We call a number peachy if every digit in the number is either a 3 or next to a 3. For example, the numbers 333, 83, 303, and 3773 are all peachy, but the numbers 32523, 786, 340, and 3999 are not peachy.

SoggyPerson May 4, 2020

#1**+2 **

A 3-digit number is peachy if it has a 3 in the middle, or it both starts and ends in a 3.

There are 9*1*10 for the first one

There is 10 of the second type,** but because we already counted 333 in the first case, so we don't have to count it again **

Without the overcounting, we get 9 new peachy numbers in the second case.

Therefore, there are \(90 + 9 = \boxed{99}\) peachy three-digit numbers.

LuckyDucky May 4, 2020