Combinatorics and Graph Theory

Combinatorics in "Battleship"

Authors: Henning Thielemann
Comments: 26 Pages. In German

We calculate the number of ways to arrange the ships in the game "Battleship." The answer: On a 10 × 10 grid, there are 26,509,655,816,984 (approximately 26.5 trillion) ways to place one ship of length 5, two ships of length 4, three ships of length 3, and four ships of length 2, with spaces between them. Rotations and reflections are not excluded from this count.
Category: Combinatorics and Graph Theory