The Fifteen Ball Puzzle

Can you arrange 15 billiard balls to form a “difference triangle” in the usual triangular configuration, that is, the arrangement that you would see before the start of a game of pool? The number 1 through 15 is arranged in such a way that each number before a pair of numbers is the positive difference between the pair. (Note: Ignore the negative signs when subtracting).





Are there other solutions?

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My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. You can find me on Twitter` and Facebook. My email is

6 thoughts on “The Fifteen Ball Puzzle

  1. Great puzzle. Obviously there are reflections, but not clear at all to me whether there is a solution with different numbers in the top row—or a different number in the bottom row.


  2. Flipping the array left/right on center lonitudinal axis is a different solution, in form but the same in terms of math expressed as sets? I dunno.


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