a) The minimum number of counters that need be placed on a nxn chessboard such that no additional counters can be placed without creating any straight line of 3;

b) The maximum number of counters that can be placed on a nxn chessboard such that no three lie in a straight line.

Remember that positions like A1, B3, and C5 are in a straight line.
(Try to continue the sequences if you can)

This problem screams 'Ramsey Theory', and consequently frightens me to death.

Although I think I have an answer to the question "The minimum number of counters that need to be placed on an nxn board such that no additional counters can be placed withouth creating any straight line of 2".  :)