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Math Help - 15 lines 16 points problem

  1. #1
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    15 lines 16 points problem

    I recently got given a problem by a friend, which I have been struggling over for a while. It is this:

    Draw 16 points, and 15 lines, with exactly 4 points on each line.

    Can anyone help?
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  2. #2
    A Plied Mathematician
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    Do the lines have to be straight? Any particular configuration of points?
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  3. #3
    Senior Member MacstersUndead's Avatar
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    Also, are intersections of lines considered points? ie. can I have four points on a line as well as an intersection not considered a point?
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  4. #4
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    Yes the lines have to be straight, sorry, and the puzzle is to find the configuration of points for which this is possible. No, intersections of lines don't have to be points, so you can have as many intersections on a line as you like.
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  5. #5
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    Place 15 points where the red dots are in the diagram. You then have 10 lines with four points on each, as shown. Now put the 16th point at the centre of the picture, where the blue dot is. You then get five more lines by joining the outer five red dots to the central dot.
    Attached Thumbnails Attached Thumbnails 15 lines 16 points problem-penta.png  
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  6. #6
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    Thank you! I've spent so much time trying to do this problem The answer is so pretty as well!
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