Suppose you are given a Turing machine M (not necessarily a decider), a string w, and a (different) magic genie. You can ask the magic genie whether a certain Turing machine accepts a certain input string, and the genie will magically give you the correct yes/no answer. You can ask the genie as many such questions as you like, about any Turing machine and any string.

Describe a strategy you can use to decide whether M halts on w. Remember to decide means to say with certainty that M halts on w or that M does not halt on w.

Note: Our magic genie decides AT M , an undecidable language. This genie really is magical.