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Arrange the numbers 1 to 19 in the circles


jasen
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     O---o---O
    / \     / \
   o   o   o   o
  /     \ /     \
 O---o---O---o---O
  \     / \     /
   o   o   o   o
    \ /     \ /
     O---o---O

Arrange the numbers 1 to 19 in the circles, so all the rows of 3 numbers between O (big o) sums to 23

Example :

     a---b---c
    / \     / \
   d   e   f   g
  /     \ /     \
 h---i---j---k---l
  \     / \     /
   m   n   o   p
    \ /     \ /
     q---r---s

a+b+c = a+e+j = c+f+j = 23, and so on....

Note :

  • There are 2 solutions, if we rule out reflections and rotations.

Bonus Puzzle : How if all the rows of 3 numbers between O (big o) sums to 22,24,25,26,27,28,29,31,32,33,34,35,36, 37, and 38. I have checked all the solutions by computer, and all those sums have solutions.

Edited by jasen
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