Henry Ernest Dudeney/Modern Puzzles/177 - The Six-Pointed Star/Mistake

Source Work

 * Magic Star Problems
 * $177$ -- The Six-Pointed Star
 * $177$ -- The Six-Pointed Star


 * Combinatorial & Topological Problems
 * Magic Star Puzzles
 * $394$. The Six-Pointed Star
 * $394$. The Six-Pointed Star

Mistake

 * There are $37$ solutions in all, or $74$ if we count complementaries.


 * $32$ of these are regular, and $5$ are irregular.


 * Of the $37$ solutions, $6$ have their points summing to $26$. These are as follows:


 * $\begin {array} {rrrrrrrrrrrr}

10 & 6 & 2 & 3 & 1 & 4 & 7 & 9 & 5 & 12 & 11 & 8 \\ 9 & 7 & 1 & 4 & 3 & 2 & 6 & 11 & 5 & 10 & 12 & 8 \\ 5 & 4 & 6 & 8 & 2 & 1 & 9 & 12 & 3 & 11 & 7 & 10 \\ 5 & 2 & 7 & 8 & 1 & 3 & 11 & 10 & 4 & 12 & 6 & 9 \\ 10 & 3 & 1 & 4 & 2 & 6 & 9 & 8 & 7 & 12 & 11 & 5 \\ 8 & 5 & 3 & 1 & 2 & 7 & 10 & 4 & 11 & 9 & 12 & 6 \\ \end {array}$




 * Also note that where the $6$ points add to $24$, $26$, $30$, $32$, $34$, $36$ or $38$, the respective number of solutions is $3$, $6$, $2$, $4$, $7$, $6$ and $9$, making $37$ in all.

Correction
There are in fact $80$ solutions, as noted by in.