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

Historical Note on Modern Puzzles by Henry Ernest Dudeney: $181$ - The Six Cottages

This problem is merely a circular version of the previous problem, The Damaged Measure.

It turns out that the road could have been $31$ miles long so that all integer distances between $1$ and $30$ could be measured.

Sources

• Aug. - Sep. 1965: Michael Goldberg: E1716: Number of Residue Classes Modulo $n$ in a Set of Sums (Amer. Math. Monthly Vol. 72, no. 7: pp. 785 – 786)  www.jstor.org/stable/2314446

• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $454$. The Six Cottages