HashSet does not seem to realize that two objects are the same.

You need to override the Object#hashCode() method in the Move class to let it return the same hashCode() value for the state of the Move instance. Don’t forget to override Object#equals() as well.

See also:

• Overriding equals and hashCode in Java

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Hint: if you’re using an IDE like Eclipse, you can also just autogenerate them. Rightclick somewhere the Move class, choose Source > Generate hashCode() and equals(). Here is how it look like then:

@Override
public int hashCode() {
    final int prime = 31;
    int result = 1;
    result = prime * result + move1;
    result = prime * result + move2;
    return result;
}

@Override
public boolean equals(Object obj) {
    if (this == obj)
        return true;
    if (obj == null)
        return false;
    if (getClass() != obj.getClass())
        return false;
    Move other = (Move) obj;
    if (move1 != other.move1)
        return false;
    if (move2 != other.move2)
        return false;
    return true;
}