Place 9 balls ("o") in the intersections of the grid below to achieve 10 straight lines, each line containing 3 and exactly 3 balls. You may assume, if you need, that each cell is a perfect square.

           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+

(In reply to Redaction (re Dej Mar) by ed bottemiller)

A line may be defined by two points, yet a line does not consist of only two points.  Even one ball can be positioned on an infinite number of lines, yet, as implied by the puzzle's specifications, the lines that are of interest are those lines where three balls, no less and no more, lie upon the line and on the intersections of the grid. 

Thus, the lines consisting of two balls only are not counted among the ten.  The lines where only one ball lies upon the line are not counted among the ten.  The lines where no balls lie upon the line are not counted among the ten. 

The number of lines that can be defined by the points of three balls of the nine balls placed upon the intersections of the 8x6 grid is ten or less, yet the puzzle asks for those lines such that ten exist.  Of these, there are the eighty-plus solutions:

           o---+---o---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           o---o---o---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           o---+---o---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+


           
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---o---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---o---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---o---o---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---o---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---o---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
  
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---o---+---o---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---o---o---o---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---o---+---o---+---o---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
   
           ... et cetera

Posted by Dej Mar on 2008-10-14 15:41:25