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Programming Enigma Puzzles

11 June 2022

Posted by on **From New Scientist #3390, 11th June 2022** [link] [link]

“Here’s your 21st birthday present”, said Amy.

“A bracelet?”, frowned Sam.

“Not just any bracelet, it is a magic number bracelet because I know you love numbers. See how it has got five beads, each with a different positive number on it. You can find all the numbers from 1 to 21. But to find most of them, you have to add together adjacent beads.”

“For example, to make the number 17 you add together these three beads”, she said, pointing to the beads in positions A, B and C on the diagram. “Other numbers are found by adding two, three or four adjacent beads. And, of course, to get 21, you add up all five”.

What are the five numbers on Sam’s bracelet?

[puzzle#171]

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We have encountered puzzles with “magic circles” before. See:

Teaser 1986,Enigma 985.In fact the solution to this puzzle is the same as

Teaser 1986.Using the

magic_circles.pyprogram given inEnigma 985we can see this is the only magic circle of size 5:Solution:The numbers on the bracelet are: 1, 3, 10, 2, 5.With (A, B, C) = (10, 2, 5).

We don’t need the number 17 requirement to find a unique solution.

A more general program: