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Battleships

In this puzzle the goal is to discover the whereabouts of the enemy fleet making use of the numbers below and next to the diagram. These numbers tell how many parts of boats there are in that particular row or column. Furthermore it is known parts of different ships never touch, not even diagonally, and often some squares are already revealed.

Usually the fleet consists of 1 boat of 4 squares, 2 boats of length 3, 3 boats of lenght 2 and 4 boats that have the size of 1 square each and the grid is 9 by 9 or 10 by 10, but there are many variations. Also sometimes not all numbers are given.

Example

As an example we will look at a smaller puzzle with a fleet of just 3 ships.

Something that strikes out in this diagram is that there is a part of a ship drawn that can only be part of the ship of size 2, because it is the end of a longer boat, but a ship of size 3 does not fit. Because the other boats are not allowed to touch this boat, not even diagonally, we can surround it with water completely (water is available by using the right mousebutton).

Striking is also the number 0 below the third column. Because there are no ships in this column we can now also mark the upper square with water. A comparable situation occurs in the second column. We need two parts of ships there, but we already know where they are. Something similar holds for the bottom row and now it's clear where the two remaining boats reside.

Note that filling in the water and keeping track of the boats found at the side of the diagram are not obligatory. When the puzzle is checked, only the positions where the ships are put matter.

Background

Already at the start of the twentieth century people played a pencil and paper game with rules that are strongly related to the rules of this puzzle, an important difference being that the puzzle is guaranteed to have exactly one solution, where in the game luck and strategy are important factors. Since 1931 a commercial version of the game is available as a board game.


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