Three digits. This one is a toughy. ?

Question

Among all three digit integers from 100 to 400, how many have exactly one digit that is 8?

Please show you worked this.

Answer 1

Since you only want from 100 to 400, there are no numbers that start with 8.

From 100 to 200, there are 10 numbers that end with 8: 108, 118,128, 138, 148, 158, 168, 178, 188, and 198. But you don't want to include 188, so there are 9 numbers that end with eight.

From 100 to 200, there are 10 numbers that have 8 as a middle digit, from 180 to 189. Again, you don't want to include 188, so there are 9 numbers that have eight as a middle digit.

9+9=18 numbers with exactly one digit that is 8 from 100 to 200.

The same rules apply from 200 to 300 and 300 to 400, so just multiply 18 by 3 to get your answer.

18x3=54