Number 3 Appearing 1-1000: Counting Stats

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SUMMARY

The number 3 appears a total of 300 times in the counting numbers from 1 to 1000. This conclusion is derived from analyzing the occurrences of the digit 3 in the units, tens, and hundreds places. Specifically, there is 1 occurrence of 3 in each complete set of ten numbers (0-9), resulting in 100 occurrences in the units place, 10 occurrences in the tens place across 100 sets (0-99), and 100 occurrences in the hundreds place (300-399). The Mathematica function Count[Flatten[IntegerDigits/@Range[1000]], 3] can be utilized to verify this count programmatically.

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How many times will the number 3 appear in counting numbers from 1 to 1000?

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Hi there,

I'm not sure if it's really statistics, and it sounds a bit like a homework question...

Here's a hint:
there's 1 3 in the units digit in every nnn0..nnn9
there's 10 3s in the tens digit in ever nn00..nn99
etc...

Mathematica can construct all of the digits and count the number of 3s using
Count[Flatten[IntegerDigits/@Range[1000]], 3]
 

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