Henry Ernest Dudeney/Modern Puzzles/170 - A Heptagon Puzzle/Solution
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Modern Puzzles by Henry Ernest Dudeney: $170$
- A Heptagon Puzzle
- 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 $19$.
Solution
- 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 $45$).
Sources
- 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $170$. -- A Heptagon Puzzle
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $399$. A Heptagon Puzzle