Find the number of positive integers that satisfy both the following conditions:

Each digit is a 1 or a 3

The sum of the digits is 12

Icebulb2 Nov 25, 2023

#1**0 **

There is only one way to make 12 with a single digit, namely with 3. There are 2 ways to make 12 with 2 digits: 11 and 31. There are 3 ways to make 12 with 3 digits: 111, 131, and 311. Finally, there are 3 ways to make 12 with 4 digits: 1131, 1331, and 3311. Thus, the total number of positive integers that satisfy the given conditions is 1+2+3+3=9.

bader Nov 25, 2023