Henry Ernest Dudeney/Modern Puzzles/170 - A Heptagon Puzzle/Solution

Modern Puzzles by Henry Ernest Dudeney: $170$

Using the fourteen numbers, $1$, $2$, $3$, up to $14$, place a different number in every circle

so that the three numbers in every one of the seven sides add up to $19$.

The diagram shows the solution.

Starting at the highest point, write the numbers $1$ to $7$ in a clockwise direction at alternate points.

Then, starting just above the $7$, write $8$ to $14$ successively in the opposite direction, taking every vacant circle in turn.

If instead you write in $1$, $3$, $5$, $7$, $9$, $11$, $13$ and then $2$, $4$, $6$, $8$, $10$, $12$, $14$,

you will get a solution with the sides adding to $22$ instead of $19$.

If you substitute for every number in these solutions its difference from $15$ you will get the complementary solutions,

adding respectively to $26$ and $23$ (the difference of $19$ and $22$ from $45$).