How Can I Create Three Random Integers Which Sum To A Specific Value? (Python)

Let's say bob = 6 I want to create 3 random integers that have a sum of 106 (100 + whatever bob's original integer is. It could be 10, but in this case, it's 6). I've got: from ran

Solution 1:

The general approach to generate numbers that add up to a certain number is like this:

import random
bob = 6
numbers = sorted(random.sample(range(100+bob), 2))
bob1 = numbers[0]
bob2 = numbers[1] - numbers[0]
bob3 = 100 + bob - numbers[1]

It selects two cut points between 0 and 100 + bob and assigns the numbers as illustrated:

This will also ensure all three numbers have the same distribution (simulated with 1m trials):

mean    34.700746   35.639730   35.659524
std     24.886456   24.862377   24.861724

As opposed to the numbers generated dependently:

mean    50.050665   27.863753   28.085582
std     29.141171   23.336316   23.552992

And their histograms:

Solution 2:

Just calculate the third value:

from random import randint
bob = 6
bob1 = randint(0, 100)
bob2 = randint(0, min(100, 100 + bob - bob1))
bob3 = 100 + bob - bob1 - bob2
print bob1
print bob2
print bob3

Solution 3:

bob1 = (randint(0,100))
bob2 = (randint(0,(100-bob1)))
bob3 = 100 - (bob1 + bob2)

Solution 4:

Here is a general function that will always randomly generate 3 numbers in [0, n] that add to n; as the intermediate values are determined by "bob"'s initial value, we pass it this value and a target total number. The function returns a tuple of 3 numbers that together with bob-initial-value add up to the target:

import random

def three_numbers_to_n(bob, target):
    n = target - bob
    a = random.randrange(0, n+1)
    b = random.randrange(a, n+1) - a
    c = n - a - b
    return a, b, c

for _ in range(5):
    bob = 6
    result = three_numbers_to_n(bob, 106)
    print(bob, result, sum(result) + bob)

sample output:

6 (13, 3, 84) 106
6 (45, 49, 6) 106
6 (27, 2, 71) 106
6 (44, 18, 38) 106
6 (100, 0, 0) 106

If you wish, you could random.shuffle(a, b, c) before returning to remove the predictability that the first number is likely larger than the second likely larger than the 3rd.