  Motivated by a game of Battleship, we consider the problem of efficiently
hitting a ship of an uncertain shape within a large playing board. Formally, we
fix a dimension $d\in\{1,2\}$. A ship is a subset of $\mathbb{Z}^d$. Given a
family $F$ of ships, we say that an infinite subset $X\subset\mathbb{Z}^d$ of
the cells pierces $F$, if it intersects each translate of each ship in $F$ (by
a vector in $\mathbb{Z}^d$). In this work, we study the lowest possible
(asymptotic) density $\pi(F)$ of such a piercing subset. To our knowledge, this
problem has previously been studied only in the special case $|F|=1$ (a single
ship). As our main contribution, we present a formula for $\pi(F)$ when $F$
consists of 2 ships of size 2 each, and we identify the toughest families in
several other cases. We also implement an algorithm for finding $\pi(F)$ in 1D.
