A function that returns a string which resemples a playing board in python

The thing that goes into a given row, column depends on the relationship of the row and column index. Specifically, if both are even or odd (have the same parity), the element will be ' '. If they are not the same parity, the element will be a '*'.

The simplest way to check parity is with

if (i % 2) == (j % 2):

The parity of a number is encoded in the last bit: 1 for even, 0 for odd. You can therefore check for sameness using the XOR operator:

if (i ^ j) & 1:

In this case & 1 removes the last bit using bitwise AND.

To insert a newline at the end of each row, you just need to add that at the end of the outer loop:

def get_playing_board(num):
    board = ''
    for i in range(num):
        for j in range(num):
            board += ' *'[(i ^ j) & 1] # The index expression is 0 or 1
        board += '\n'
    return board

get_playing_board(5)

There is a clever alternative to manually generating each row. Instead, you can generate a string that is one element longer than num and grab a subset for each row:

def get_playing_board(num):
    row = ' *' * ((num + 2) // 2)
    board = ''
    for i in range(num):
        board += row[i % 2:num + i % 2] + '\n'
    return board

You can write either approach as a one-liner:

'\n'.join(''.join(' *'[(i ^ j) & 1] for j in range(num)) for i in range(num))

'\n'.join((' *' * ((num + 2) // 2))[i % 2:num + i % 2] for i in range(num))

I don't particularly recommend the bottom two approaches.