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 part a), doing a quick trial and error I've found:

 n  minimum
-----------
 3    4
 4    4
 5    8 
 6    8
 7    12

I don't know if those are the actual minimums required, but it's the best I've been able to accomplish so far, and it seems to make a nice little pattern...