math - How to generate numbers in range with specific average with Python?

Question

For example I would like to generate 22 numbers between 20 and 46 with an average value of 27. And I would like the numbers to cover the range as well as possible.

EDIT: These numbers don't need to be random.

Answer 1

Warning: this is not the optimal solution but it works quite fast with your input parameters:

import random


def gen_avg(expected_avg=27, n=22, a=20, b=46):
    while True:
        l = [random.randint(a, b) for i in range(n)]
        avg = reduce(lambda x, y: x + y, l) / len(l)

        if avg == expected_avg:
            return l

for i in range(100):
    print gen_avg()

In my laptop will give 100 random sequences in ~2.5s:

[21, 20, 20, 23, 25, 24, 29, 22, 42, 23, 31, 26, 30, 25, 29, 38, 20, 31, 46, 28, 41, 20]
[20, 30, 39, 26, 24, 31, 35, 36, 22, 22, 20, 32, 23, 21, 42, 32, 23, 24, 26, 28, 29, 25]
[23, 43, 21, 31, 44, 24, 24, 20, 27, 31, 28, 22, 26, 33, 25, 30, 21, 26, 33, 20, 31, 25]
[36, 28, 24, 29, 32, 21, 36, 28, 24, 27, 24, 22, 28, 28, 33, 21, 20, 32, 23, 30, 35, 21]
[21, 34, 25, 32, 20, 37, 31, 20, 46, 25, 21, 25, 35, 36, 21, 26, 21, 35, 24, 21, 30, 28]
[28, 23, 43, 22, 20, 23, 30, 41, 25, 32, 20, 21, 21, 30, 26, 22, 46, 40, 27, 26, 26, 21]
[21, 26, 38, 27, 42, 36, 43, 21, 29, 32, 22, 29, 26, 20, 23, 22, 21, 38, 23, 21, 21, 23]
[28, 21, 27, 34, 38, 21, 25, 37, 27, 22, 36, 38, 27, 20, 32, 35, 20, 24, 31, 22, 24, 24]
[28, 31, 23, 26, 36, 23, 30, 36, 32, 23, 20, 25, 23, 25, 25, 40, 21, 27, 21, 25, 28, 38]
[30, 24, 24, 25, 38, 27, 35, 31, 21, 31, 27, 22, 25, 25, 39, 31, 22, 23, 30, 29, 20, 23]
[25, 21, 42, 24, 24, 31, 22, 34, 32, 21, 23, 27, 20, 35, 31, 23, 26, 33, 20, 23, 22, 43]
[23, 23, 20, 40, 27, 22, 22, 41, 20, 21, 45, 26, 22, 28, 29, 39, 24, 23, 26, 34, 20, 38]
[22, 44, 27, 36, 29, 22, 24, 35, 30, 20, 20, 31, 38, 23, 20, 31, 25, 29, 30, 21, 24, 28]
[27, 30, 21, 28, 39, 30, 33, 33, 25, 21, 26, 33, 33, 24, 31, 20, 24, 25, 22, 27, 28, 20]
[23, 28, 24, 20, 35, 29, 33, 22, 23, 21, 31, 39, 32, 22, 24, 39, 22, 21, 29, 32, 34, 25]
[38, 25, 20, 22, 21, 44, 32, 20, 26, 20, 21, 29, 25, 20, 37, 27, 33, 23, 20, 39, 28, 27]
[29, 22, 30, 20, 31, 23, 23, 24, 28, 28, 46, 27, 24, 23, 21, 35, 20, 21, 45, 29, 27, 34]
[21, 29, 21, 33, 38, 44, 21, 20, 41, 30, 26, 23, 23, 29, 21, 32, 20, 29, 32, 29, 21, 26]
[21, 20, 24, 40, 30, 30, 31, 27, 20, 34, 28, 37, 31, 20, 38, 43, 25, 25, 21, 20, 27, 22]
