# Counting Zeroes

Let $$N$$ be the number of $$0$$ digits in all the integers from $$0$$ to $$M$$ (including the initial $$0$$). Find the [smallest] non-trivial value of $$M > 1$$ where $$N=M$$.

For example, for $$M=100$$, $$N=12$$ (because it includes the initial 0), hence $$N≠M$$, so that $$M=100$$ wouldn't be the answer. There is [not] exactly one non-trivial $$M$$ for which this is true, other than the trivial case $$M=1$$.

You may use the computer or Wolfram Alpha.

Start counting the zeroes from $$0$$, not $$1$$, otherwise your program (if you're using one) will be a good example of Turing's Halting Problem.

{Edit, problem correction. Others have alerted me of the existence of at least 2 other M, both larger than the one stated as the solution, that meets the condition. I stand corrected, and the problem has been re-worded to ask for the smallest such non-trivial M. I think this problem now has just become more interesting, thanks to the contributors.]

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