Dividing Dice

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A standard six-sided die spontaneously starts to divide like a living cell. The spots on the die move during the process and spread across the faces of the resulting pair of dice. That is, the two daughter dice share between them the spots from the original parent die, but possibly in new locations. After a while the new spots are fixed in place.

It turns out that when the two new dice are rolled at the same time, the possible totals are still the numbers from 1 to 6, and they are all still equally likely. How could the spots be arranged on the two dice?


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