[27, 35, 30, 21, 36, 37, 41, 21, 23, 24, 23, 32, 23, 25, 20, 23, 36, 40, 30, 24, 20, 24]
[39, 30, 30, 21, 26, 23, 20, 25, 36, 22, 23, 29, 23, 42, 20, 23, 32, 20, 30, 36, 25, 31]
[24, 24, 25, 41, 20, 27, 35, 31, 21, 24, 31, 36, 20, 25, 22, 32, 31, 30, 21, 22, 33, 25]
[22, 34, 33, 20, 29, 24, 34, 27, 27, 31, 20, 24, 22, 33, 36, 22, 21, 31, 21, 38, 21, 44]
[20, 43, 29, 23, 22, 32, 20, 21, 26, 23, 26, 33, 34, 22, 26, 20, 38, 21, 29, 32, 24, 33]
[23, 38, 39, 35, 21, 33, 25, 39, 33, 28, 23, 20, 22, 22, 25, 30, 20, 26, 28, 31, 24, 30]
[21, 36, 32, 42, 25, 25, 20, 46, 24, 22, 22, 22, 33, 32, 22, 29, 24, 26, 30, 23, 22, 21]
[25, 34, 20, 23, 44, 21, 40, 21, 25, 20, 26, 25, 44, 20, 24, 32, 21, 23, 31, 21, 43, 22]
[34, 31, 23, 20, 25, 30, 22, 23, 30, 22, 31, 21, 41, 42, 21, 22, 36, 20, 26, 24, 31, 32]
[27, 27, 35, 34, 31, 36, 21, 21, 24, 39, 22, 29, 29, 20, 20, 46, 23, 30, 27, 24, 28, 21]
[28, 37, 30, 31, 38, 23, 21, 20, 21, 32, 29, 24, 32, 20, 20, 21, 28, 20, 32, 41, 25, 40]
[27, 25, 24, 46, 23, 24, 26, 28, 30, 23, 23, 27, 38, 20, 44, 21, 27, 25, 20, 23, 26, 28]
[20, 28, 24, 33, 25, 22, 28, 27, 22, 27, 42, 25, 43, 27, 20, 26, 29, 33, 29, 24, 36, 23]
[39, 31, 27, 20, 23, 25, 22, 22, 24, 26, 25, 42, 21, 22, 21, 21, 28, 24, 44, 31, 35, 34]
[20, 20, 31, 30, 41, 30, 40, 20, 28, 20, 21, 25, 23, 30, 28, 25, 29, 21, 28, 28, 38, 24]
[35, 37, 30, 20, 24, 25, 36, 21, 23, 29, 25, 23, 21, 27, 22, 44, 41, 24, 33, 30, 22, 20]
[22, 22, 25, 20, 22, 29, 25, 25, 21, 33, 23, 20, 21, 42, 39, 32, 33, 30, 46, 34, 21, 22]
[26, 25, 27, 35, 30, 39, 20, 26, 43, 20, 29, 33, 23, 27, 35, 21, 20, 36, 24, 27, 21, 28]
[20, 30, 24, 31, 36, 23, 24, 46, 30, 28, 24, 25, 24, 22, 20, 33, 20, 21, 24, 23, 39, 27]
[20, 22, 33, 22, 33, 22, 38, 24, 29, 36, 23, 31, 26, 24, 28, 28, 26, 28, 43, 24, 25, 20]
[36, 26, 24, 24, 24, 33, 21, 28, 27, 29, 31, 31, 21, 27, 25, 24, 34, 20, 33, 37, 23, 30]
[25, 33, 24, 27, 30, 35, 25, 30, 23, 23, 20, 20, 28, 30, 29, 38, 25, 25, 32, 21, 25, 33]
[30, 21, 27, 33, 21, 43, 23, 23, 25, 29, 23, 38, 28, 24, 21, 44, 22, 31, 32, 21, 20, 27]
[21, 33, 26, 26, 33, 27, 26, 32, 41, 31, 25, 29, 33, 22, 26, 38, 24, 22, 21, 28, 21, 21]
[26, 28, 31, 20, 38, 20, 26, 23, 24, 24, 30, 21, 21, 33, 26, 33, 38, 28, 40, 24, 21, 26]
[21, 27, 30, 22, 24, 28, 38, 27, 20, 23, 41, 20, 26, 41, 26, 24, 29, 22, 20, 43, 21, 42]
[22, 28, 21, 25, 25, 46, 29, 27, 24, 34, 24, 27, 23, 23, 34, 21, 37, 26, 20, 44, 28, 24]
