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Math Help - fun question

  1. #1
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    fun question

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  2. #2
    Senior Member
    Joined
    Dec 2010
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    All hexagons can be made by cutting away 3 equilateral triangles from a larger equilateral triangle.

    All possible n is of the form:
    n = k^2 - k_1^2 - k_2^2 - k_3^2
    where k_i + k_j + 1 \leq k for i\neq j

    e.g.  6 = 3^2 - 1^2 - 1^2 - 1^2
     10 = 4^2 - 2^2 - 1^2 - 1^2
     13 = 4^2 - 1^2 - 1^2 - 1^2

    The next few would be
     5^2 - 2^2 - 2^2 - 2^2 = 13
     5^2 - 3^2 - 1^2 - 1^2 = 14
     5^2 - 2^2 - 2^2 - 1^2 = 16
     5^2 - 2^2 - 1^2 - 1^2 = 19
     5^2 - 1^2 - 1^2 - 1^2 = 22
    ...
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