Henry Ernest Dudeney/Modern Puzzles/151 - Sinking the Fishing-Boats/Historical Note
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Historical Note on Modern Puzzles by Henry Ernest Dudeney: $151$ - Sinking the Fishing-Boats
This solution appears both in Henry Ernest Dudeney's Modern Puzzles and Sam Loyd's Cyclopedia of Puzzles.
Loyd claims to have first given the puzzle in $1908$, but whether he copied it from Dudeney of vice versa has not been determined.
Note that this puzzle is also a solution for the queen's tour on a $7 \times 7$ chessboard in $12$ moves.
Martin Gardner, in his $1968$ repackaging 536 Puzzles & Curious Problems, reports on:
- John L. Selfridge's proof that $2 n - 2$ straight line segments are necessary for a closed path on all squares
- Murray Seymour Klamkin's proof that, for a square array of $n$ dots on a side, as few as $2 n - 2$ straight line segments can be used to draw through them all, for $n > 2$
- Solomon Wolf Golomb's proof that $2 n - 2$ straight line segments are sufficient for a closed path on all such squares where $n > 3$
He also reports on the sizes of squares meeting the restriction that none of the segments go outside the borders.
Sources
- 1955: M.S. Klamkin: E1123: Polygonal Path Covering a Square Lattice (Amer. Math. Monthly Vol. 62: p. 124) www.jstor.org/stable/2308156
- 1955: John L. Selfridge: E1123: Polygonal Path Covering a Square Lattice (addendum) (Amer. Math. Monthly Vol. 62: p. 443) www.jstor.org/stable/2307008
- 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $416$. Sinking the Fishing-Boats