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Getting 13 (Posted on 20140721) 

Using integers 1,2,3 & 4 only , in how many distinct ways a sum of 13 can be achieved?
Rem: The order matters i.e. 1,4,4; 4,1,4; & 4,4,1 are considered distinct.

Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)


Solution:

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Let f(n) = number of ways of achieving total n.
f(0)=1 f(1)=2 and the recursion formula is:
f(n) = f(n4) + f(n3) + f(n2) + f(n1).
f(13) = 2872
See Steve Herman detailed soltion. 
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