+0  
 
0
1
1
avatar+1147 

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 2 or a 3
- The sum of the digits is 5

 
 Jun 11, 2024
 #1
avatar+759 
+1

We could probably use casework to solve this problem.

 

The first case to look for is only two digit numbers. 

We have 23 and 32, so there are 2 possibilities. 

 

Next, consider 3 digit numbers. 

We have 311, 131, 113 for 3 more. 

We also have 221, 212, and 122 to add 3 more on. 

 

Next, consider 4 digit numbers. 

The only numbers that work are numbers with three 1s and one 2. There are 4 ways we could do this. 

 

Lastly, we have 5 digit numbers. The only one we have to consider is \(11111\), one possibility. 

 

Now, we add up the numbers. We get \(2+3+3+4+1 = 13. \)

 

So 13 is our answer!

 

Thanks! :)

 Jun 11, 2024

4 Online Users

avatar
avatar
avatar