Problem of the Week 937

Counting Cards?

Charlie has 7 cards numbered 1, 2, 3, 4, 5, 6 and 7 and randomly deals 3 of them to Alice and 3 to Bob. All three people look at the cards that they hold.

Can Alice and Bob communicate with each other, in the presence of Charlie, so that after the communication Alice knows which cards Bob has, and Bob knows which cards Alice has, but, for any card except the one he has, Charlie does not know whether Alice or Bob has it?

Source: Math Intelligencer, Winter 2001
© Copyright 2001 Stan Wagon. Reproduced with permission.

27 Apr 2001