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I’m doing a review exercise that gives me the list of numbers from 100 to 1000.

I need to find the number of different numbers that have a 0.

I suppose I could do this with the Pigeonhole principle, but I’m not sure how to implement it.

Thanks.

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    **At least** one zero or **exactly** one zero? For "at least" I would find the number $n$ of numbers $100$ to $999$ that have no zero. This is easy, turns out that $n=729$. There are $900$ numbers $100$ to $999$, so $171$ with at least one zero. Finally, let's remember about $1000$, which has been sadly neglected. So we get an answer of $172$. If you want instead exactly one zero, don't need to bother about $1000$, adjust the $171$ at the end to remove the two zero people.2011-06-17

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I don't really know how you would do this with the pidgeonhole principle. I would count how many numbers have no zeros, then how many numbers have 2 zeros (hint, it's 9), then use that to find how many numbers have 1 zero. Then you can use all of that information to get the total number of zeros.

There's a common theme when counting that it's sometimes easier to count everything except what you're asked to count and then subtract.