Henry Ernest Dudeney/Modern Puzzles/179 - Two Eight-Pointed Stars

Modern Puzzles by Henry Ernest Dudeney: $179$

Two Eight-Pointed Stars: The puzzles of stars with five, six, and seven points that I have given lead up to the eight-pointed star.

The star may be formed in two different ways, as shown in our diagram, and the first example is a solution.

The numbers $1$ to $16$ are so placed that every straight line of four adds up to $34$.

If you substitute for every number its difference from $17$ you will get the complementary solution.

$\qquad$

Let the reader try to discover some of the other solutions, and he will find it a very hard nut, even with this one to help him.

But I will present the puzzle in an easy and entertaining form.

When you know how, every arrangement in the first star can be transferred to the second one automatically.

Every line of four numbers in the one case will appear in the other, only the order of the numbers will have to be changed.

Now, with this information given, it is not a difficult puzzle to find a solution for the second star.

1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Magic Star Problems: $179$. -- Two Eight-Pointed Stars
1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Magic Star Puzzles: $396$. Two Eight-Pointed Stars