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)

For n=3, I get the following:

a) Four markers (in the corners) will force a straight line of 3.

b) Six markers can be placed without a straight line (leave one diagonal UNmarked).