How to generate a list of random numbers so their sum would be equal to a randomly chosen number

Question

I want to generate a list of random distribution of numbers so their sum would be equal to a randomly chosen number. For example, if randomly chosen number is 5, the distrib

Answer 1

Let n be the number you want values to add up to. Generate a random sample of random size (less than n), consisting of values in the range 1 to n exclusive of n. Now add the endpoints 0 and n, and sort. Successive differences of the sorted values will sum to n.

import random as r

def random_sum_to(n):
    a = r.sample(range(1, n), r.randint(1, n-1)) + [0, n]
    list.sort(a)
    return [a[i+1] - a[i] for i in range(len(a) - 1)]

print(random_sum_to(20))  # yields, e.g., [4, 1, 1, 2, 4, 2, 2, 4]

If you'd like to be able to specify the number of terms in the sum explicitly, or have it be random if unspecified, add an optional argument:

import random as r

def random_sum_to(n, num_terms = None):
    num_terms = (num_terms or r.randint(2, n)) - 1
    a = r.sample(range(1, n), num_terms) + [0, n]
    list.sort(a)
    return [a[i+1] - a[i] for i in range(len(a) - 1)]

print(random_sum_to(20, 3))   # [9, 7, 4] for example
print(random_sum_to(5))       # [1, 1, 2, 1] for example