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Getting 13 (Posted on 2014-07-21) Difficulty: 3 of 5
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.

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Solution Elegant(?) approach | Comment 2 of 5 |
I confirm 2,872

Let f(n) = number of ways of achieving total n.
These can be achieved be adding a 1 to the left of all ways of achieving (n-1), or by adding a 2 to the left of all ways of achieving (n-2), or by adding a 3 to the left of all ways of achieving (n-3), or by adding a 4 to the left of all ways of achieving (n-4). 

In other words, f(n) = f(n-4) + f(n-3) + f(n-2) + f(n-1).  It's an extended fibonacci.

f(0) = 1
f(1) = 1
f(2) = 2
f(3) = 4
f(4) = 8 (ie, 1+1+2+4)
f(5) = 15 (ie, 1+2+4+8)
f(6) = 29 (ie, 2+4+8+15)
f(7) = 56
f(8) = 108
f(9) = 208
f(10) = 401
f(11) = 773
f(12) = 1490
f(13) = 2872

  Posted by Steve Herman on 2014-07-21 19:17:46
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