Henry Ernest Dudeney/Modern Puzzles/168 - The Magisterial Bench

Modern Puzzles by Henry Ernest Dudeney: $168$

The Magisterial Bench

A friend at Singapore asked me some time ago to give him my solution to this problem.

A bench of magistrates consists of two Englishmen, two Scotsmen, two Welshmen, one Frenchman, one Italian, one Spaniard, and one American.

The Englishmen will not sit beside one another, the Scotsmen will not sit beside one another, and the Welshmen also object to sitting together.

Now, in how many different ways may the ten men sit in a straight line so that no two men of the same nationality shall ever be next to one another?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Combination and Group Problems: $168$. -- The Magisterial Bench
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $447$. The Magisterial Bench