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 will give a hyper-hypercube interpretation of the game which will allow us to generate some balanced strategies in the 2-colored version of the game. We will also discuss the limited hats game and give a bound for it by using the hyper-hypercube interpretation.