We will consider a hat guessing game. This game is composed of $n$ players who have one of $k$ different colored hats placed on their heads they are allowed to see what other players are wearing, but not their own hat. They then must guess their own hat. No communication is allowed. Before the hats are placed the players are allowed to come up with a public strategy. The goal of the strategy is to maximize the guaranteed number of correct guesses. We will show that the best possible is $\lfloor n/k \rfloor$. \vskip .1in \noindent We then consider several variations of the game including the limited vision problem, constructing balanced strategies and the hat placement problem.