Fill in the Blanks

This is a fun puzzle from John Bassey at Puzzle Sphere.

“The diagram shows a heptagon with three circles on each side. Some circles already have the numbers 8 to 14 filled in, while the remaining circles need to be filled with the numbers 1 to 7. Each circle must contain one number, and the sum of the numbers in every set of three circles along a line must be the same.  Arrange the numbers!!!”

Answer.

See Fill in the Blanks for a solution.

One thought on “Fill in the Blanks

  1. Sanjay Godse

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    Let the heptagon be ABCDEFG.

    Let the numbers at the vertices be A,B,etc.

    The sum of 7 side sums will be (8+10+..+14)+(1+2+..+7)+(1+2+..+7)

    = (1+2+3..+14) + (1+2..+7)

    = 14*15/2 + 7*8/2

    = 105 + 28 = 133

    Hence each side sum is 133/7 = 19.

    The side AB has 14 as midpoint number. It can have numbers either 1,4 or 2,3 at A and B.

    The side GA has 8 as midpoint number. It can have numbers either 4,7 or 5,6 at G and A.

    From above, A can be 4.

    Rest is easy.

    B = 19 – 14 -4 = 1
    C = 19 – 13 – 1 = 5
    D = 19 – 12 – 5 = 2
    E = 19 – 11 – 2 = 6
    F = 19 – 10 – 6 = 3
    G = 19 – 9 – 3 = 7

    The 7 numbers at the 7 vertices A,B,C,D,E,F,G are 4,1,5,2,6,3,7 respectively.

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