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

Source Work

 * Magic Star Problems
 * $178$ -- The Seven-Pointed Star
 * $178$ -- The Seven-Pointed Star


 * Combinatorial & Topological Problems
 * Magic Star Puzzles
 * $395$. The Seven-Pointed Star
 * $395$. 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 in.