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I think we are looking for a mathematical solution, not one that can be foiled by either player having a perfect memory.

I think I've solved it. If this works it is pretty elegant:

<font color=" white">C shuffles the deck.

A and B agree on an order to listen to the phone, so that during each 5 second interval for the next 2 minutes, exactly one of them will be listening. For example, A could listen for the first minute, then B listens for the next minute. Or A listens for 5 seconds, then B for 10, etc. They make sure each of them is listening for a total of 12 5-second intervals.

Every 5 seconds for 2 minutes, C deals out one of the remaining card and calls its name down the phone.

C takes the remaining 12 cards and they start to play.</font>

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So C knows everyone's cards???