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