Henry Ernest Dudeney/Modern Puzzles/181 - The Six Cottages

Modern Puzzles by Henry Ernest Dudeney: $181$

The Six Cottages

A circular road, $27$ miles long, surrounds a tract of wild and desolate country,

and on this road are $6$ cottages so placed that one cottage or another is at a distance of one, two, three up to $26$ miles inclusive from some other cottage.

Thus, Brown may be a mile from Stiggins, Jones two miles from Rogers, Wilson three miles from Jones, and so on.

Of course, they can walk in either direction if required.

Can you place the cottages at distances that will fulfil the conditions?

The illustration is intended to give no clue as to the relative distances.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Measuring, Weighing, and Packing Puzzles: $181$. -- The Six Cottages
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Combinatorial & Topological Problems: Miscellaneous Combinatorial Puzzles: $454$. The Six Cottages