Smart Five in a Row
Player #1 intelligence:
Player #1 and player #2 (computer) mark circles and X's to try and block the other player from forming a line of circles or X's while being first to get 5 in a line in any row, column, or diagonal. If any player is stupid then they pick squares at random and would hardly ever get lucky to win, especially if the other player is "smart". However, if both are "stupid" then either has a chance. If both players are smart there is likely to be a CAT GAME where nobody wins.
The Number of possible arrangements just now is:
How many ways can one place five x's (or o's) in a row, either in the columns, rows, or diagonally?
It seems there are 4 ways to put five in a row in a column x 8 columns = 32 ways, and the same for rows = 32, then in the longest diagonal there are 4 ways, in the next longest diagonal there are 3 ways (but two such diagonals), then 2 ways (x2) and one way (x2) = 4+3+3+2+2+1+1 = 16 for the left to right downward diagonals, and 16 ways for the right to left downward diagonals which means there are 32 ways for the diagonals. This gives a total of 32+32+32 = 96 ways to place five in a row. Right?