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how many ways to get to nine in addition only using the number 3 and 1

 

help

 Jul 20, 2020
 #1
avatar+28021 
+1

3 + 3 + 3

3 + 3 + 1 + 1 + 1

3 + 1 + 1 + 1    + 1 + 1 +1

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1

 Jul 20, 2020
 #2
avatar+1039 
+3

Let's do some casework for this one. 

How many 3s How many 1s
0 9
1 6
2 3
3 0

 

As you can see, we only have 4 options for this case.

 Jul 20, 2020

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