It is interesting for me to remember my very first programming task. The very first day I was introduced to programming with Pascal (I think I was 14), I was taught variables, assignments, arithmetic and was given a task to switch two variables (swap). I quickly solved it using third variable, but then I was asked to do it without third variable. It was very hard task for me, I spent few hours at home tackling it, but finally I solved it with a trick conceptually similar to XOR:

    a := a + b;
    b := a - b;
    a := a - b;