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)

With the additional restriction now in place, The adjustments for the found MAXIMUMs for 5x5 and 6x6 are reduced by 1. As implied in an earlier post, with this restriction, the 7x7 MINIMUM can be reduced to 8 (as is shown in the corresponding grid below).

5x5_MAX=9
X . . . X
. X . X .
X . . . X
. . X . .
. X . X .

6x6__MAX=11
. X . X . .
. . . X X .
X X . . . .
. . . . . X
X . . . X .
. . X . . X

7x7_____MIN=8
X X . . . . .
X . . X . . .
. . . . . . .
. X . . X . .
. . . X X . .
. . . . . . .
. . . . . . .

Edited on April 27, 2006, 11:28 pm

Posted by Dej Mar on 2006-04-27 21:41:39