https://www.youtube.com/watch?v=G4QbuWB0EpY

a_not_so_magic_square.c

#include <stdio.h>

typedef int square;
typedef int row;
typedef int col;

int is_valid_row(row n)
{
    return (
        n == 0b0011 ||
        n == 0b0101 ||
        n == 0b1001 ||
        n == 0b0110 ||
        n == 0b1010 ||
        n == 0b1100
    );
}

int is_valid_col(col n)
{
    return (
        n == 0x0011 ||
        n == 0x0101 ||
        n == 0x1001 ||
        n == 0x0110 ||
        n == 0x1010 ||
        n == 0x1100
    );
}

row get_row(square sq, int r)
{
    return (sq & (0b0000000000001111<<(4*r))) >> 4*r;
}

col get_col(square sq, int c)
{
    return ((sq & 0b0001000100010001<<c) >> c);
}

int is_valid_square(square sq)
{
    return (
        is_valid_row(get_row(sq, 0)) &&
        is_valid_row(get_row(sq, 1)) &&
        is_valid_row(get_row(sq, 2)) &&
        is_valid_row(get_row(sq, 3)) &&
        is_valid_col(get_col(sq, 0)) &&
        is_valid_col(get_col(sq, 1)) &&
        is_valid_col(get_col(sq, 2)) &&
        is_valid_col(get_col(sq, 3))
    );
}

int main() {
    int counter = 0;

    for (int i=0; i<0x10000; i++)
    {
        if (is_valid_square(i)) {
            counter++;
        }
    }

    printf("%d\n", counter);

    return 0;
}