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
re: Possible minimum? by tomarken)
tomarken,
this is a "minimum" pattern I found for the 7x7 grid using only 9 counters:
X X _ _ _ _ _
X _ _ X _ _ _
_ _ _ _ _ _ X
_ X _ _ X _ _
_ _ _ X X _ _
_ _ _ _ _ _ _
_ _ _ _ _ _ _
Though not specified, I have made the assumption that both diagonal and orthogonal lines create the "three-in-a-row" restriction, and only these lines. A line can theoretically be drawn from A1, D2 and G3 here, yet that would greatly alter the possible solutions.
Edited on April 26, 2006, 6:40 pm
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Posted by Dej Mar
on 2006-04-26 18:30:38 |
re(2): Possible minimum?
