I&#x27;ve just thought of an even simpler formulation. Imagine that Alice tells you: &quot;I have three coins, each of them is either heads or tails. You can ask me about one of them, but then the other two will disappear.&quot; Bob, who is far away from Alice, tells you the same thing. They also claim that their sets of coins are &quot;identical&quot;, though you&#x27;re not sure what that means.<p>1) If you ask Alice and Bob about the same coin, their answers always agree.<p>2) If you ask Alice about coin 1 and Bob about coin 2, they are different about 5% of the time.<p>3) If you ask Alice about coin 2 and Bob about coin 3, they are different about 5% of the time.<p>4) If you ask Alice about coin 1 and Bob about coin 3, they are different about 20% of the time!<p>Why is it shocking you ask? Well, if coin 1 is different from coin 3, then at least one of them must be different from coin 2, which you didn&#x27;t ask about, but could have. So the probability of the last situation can&#x27;t be larger than the sum of the previous two. But here it is, almost twice larger. Quantum magic :-)