A group of $n$ number theorists attend a party where they play the following game. Each of them is given a hat with an integer from $1$ to $n$ written on it, possibly with repetitions. They can see everyone else’s number, but it is impossible for them to see their own. Moreover, once the hats are given no form of communication between them is allowed. At the count to three they all simultaneously try to guess the number on their own hat. If they are given time to discuss a strategy beforehand, show that they can guarantee that at least one person makes a correct guess.