Six Languages

At a recent international conference English was the principal language spoken, but interpreters were also present who could, if required, translate what was said into French, German, Dutch, Spanish, Arabic, and Turkish. Mr. Polyglot, of the Foreign Office, went to the trouble of engaging  interpreters whose surnames corresponded to these six foreign tongues. Each of his six interpreters spoke two of the six foreign languages; no two of them spoke the same two languages; each of the six languages was spoken by just two of them. And none of them spoke the language of which he is the namesake.

Mr. Spanish, for example, could speak Dutch and German, while one of his colleagues (his brother-in-law) spoke Dutch and Arabic. Mr. French and Mr. Dutch, between them, spoke all four of the languages of which neither is the namesake. Of the two languages spoken by Mr. Dutch, both the namesakes spoke French.

Neither of the German-speaking interpreters had any knowledge of Arabic.

What two languages were offered by Mr. Turkish?

(Source: My Best Puzzles in Logic and Reasoning by Hubert "Caliban" Phillips)

An initial tabulation shows everything given:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗		✗
Mr. German		✗
Mr. Dutch	✗		✗
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic					✗
Mr. Turkish						✗

The most productive thing to do next is to focus in on the proposition: "Of the two languages spoken by Mr. Dutch, both the namesakes spoke French." Only three of the translators can possibly speak French. Of them, there are three pairs:

1. Mr. German and Mr. Arabic
2. Mr. German and Mr. Turkish
3. Mr. Arabic and Mr. Turkish

The first possibility is excluded by virtue of the fact that none of the two German interpreters speaks Arabic. But consider what happens when Mr. Dutch speaks German and Turkish and consequently also when Mr. German and Mr. Turkish both speak French:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗	✗	✗
Mr. German	✓	✗
Mr. Dutch	✗	✓	✗	✗	✗	✓
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic	✗	✗			✗
Mr. Turkish	✓	✗				✗

It was said that somebody has got to speak both Dutch and Arabic. Obviously, because of the name, it can't be Mr. Arabic. It can't be Mr. Turkish either, because one of his two slots is already taken up by French. That leaves Mr. German:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗	✗	✗
Mr. German	✓	✗	✓		✓
Mr. Dutch	✗	✓	✗	✗	✗	✓
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic	✗	✗	✗		✗
Mr. Turkish	✓	✗	✗			✗

But now Mr. German speaks three languages, which was stipulated not to be possible. The only remaining possibility of the three named earlier is that Mr. Dutch speaks Arabic and Turkish and consequently that Mr. Arabic and Mr. Turkish both speak French:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗		✗
Mr. German		✗
Mr. Dutch	✗	✗	✗	✗	✓	✓
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic	✓				✗
Mr. Turkish	✓					✗

It was stated that one of the interpreters speaks both Dutch and Arabic. It can't be Mr. Arabic for the obvious reason of his name. Nor can it be Mr. Turkish because one of his two slots is already taken up by French. The others were ruled out at the outset. That leaves only Mr. German:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗		✗		✗
Mr. German	✗	✗	✓	✗	✓	✗
Mr. Dutch	✗	✗	✗	✗	✓	✓
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic	✓		✗		✗
Mr. Turkish	✓		✗		✗	✗

It was also stated that "Mr. French and Mr. Dutch, between them, spoke all four of the languages of which neither is the namesake.". This means that Mr. French speaks German and Spanish and, with this information, the last cells can be filled in:

	French	German	Dutch	Spanish	Arabic	Turkish
Mr. French	✗	✓	✗	✓	✗	✗
Mr. German	✗	✗	✓	✗	✓	✗
Mr. Dutch	✗	✗	✗	✗	✓	✓
Mr. Spanish	✗	✓	✓	✗	✗	✗
Mr. Arabic	✓	✗	✗	✗	✗	✓
Mr. Turkish	✓	✗	✗	✓	✗	✗

Final answer: Mr. Turkish speaks French and Spanish.