A piece of code to find the optimal strategy for placing tokens on a n by n board without getting a n-token line on a row or diagonal.

bingo.py

import itertools, math

# Determines the width/height of a square board.
def size(board):
    return int(math.sqrt(len(board)))

# Determines whether a flat bingo board (list of length size**2) has five 
# in a row on any row, column, or diagonal. 
def bingo(board): 
    s = size(board)
    for i in range(s):
        row = [ board[j + i * s] for j in range(s) ] 
        col = [ board[i + j * s] for j in range(s) ]
        if all(row) or all(col):
            return True 

    left_diag  = [ board[j + s * j] for j in range(s) ]
    right_diag = [ board[ ((s - 1) - j) + s * j ] for j in range(s) ]

    if all(left_diag) or all(right_diag):
        return True 

    return False 

# Displays the board on the terminal using the mapping defined in symbols.
def display(board):
    s = size(board) 
    symbols = { False: 'o', True: 'x' }
    for i in range(s):
        print ''.join([ symbols[board[j + i * s]] for j in range(s) ])
       
s = 5
boards = itertools.product([False, True], repeat=s**2)
valids = filter(lambda b: not bingo(b), boards)

highest = max([ board.count(True) for board in valids ])
for board in [ board for board in valids if board.count(True) == highest ]:
    display(board)
    print '\n'