Six people from different countries — Germany, Italy, Britain, Spain, Poland, and France — are seated around a table. Polish sits next to British. German sits next to Italian, or British, or both. Italian does not sit next to the French. Spanish sits immediately after British. Who sits on the sides of the German?

Six people from different countries — Germany, Italy, Britain, Spain, Poland, and France — are seated around a table. Polish sits next to British. German sits next to Italian, or British, or both. Italian does not sit next to the French. Spanish sits immediately after British. Who sits on the sides of the German?

• A. British and Italian
• B. Polish and British
• C. Italian and French
• D. British and French

Answer: (C)

On a circular seating problem, every constraint about who sits next to whom locks in who can be adjacent to whom, and you propagate those restrictions step by step. First, Polish sits next to British, and Spanish sits immediately after British. That means British has two neighbors: Polish on one side and Spanish on the other. So the seats next to British are already taken by Polish and Spanish, leaving German no chance to sit beside British. The rule that German sits next to Italian or British (or both) now forces German to sit next to Italian, since German can’t be next to British. So Italian must be a neighbor of German. Italian cannot sit next to French, so the seat next to Italian on the other side cannot be French. With British flanked by Polish and Spanish, the remaining three people to place are German, Italian, and French in a block adjacent to Spanish. The only way to place Italian next to German while keeping Italian not next to French is to have Italian sit next to Spanish, German next to Italian, and French on the other side of German. That yields German sitting between Italian and French. Thus the two people sitting on the sides of the German are Italian and French.

On a circular seating problem, every constraint about who sits next to whom locks in who can be adjacent to whom, and you propagate those restrictions step by step.

First, Polish sits next to British, and Spanish sits immediately after British. That means British has two neighbors: Polish on one side and Spanish on the other. So the seats next to British are already taken by Polish and Spanish, leaving German no chance to sit beside British.

The rule that German sits next to Italian or British (or both) now forces German to sit next to Italian, since German can’t be next to British. So Italian must be a neighbor of German.

Italian cannot sit next to French, so the seat next to Italian on the other side cannot be French.

With British flanked by Polish and Spanish, the remaining three people to place are German, Italian, and French in a block adjacent to Spanish. The only way to place Italian next to German while keeping Italian not next to French is to have Italian sit next to Spanish, German next to Italian, and French on the other side of German. That yields German sitting between Italian and French.

Thus the two people sitting on the sides of the German are Italian and French.