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)
my best minimums are the same as Dej Mar's (4,4,6,8,8,12),
but I got maximums equal to nx2:
4x4: 8
X X . .
. . X X
X X . .
. . X X
5x5: 10
. X X . .
X . . X .
X X . . .
. . . X X
. . X . X
6x6: 12
. . X . X .
X . . X . .
. X . . . X
X . . . X .
. . X . . X
. X . X . .
7x7: 14
. . . X . X .
. . X . X . .
X . . . . . X
. X . . . X .
X . . . . . X
. . X . X . .
. X . X . . .
I haven't tried 8x8 yet but I think I can fit 16..
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Posted by Josh
on 2006-04-28 01:47:11 |
so far...
