What is n-Queen Problem?

The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, Column, or diagonal. The eight queens puzzle is an example of the more general n queens problem of placing n non-attacking queens on an n×n chessboard, for which solutions exist for all natural numbers n with the exception of n = 2 and n = 3.

Problem Statement:
The n-queen problem is the problem of placing n queens on an n x n chessboard such that no queen can attack another queen.

Solution:
Python Program to Solve n-Queen Problem without Recursion

class QueenChessBoard:
    def __init__(self, size):
        # board has dimensions size x size
        self.size = size
        # columns[r] is a number c if a queen is placed at row r and column c.
        # columns[r] is out of range if no queen is place in row r.
        # Thus after all queens are placed, they will be at positions
        # (columns[0], 0), (columns[1], 1), ... (columns[size - 1], size - 1)
        self.columns = []
 
    def place_in_next_row(self, column):
        self.columns.append(column)
 
    def remove_in_current_row(self):
        return self.columns.pop()
 
    def is_this_column_safe_in_next_row(self, column):
        # index of next row
        row = len(self.columns)
 
        # check column
        for queen_column in self.columns:
            if column == queen_column:
                return False
 
        # check diagonal
        for queen_row, queen_column in enumerate(self.columns):
            if queen_column - queen_row == column - row:
                return False
 
        # check other diagonal
        for queen_row, queen_column in enumerate(self.columns):
            if ((self.size - queen_column) - queen_row
                == (self.size - column) - row):
                return False
 
        return True
 
    def display(self):
        for row in range(self.size):
            for column in range(self.size):
                if column == self.columns[row]:
                    print('Q', end=' ')
                else:
                    print('.', end=' ')
            print()
 
 
def solve_queen(size):
    """Display a chessboard for each possible configuration of placing n queens
    on an n x n chessboard and print the number of such configurations."""
    board = QueenChessBoard(size)
    number_of_solutions = 0
 
    row = 0
    column = 0
    # iterate over rows of board
    while True:
        # place queen in next row
        while column 
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