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

by : $179$

 * 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.


 * Dudeney-Modern-Puzzles-179.png


 * 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.