Did you solve it? The EU interpreter puzzle

The solution to todays question about Rons tongues

Earlier today I set you this puzzle:

Fran French, Geraldine German, Dudley Dutch, Spike Spanish, Polly Polish and Ron Romanian are six British interpreters at the EU.

They each speak two European languages, as well as English, but none speaks the language indicated by their name.

No two interpreters speak the same two foreign languages and each of the six foreign languages is spoken by only two of them.

Spike speaks Dutch and German while his cousin speaks Dutch and Polish.

Fran and Dudley speak all the four languages not indicated by their names. Of the two languages that Dudley is fluent in, both of their namesakes speak French. No German speakers knows any Polish.

Which two languages does Ron speak?

The answer is French and Spanish, and heres why:

If the languages are F, G, D, S, P and R then we know:

1) Spike speaks D and G

2) Fran and Dudley speak G, S, P and R.

There are six possible combinations of splitting these four languages between Fran and Dud:

(i) Fran speaks G, P and Dud speaks S, R: IMPOSSIBLE since no German speakers know Polish.

(ii) Fran speaks S, R, and Dud speaks G, P: IMPOSSIBLE since no German speakers know Polish.

(iii) Fran speaks G, R, and Dud speaks S, P: IMPOSSIBLE since namesakes of both of Duds languages can speak French, but we know Spike Spanish does not speak French.

(iv) Fran speaks P, R and Dud speaks S, G: IMPOSSIBLE since namesakes of both of Duds languages can speak French, but we know Spike Spanish does not speak French.

(v) Fran speaks S, P and Dud speaks G, R: IMPOSSIBLE since this would mean that both Geraldine and Ron speak French, which means that Spikes cousin, the only one left, is Polly, who speaks Dutch and Polish. But Ms Polish cannot speak Polish because no one speaks the language indicated by their name.

(vi) Fran speaks G, S and Dud speaks P, R: This would mean that both Polly and Ron speak French, and therefore Spikes cousin is Geraldine who speaks Dutch and Polish. Since each language is spoken by two of the interpreters, the second Romanian speaker must be Polly (since it cant be Ron) and the second Spanish speaker must be Ron. This is the unique solution: Ron speaks French and Spanish.

I post a puzzle here on a Monday every two weeks.

If you are reading this on the Guardian app, click where it says Follow Alex Bellos and youll get an alert when I publish the next puzzle.

If you want to propose a puzzle for this column, please email me Id love to hear it.

Im the author of three popular maths books including Alexs Adventures in Numberland and the maths colouring book Snowflake Seashell Star.

You can check me out on Twitter, Facebook, Google+, my personal website or my Guardian maths blog.

Read more: https://www.theguardian.com/science/2016/jul/04/did-you-solve-it-the-eu-interpreter-puzzle