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jasen

Arrange the numbers 1 to 19 in the circles

Question

     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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1 answer to this question

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Spoiler

1,19,3,12,16,14,18,10,7,6,15,2,5,9,13,17,8,11,4

1,19,3,18,16,14,12,4,13,6,9,8,17,15,7,5,2,11,10

Set a, b, and c to 1, 19, and 3 to constrain the only way 19 can fit with the requirements. Used excel to solve for the remaining corners and center.

 

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