364 Answers- SINKING THE FISHING-BOATS
The diagram shows how the warship sinks all the forty-nine boats in twelve
straight courses, ending at the point from which she sets out. Follow every
line to its end before changing your direction.[M. S. Klamkin, in American Mathematical Monthly, February 1955, p. 124,
proved that a continuous path of as few as 2n - 2 straight line segments
could be drawn through all the dots in a square array of n dots on the side,
provided n is greater than 2. The case of n = 3 is a well-known puzzle which
most people fail to solve in four moves because they do not think of extend-
ing line segments beyond the square's borders. The 5 X 5 is the smallest
square that can be solved in 2n - 2 segments without going outside the
borders.
S. W. Golomb has shown that a path of 2n - 2 segments is also sufficient
for a closed path (one that ends, as in the above problem, at the starting
point) on all squares with sides greater than 3. The 7 X 7 is the smallest odd-
sided square with a closed path of 2n - 2 segments that lies entirely within
its border. (The smallest even-sided square on which such a path can be
drawn is the 6 X 6.) The solution given here by Dudeney also appears