**From New Scientist #1052, 19th May 1977** [link]

There has been a lot of excitement recently about an examination which four of our employees — Alf, Bert, Charlie and Duggie — have been having in French and mathematics.

Now that we are in the Common Market it is important that we should move with the times and learn some French. And in a modern factory such as ours we must know about all the latest mathematical ideas.

It is interesting that Bert’s French place was a much above his mathematics place as Charlie’s mathematics place was below his French place. Alf’s place was even at both subjects, and Duggie’s place was odd at both. Bert was not top at either subject, and no one had the same place at both. There were no ties.

Find the order in both subjects.

This was the first in a series of puzzles called *Puzzle* set by Eric Emmet in **New Scientist** between May 1977 and February 1979 (when it was replaced by *Enigma*). As with his *Enigma* puzzles these seem to consist mostly of substituted sums, substituted divisions and football table problems.

[puzzle1]

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Solution:In Mathematics: 1st = Duggie, 2nd = Alf, 3rd = Charlie, 4th = Bert. In French: 1st = Charlie, 2nd = Bert, 3rd = Duggie, 4th = Alf.This is the published solution, and is the only solution

ifwe assume that Bert’s placement in French was better than his placement in Maths. If we allow it to be worse (so the amount his placement in French was above his placement in Mathematics would be negative) then there is a further solution:In Mathematics: 1st = Charlie, 2nd = Bert, 3rd = Duggie, 4th = Alf. In French: 1st = Duggie, 2nd = Alf, 3rd = Charlie, 4th = Bert.

This solution has the same positions as the published solution, but with the subjects swapped over.

A piece of history here, mentioning the Common Market!

By setting the Configuration in MiniZinc to multiple solutions, I managed to get the two solutions mentioned by Jim, the first solution being the published solution