[2025-01-02] Chessboard parity (odd/even sums across rows and columns)

marbles.py

# See: https://www.youtube.com/watch?v=EONem7cdmSM

import fractions

import numpy as np


def even_sum(m, n):
    for i in range(n):
        s = sum(m[i, :])
        if s % 2 != 0:
            return False

    for j in range(n):
        s = sum(m[:, j])
        if s % 2 != 0:
            return False

    return True


def chessboard_parity(n):
    s = n**2

    match_count = 0
    total_count = 0
    for i in range(2**s):
        as_bin = bin(i)[2:].zfill(s)
        d = [int(c) for c in as_bin]
        m = np.array(d).reshape((n, n))
        total_count += 1
        if even_sum(m, n):
            match_count += 1

    f = fractions.Fraction(match_count, total_count)
    expected = fractions.Fraction(2, 4**n)
    print(f"n = {n}: {match_count}/{total_count} = {f} (expected: {expected})")


def main():
    chessboard_parity(3)
    chessboard_parity(4)
    chessboard_parity(5)


if __name__ == "__main__":
    main()