[32, 27, 21, 35, 28, 37, 21, 32, 23, 20, 21, 20, 31, 21, 32, 24, 35, 26, 42, 35, 22, 24]
[22, 36, 41, 35, 27, 20, 25, 21, 28, 32, 31, 30, 23, 26, 23, 26, 28, 33, 23, 35, 20, 23]
[28, 24, 27, 39, 37, 25, 21, 29, 36, 27, 24, 24, 26, 27, 37, 27, 28, 23, 27, 21, 22, 26]
[32, 33, 24, 31, 22, 35, 39, 20, 39, 39, 22, 21, 23, 28, 34, 23, 20, 21, 35, 24, 23, 22]
[25, 20, 20, 25, 28, 23, 37, 30, 34, 27, 22, 20, 41, 22, 22, 23, 42, 27, 39, 25, 22, 24]
[20, 36, 22, 21, 21, 38, 20, 45, 36, 28, 23, 23, 35, 26, 20, 30, 31, 28, 33, 22, 25, 31]
[30, 23, 21, 45, 20, 31, 35, 21, 22, 24, 29, 32, 34, 30, 23, 31, 20, 20, 31, 35, 29, 20]
[22, 21, 22, 32, 42, 24, 35, 22, 26, 21, 28, 23, 24, 21, 31, 20, 27, 39, 42, 21, 37, 33]
[26, 28, 24, 20, 42, 23, 22, 20, 22, 33, 24, 25, 24, 28, 38, 26, 44, 28, 31, 20, 28, 25]
[25, 42, 32, 20, 25, 20, 27, 22, 21, 20, 31, 28, 21, 31, 25, 25, 46, 28, 30, 41, 25, 20]
[20, 27, 28, 26, 34, 23, 20, 22, 34, 20, 36, 30, 21, 23, 26, 23, 31, 37, 23, 34, 40, 29]
[28, 30, 22, 21, 20, 35, 20, 24, 23, 24, 34, 33, 37, 34, 24, 21, 24, 21, 41, 32, 22, 30]
[21, 20, 21, 28, 24, 42, 36, 26, 29, 33, 26, 22, 33, 28, 26, 31, 20, 22, 29, 32, 27, 28]
[23, 41, 24, 39, 22, 23, 25, 21, 24, 35, 20, 27, 31, 43, 34, 29, 24, 22, 23, 21, 37, 21]
[20, 29, 32, 21, 27, 25, 32, 36, 24, 34, 33, 31, 25, 21, 29, 26, 21, 32, 23, 33, 20, 29]
[21, 32, 22, 26, 40, 40, 23, 28, 26, 25, 31, 21, 20, 37, 30, 30, 25, 35, 27, 24, 24, 21]
[25, 25, 27, 21, 27, 23, 20, 39, 20, 43, 29, 21, 38, 27, 30, 23, 24, 29, 20, 24, 36, 30]
[26, 20, 22, 25, 28, 22, 21, 29, 30, 37, 23, 39, 20, 34, 33, 23, 25, 30, 27, 41, 27, 26]
[29, 20, 32, 22, 26, 27, 21, 20, 27, 26, 22, 42, 28, 24, 26, 23, 40, 24, 27, 42, 23, 44]
[21, 38, 25, 26, 35, 28, 21, 40, 37, 28, 25, 23, 26, 22, 22, 21, 46, 29, 23, 23, 21, 32]
[39, 23, 20, 37, 26, 22, 30, 21, 25, 25, 32, 20, 39, 20, 33, 23, 24, 32, 38, 22, 33, 27]
[21, 21, 21, 20, 34, 20, 27, 36, 25, 20, 20, 26, 34, 40, 32, 32, 30, 22, 28, 29, 36, 35]
[37, 30, 23, 20, 21, 38, 26, 21, 41, 34, 33, 26, 36, 26, 25, 34, 34, 20, 24, 21, 20, 25]
[28, 24, 25, 29, 41, 24, 24, 29, 34, 37, 20, 29, 21, 30, 21, 28, 33, 20, 22, 43, 27, 20]
[35, 36, 20, 29, 26, 30, 26, 26, 34, 22, 24, 25, 21, 35, 34, 34, 25, 21, 23, 31, 24, 20]
[24, 25, 22, 22, 31, 28, 38, 42, 33, 24, 37, 27, 21, 42, 22, 28, 25, 20, 21, 25, 22, 29]
[26, 38, 33, 40, 22, 22, 21, 26, 29, 26, 23, 25, 35, 21, 27, 23, 35, 21, 43, 29, 20, 29]
