How many possible combinations are there of these 4 numbers to add to multiples of 4? If I have the numbers 0 1 2 and 3, how many combinations of any size but maximum of 4 add to a multiple of 4?
EG:
0000 = 0 ( so 0*4), 


*

*1111 = 4,

*0000 = 0 ( so 0*4), 

*0112


How many combinations are there?

For length $4$. Suppose you already picked the first three. Then there is exactly one number that you can put in the end to make it a multiple of 4. Therefore there are $4^3=64$ such lists.
Using the same method we see the total is $4^0+4^1+4^2+4^3$=$\frac{4^4-1}{4-1}=\frac{255}{3}=85$
