4 ms·

This isn't right though. Let's say Alice tells Bob what she's going to write in the boxes, and Bob can fill out his however he wishes. Due to the constraints gi

This isn't right though. Let's say Alice tells Bob what she's going to write in the boxes, and Bob can fill out his however he wishes. Due to the constraints given in the problem (the way the rows and columns add up), Bob can only pick the "correct" value to put in 8 of his 9 squares. That is: the problem constraints were designed so that there's no 3x3 grid that wins in all 9 squares for Alice and Bob and that simultaneously satisfies the row constraints. This is why the best Alice and Bob can do is win 89% of the time -- the best grid layout (even when they preshare information) satisfying the problem constraints only wins in 8 of the 9 squares. The point of the analogy is that in the quantum version there is a way to work around this unavoidable constraint in the classical problem.

californical 7y ago
This description greatly helped in making the problem "click" for me, thanks! The fact that they can't know which row/column they're going to be assigned makes it impossible to know with more than 8/9 certainty what the correct move would be. Even if they agree ahead of time what the values should be, the fact that they only know half of the information makes it impossible (classically) to win more often than 8/9 of the time. They have no control over and no way of knowing which row/column the other was given. If I'm understanding correctly, the "quantum version" lets you increase that precision arbitrarily depending on how many measurements you make, up to 99.9999999...% Really neat stuff