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Programming Enigma Puzzles

7 January 2012

Posted by on **From New Scientist #2770, 24th July 2010** [link]

As a novelty calendar, I have made three cubes, and on each of the 18 sides I have painted one different capital letter, with at least one vowel on each cube. These are packed in a rectangular box, on one of whose sides is a picture of how the three cubes might look if laid side-by-side in a row displaying the first three letters of one month: for example, JAN for January. The first three letters of all the remaining months can be formed by shuffling and turning the cubes.

(a) What month is actually on the box?

(b) What other letters, in alphabetical order, are on the cube carrying the N?

[enigma1605]

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The following Python program runs in 442ms.

Solution:(a) AUG, (b) E L R T Y.Using a ‘brute force’ program in Basic (which I’m sure nobody wants to see) I found that B and F can be swapped, so there are two overall solutions.

I then relaxed the condition that each cube must have a vowel, and found four more.

A, S, and U must go on one cube, M and P on another, E, R, T, and Y on the third.

That allows MAR, APR, MAY, SEP. Clearly J, A, N and so on must be on different cubes.

D and O must go together on the first or second cube, L and N together on the second or third.

It doesn’t help to let U double as V or a sideways C, nor even to misuse C as G: AUG remains impossible. In fact that follows if both JAN and JUN are to be possible. The twelve months between them use 19 letters, so something has to give.

In his book

The Magic Numbers of Dr MatrixMartin Gardner showed how it can be done with lower-case letters, where n can be turned upside down to make u, and p to make d.The letters on his three cubes were f g j m o p; a e l t u v; b c n r s y.