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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.


 

 May 4, 2020
edited by SoggyPerson  May 4, 2020
 #1
avatar+657 
+1

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.

 

coolsmileycool
 

 May 4, 2020
edited by LuckyDucky  May 5, 2020
 #2
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-1

You just copied the AoPS solution.

 May 5, 2020
 #3
avatar+657 
0

That's not true at all this is my own.

LuckyDucky  May 5, 2020

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