[26, 31, 25, 20, 20, 21, 25, 25, 24, 28, 22, 30, 22, 22, 40, 37, 29, 46, 20, 38, 22, 24]
[24, 26, 23, 22, 34, 26, 30, 20, 24, 21, 32, 24, 24, 31, 31, 27, 28, 31, 32, 45, 25, 33]
[30, 32, 24, 27, 24, 21, 25, 22, 23, 39, 39, 22, 27, 23, 37, 23, 32, 23, 38, 21, 36, 22]
[27, 23, 22, 24, 28, 42, 26, 33, 28, 20, 20, 35, 22, 20, 31, 27, 34, 23, 32, 36, 23, 38]
[31, 35, 23, 28, 21, 28, 37, 20, 38, 34, 27, 20, 24, 27, 22, 26, 20, 29, 35, 31, 28, 21]
[28, 21, 33, 31, 24, 29, 20, 23, 25, 22, 28, 27, 30, 25, 29, 28, 26, 22, 38, 39, 30, 33]
[23, 36, 41, 26, 23, 29, 29, 45, 20, 23, 34, 21, 22, 39, 35, 24, 20, 24, 24, 25, 23, 28]
[25, 25, 21, 32, 44, 24, 32, 28, 33, 21, 22, 38, 32, 22, 25, 29, 22, 27, 29, 26, 26, 32]
[35, 28, 35, 24, 27, 34, 25, 30, 25, 42, 29, 26, 20, 36, 25, 25, 20, 20, 23, 21, 31, 34]
[44, 23, 20, 25, 24, 28, 20, 23, 38, 21, 24, 28, 35, 30, 20, 45, 23, 28, 39, 26, 23, 25]
[22, 25, 22, 45, 21, 22, 31, 37, 42, 28, 21, 24, 26, 25, 30, 25, 20, 36, 23, 25, 23, 29]
[32, 21, 28, 20, 20, 41, 25, 20, 46, 21, 38, 31, 25, 26, 21, 30, 20, 31, 39, 24, 22, 24]
[34, 24, 23, 26, 33, 20, 26, 26, 24, 20, 24, 25, 21, 29, 31, 30, 39, 34, 28, 27, 25, 41]
[26, 36, 20, 27, 23, 23, 20, 27, 32, 23, 24, 36, 34, 23, 24, 43, 25, 25, 33, 24, 31, 31]
[23, 21, 28, 20, 33, 46, 20, 43, 21, 24, 28, 21, 22, 34, 38, 25, 20, 20, 20, 25, 44, 32]
[30, 35, 26, 21, 28, 20, 21, 22, 24, 35, 23, 22, 21, 26, 24, 31, 41, 37, 27, 20, 43, 25]
[34, 42, 21, 20, 26, 21, 40, 20, 41, 21, 21, 23, 29, 22, 21, 26, 30, 25, 32, 29, 39, 27]
[31, 44, 40, 27, 22, 21, 44, 21, 30, 26, 20, 34, 22, 20, 20, 20, 29, 36, 22, 21, 22, 38]
[21, 43, 46, 28, 32, 22, 23, 21, 24, 21, 28, 21, 20, 33, 21, 24, 36, 22, 23, 28, 45, 32]
[21, 22, 24, 39, 21, 25, 25, 20, 23, 20, 22, 26, 40, 39, 22, 28, 41, 38, 20, 20, 33, 33]
[34, 22, 26, 23, 28, 20, 32, 25, 24, 20, 39, 28, 41, 24, 29, 32, 24, 33, 23, 34, 24, 23]
[22, 39, 36, 22, 24, 20, 28, 23, 30, 39, 23, 33, 37, 25, 27, 20, 23, 27, 34, 31, 25, 20]
[34, 20, 20, 22, 26, 21, 26, 40, 23, 20, 42, 23, 31, 25, 46, 31, 27, 28, 22, 31, 34, 23]
[24, 29, 39, 24, 39, 26, 25, 25, 29, 23, 27, 20, 46, 21, 27, 25, 20, 41, 24, 31, 25, 22]
[42, 25, 23, 30, 22, 23, 37, 20, 29, 32, 28, 22, 35, 36, 22, 20, 27, 39, 21, 20, 22, 32]
[24, 26, 37, 44, 26, 23, 21, 23, 34, 33, 36, 22, 22, 22, 21, 27, 35, 24, 22, 44, 21, 20]
[24, 27, 22, 30, 20, 27, 21, 24, 31, 22, 30, 33, 35, 24, 23, 20, 32, 28, 30, 44, 26, 29]