Decidability

Question

A turing machine $M$ halts if started with a blank tape.  This is undecidable .  Can somebody explain this in easiest way possible.

Answer 1

we can reduce this problem to halting problem of turing machine(known to undecidable).

 at first make a new TM that always starts with a blank tape, and writes the normal halting problem input to the tape as its first set of steps - so if this modified machine halts when starting with an empty tape, the normal halting problem input halts with whatever its input. Therefore we can't decide the blank tape halting problem.becz halting problem is undecidable.