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9 balls, 10 straight lines (Posted on 2008-10-12) Difficulty: 2 of 5
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.
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+
           |   |   |   |   |   |   |   |   |
           +---+---+---+---+---+---+---+---+

See The Solution Submitted by pcbouhid    
Rating: 2.0000 (3 votes)

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Is that all there is, my friend, then ... | Comment 12 of 21 |

Did pcbouhid really intend such a simple solution? He won't say. The diagram by Dej Mar is essentially that presented by Leming in the first Comment, just rotated 90 degrees.  Both meet the specs if we may simply ignore any lines which contain other than three balls (i.e. if two, four, etc.). We are clearly not to define "lines" as solely the grid lattice presented.

Why would the proposer present a grid of 7x9 (I think we should designate the size by the number of intersection points, not by counting cells which do not figure as such in the problem -- but machts nichts), if in fact a 3x5 grid (DejMar and Leming) easily meets the conditions?  I also believe that a proper puzzle of this genre should allow only a single solution, whereas a 7x9 grid allows many (not all are just placement or rotational symmetries of the one diagram, but many would be).

Charity forfends the suggestion that the proposer intended the heart of his puzzle to be to overcome the misdirection implied by the size of the grid.  (Can you name all the even primes under ten billion? Think about it: perhaps "prime" has a secondary meaning, just as "lines" might.)  I am not sure what the category "General" for this puzzle is supposed to mean, but perhaps it allows such whimsies - and should be shunned.  I will downgrade the provisional rating I voted, unless the proposer or someone else shows a "strong" solution.

 

 


  Posted by ed bottemiller on 2008-10-14 18:04:34
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