## Random Total

### June 12, 2015

Our task today is to generate a set of k random positive integers that add up to a given totaln. For instance, if we want 4 random numbers that add up to 9, there are six possible results (not counting permutations of them): {6,1,1,1}, {5,2,1,1}, {4,3,1,1}, {4,2,2,1}, {3,3,2,1} and {3,2,2,2}.

An easy way to do that is to choose k−1 random numbers r with 0 ≤ r < nk, sort them, calculate the differences between them, calculate the difference between 0 and the smallest, calculate the difference between nk and the largest, shuffle the differences, and add 1 to each; subtracting k and adding 1 ensures that all the numbers are positive. For our example above, choose three random non-negative integers less than nk = 5, say 1, 3, and 3, the differences are 1, 2, 0 and 2, and the four resulting numbers are 2, 3, 1 and 3, which form the fifth of the six sets shown above.

Your task is to write the program that generates a random set of integers that adds to a given total, as described above. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.