input $w$?

How to prove that the problem is undecidable?

I was trying to prove undecidability by Rice's theorem which states that languages having non-trivial property are undecidable. But how can I adjust the problem to the theorem?

• – Raphael May 13 '15 at 8:28