Last week I explored one concept of "line" in a puzzle, converting a Slitherlink from a loop to a single line. This week I want to introduce another variation that uses "lines" in a different way. In this variation on battleships, the fleet is connected from largest ship to smallest ship by a set of tow lines that can each be stretched to at most 3 cell lengths. This limits how far apart certain ships can be from each other, and introduces some more snake-like logic to this familiar puzzle type. Enjoy.

Rules: Locate the 10-ship fleet in the grid so that each segment of a ship occupies a single cell. Ships are oriented either horizontally or vertically, and do not touch each other, not even diagonally. The numbers on the right and bottom edges of the grid reveal the total number of ships segments that appear in that row or column. Additionally, all the ships in the fleet are connected by tow lines, as indicated, which can be stretched to at most 3 cell lengths.

ETA: Examples are your friends. Since the discussion took off with lots of questions, let me clarify that the example shows valid (Euclidean) distances measured from roughly the centers of the cells containing the end segments. The longest possible distance for a tow line is seen in the leftmost column. Because of the choice of a length of 3 units, you will most likely not run into a case where lines can intersect or cross over another ship that is not part of the line. The unique assignment of lines - while not a requirement of this variation - is a property of my solution and the example.

Rules: Locate the 10-ship fleet in the grid so that each segment of a ship occupies a single cell. Ships are oriented either horizontally or vertically, and do not touch each other, not even diagonally. The numbers on the right and bottom edges of the grid reveal the total number of ships segments that appear in that row or column. Additionally, all the ships in the fleet are connected by tow lines, as indicated, which can be stretched to at most 3 cell lengths.

ETA: Examples are your friends. Since the discussion took off with lots of questions, let me clarify that the example shows valid (Euclidean) distances measured from roughly the centers of the cells containing the end segments. The longest possible distance for a tow line is seen in the leftmost column. Because of the choice of a length of 3 units, you will most likely not run into a case where lines can intersect or cross over another ship that is not part of the line. The unique assignment of lines - while not a requirement of this variation - is a property of my solution and the example.

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