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
so far... by Josh)
Good job Josh!
When I saw the "triangle" formation of the counters in my own 5x5, seeing how the tight group reduced the number of lines restricting the placement of other counters, I thought it might work for other grids too. I just did not have the time to explore it. Of course, it did not help that my own 5x5 grid could only support 9 counters. Below is the 8x8 with n*2 = 16 counters.
8x8______MAX=16
. . X . X . . .
. . . X . X . .
. X . . . . . X
X . . . . . X .
. X . . . . . X
X . . . . . X .
. . X . X . . .
. . . X . X . .
Edited on April 28, 2006, 6:12 am
|
|
Posted by Dej Mar
on 2006-04-28 04:23:40 |
re: so far...
