For n=3,4,5,6,7,8 find:
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)
(In reply to
Minimum and Maximum by Dej Mar)
Yor maximums for 5x5, 6x6, 7x7, and 8x8 contain 3 in a line as the note points out these are disallowed (In the example below X's replaced with O's are in a straight line.)
____(8)____6x6___(12)____
X X . . . .  X . . O . .
X . . X . .  X . . X . .
. . . . . .  . X . . O .
. X . . X .  . X . . X .
. . . X X .  . . X . . O
. . . . . .  . . X . . X
Edited on April 27, 2006, 1:27 pm

Posted by Jer
on 20060427 13:23:57 