**From New Scientist #2415, 4th October 2003** [link]

As part of an exam the letters A to F were written down in some order and briefly shown to the candidates, who then tried to memorise the order. Their individual recollections were:

candidate 1: BCDAEF;

candidate 2: DAEFBC;

candidate 3: ABEFDC;

candidate 4: BCFDEA;

candidate 5: AEBDFC;

candidate 6: CFEABD;

candidate 7: DCAEFB.

Then the written exam consisted of a list of questions: for each pair of the letters the candidates were asked which came first. So, for example, one of the questions was “Which came first, A or B?” and another question was “Which came first, A or C?” and so on.

The candidates based their answers on their own individual recollections of the order and, as a consequence, each candidate got a different, even number of the questions right.

What was the correct order?

[enigma1259]

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It’s easy enough to consider all the possible permutations of the letters.

This Python program runs in 204ms.

Solution:The correct order was DAEFCB.