The number of solutions to the 8 queens puzzle

Modify the code considered in the lectures to find out the number of solutions to the 8 queens puzzle. For example, as was explained in the videos, for the 4 queens puzzle there are 2 solutions.

import itertools as it

def is_solution(perm):
    for (i1, i2) in it.combinations(range(len(perm)),2):
        if abs(i1-i2)==abs(perm[i1]-perm[i2]):
            return False
    return True

assert(is_solution([1,3,0,2]) == True)
assert(is_solution([3,1,0,2]) == False)

print(is_solution([1,3,0,2]))  # should print True
print(is_solution([3,1,0,2]))  # should print False

True
False

---

Solution) 

def count_n_queens_solutions(n):
    def is_valid(board):
        current_queen_row, current_queen_col = len(board) - 1, board[-1]
        for row, col in enumerate(board[:-1]):
            diff = abs(current_queen_col - col)
            if diff == 0 or diff == current_queen_row - row:
                return False
        return True

    def solve(board):
        if len(board) == n:
            return 1
        count = 0
        for col in range(n):
            board.append(col)
            if is_valid(board):
                count += solve(board)
            board.pop()
        return count

    return solve([])

# Finding the number of solutions for the 8 queens puzzle
num_solutions_8_queens = count_n_queens_solutions(8)
num_solutions_8_queens

The answer is 92.