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Programming Enigma Puzzles

26 September 2014

Posted by on **From New Scientist #1371, 18th August 1983** [link]

The picture shows a cuboctahedron, A semi-regular solid with six square faces and eight triangular ones. It has 12 vertices, lettered from A to L.

Can you place the numbers 1 to 14, one on each face, so that the numbers round each vertex add up to the same “magic sum”?

That magic sum should be made as small as possible, please.

Please let me know:

(A) What the magic sum is.

(B) What numbers are on the faces having an edge in common with the 7-face.

**Note:** I am waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The current estimate is that the line will be connected at the end of September 2014.

[enigma225]

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This Python 3 program runs in 392ms.

Solution:(A) The magic sum is 28. (B) The faces with 3, 5 and 6 on share an edge with the face with 7 on.Here’s a diagram of the solution:

(The cuboctahedron is “punctured” in the middle of the face IJKL, and the hole is then stretched out to make the perimeter of a flat disc).

There are multiple solutions where the magic sum is 30. In this case the 7 face can be surrounded by (1, 9, 10), (2, 10, 12), (4, 6, 14), (4, 5, 6) or (9, 10, 12) if it is on a triangular face, or (1, 9, 10, 11) if it is on a square face.

There is also a solution where the magic sum is 32. In this case the 7 face is surrounded by (9, 11, 13).