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.

I was about  to provide a hint, to address tomarkin's doubts and after reading your solution I admit that what you did is exactly what I had in mind.

Although both of you reacched the correct answers, F(13)=1782
it  is quite difficult  to evaluate, say,  F(33) using the direct method, while it  is a single column in Excel to get it in no time.

I am going to use your detailed explanation as the official solution.

  

Posted by Ady TZIDON on 2014-07-22 10:05:47