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There aren't going to be any 7's in the hundreds digit, so first we look at how many there will be in the ones digit.

Since there will be a 7 for every 10 numbers, and there are 501 numbers between 100 and 600 inclusive), we'll have floor(501 / 10) = 50 sevens in the ones digit.

For the tens digit, we'll encounter 10 sevens for every 100, from 70 to 79, and so we have floor(501 / 100) = 5 times we'll have 70 - 79 so that's 5 * 10 = 50 sevens in the tens digit.

However, we don't want to know how many sevens there are, we want to exclude overlaps. Thus we subtract every instance of 77 we see (overlap!), and we have floor(501 / 100) = 5 overlaps.

50 + 50 - 5 = 95, so a total of 95 numbers will have the digit 7 at least once.

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Q: How many numbers between 100 and 600 have a 7 for at least one of the digits?
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