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3 in a row = bad (Posted on 2006-04-26) Difficulty: 4 of 5
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)

See The Solution Submitted by Jer    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Minimum and Maximum | Comment 8 of 13 |
(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 2006-04-27 13:23:57

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