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There are 900 3-digit numbers, 100 to 999.

The 3 may be in the hundreds place, the tens place, or the ones.

The numbers 300 - 399 have 3 in the hundreds place.

The numbers 130, 131 ... 938, 939 have 3 in the tens place.

The numbers 103, 113, 123 ... 993 have 3 in the ones place.

That would total 100 + 90 + 90 = 280 except that now we have double counted some numbers with 2 or more threes in them. I believe if you count carefully you will find 19 double counted numbers in the 300 - 399 group and 8 numbers with the tens digit and ones digit equal to 3. Lastly, the number 333 was triple counted. 280 - 28 = 252. There are several ways to solve this problem. I encourage you to double-check my results ... who is to say this is correct?

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