How many three-digit whole numbers have at least one 7 or one 9 as digits?

gueesstt
Apr 22, 2018

#1**0 **

There are 999 - 100 + 1 = 900 3-digit numbers

Between 100 and 200, you have:

107, 117, 127, 137, 147, 157, 167, 177, 187, 197 =11 sevens. This pattern repeats 9 times between 100 and 999.

So, you have: 11 x 9 =99 sevens between 100 and 999.

Then you have: 700 to 799, or 799 - 700 + 1=100 sevens.

So, 100 + 99 =199 sevens that appear in all 3-digits numbers.

This same reasoning should apply to all 3-digit numbers that have a 9 in them. Or, 199 nines between 100 and 999

So, the total number of 3-digit whole numbers that have a 7 or a 9 in them should be:

199 + 199 =398 numbers in total.

**Note: Some numbers that have a 7 AND a 9 in them have been counted twice, such as 179, or 197....etc, once for 7s and once for 9s.**

Guest Apr 22, 2018

edited by
Guest
Apr 22, 2018