The best solution I have ever seen.

I attempt 9 tests for 1.7 seconds. Here are they:

test.assert_equals(proper_fractions(1), 0)

test.assert_equals(proper_fractions(2), 1)

test.assert_equals(proper_fractions(40), 16)

test.assert_equals(proper_fractions(13), 12)

test.assert_equals(proper_fractions(25), 20)

test.assert_equals(proper_fractions(15), 8)

test.assert_equals(proper_fractions(1532420), 608256)

test.assert_equals(proper_fractions(500000003), 500000002)

test.assert_equals(proper_fractions(9999999), 6637344)

P.S. Can I know how many tests are there?

Already fixed.

Python:
I can't figure out why this is True:
Test.assert_equals(geo_mean([1, 2], 3), 2.2894284851066637)
The missing number is 6, because (1+2 + X) / 3 = 3;
X = 6
So, the answer is sqrt(6 * 2) ~ 3.464

Any help?

Thanks for comment. I will correct it.

Thank you so much! I have done random tests.

Hello coders.
I would like my kata had some random test cases. But I don't know how to do them. Could you please send me a code for these tests?
Here is the kata:https://www.codewars.com/kata/5919f3bf6589022915000023
Language is Python 3.4