Henry Ernest Dudeney/Modern Puzzles/178 - The Seven-Pointed Star/Mistake

Source Work

1926: Henry Ernest Dudeney: Modern Puzzles:

Magic Star Problems

$178$ -- The Seven-Pointed Star

1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems:

Combinatorial & Topological Problems

Magic Star Puzzles

$395$. The Seven-Pointed Star

Mistake

There are $56$ different arrangements, counting complements.

Class $\text I$ is those as above, where pairs in the positions $7 - 8$, $13 - 2$, $3 - 12$, $14 - 1$ all add to $15$, and there are $20$ such cases.

Class $\text {II}$ includes cases where pairs in the positions $7 - 2$, $8 - 13$, $3 - 1$, $12 - 14$ all add to $15$, and there are $20$ such cases.

Class $\text {III}$ includes cases where pairs in the positions $7 - 8$, $13 - 2$, $3 - 1$, $12 - 14$ all add to $15$, and there are $16$ such cases.

Correction

There are in fact $72$ solutions, as noted by Martin Gardner in 536 Puzzles & Curious Problems.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $178$. -- The Seven-Pointed Star
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $395$. The Seven-Pointed Star
• 1975: Martin Gardner: Mathematical Carnival: $5$: Magic Stars and Polyhedrons