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Numbers in Triangle Rows of 3 are equal rows of 4 are equal

  1. Oct 14, 2008 #1
    Ok I'm new here and I don't know how to find answers to puzzles.

    I've got a few and my brain isn't working.

    Picture a triangle with circles in it. Place the numbers 1-10 in the circles on the triangle so that the sum of Rows of 3 are equal and the sum of rows of 4 are equal

    O O
    O O O
    O O O O

    (If the picture of the triangle doesn't come out it 1 circle on top, then 2, then 3 then 4. The perimeter has 4 circles on all three sides.
  2. jcsd
  3. Oct 15, 2008 #2
    Just to help with the picture, try to code tag

    Code (Text):

        o  o
      o  o  o
    o  o  o  o
  4. Oct 16, 2008 #3
    I believe there are 12 solutions to this, which are variants on 2 different patterns. You can rotate by 120 degrees and get a "new" solution effectively, or flip it along one of the 3 axes of symmetry-- giving you 6 variants on a single solution, and 12 patterns all together, since there are 2 "core" solutions.

    Two of the variants on the core solutions are:
    7 8
    3 4 10
    9 5 6 1

    8 6
    4 7 5
    9 3 1 10

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