Henry Ernest Dudeney/Modern Puzzles/151 - Sinking the Fishing-Boats/Solution

Modern Puzzles by Henry Ernest Dudeney: $151$

Sinking the Fishing-Boats

There are forty-nine fishing-boats in the North Sea.

How could an enemy ram and sink the lot in twelve straight courses,

starting at $A$ and finishing up at the same place?

Solution

Historical Note

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

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Solutions: $151$. -- Sinking the Fishing-Boats
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Answers: $416$. Sinking the Fishing-Boats