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# 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

## Recommended Posts

• 0

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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