|
|
|
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: unknown
Yes. Alice and Bob both announce the sum, mod 7, of their cards. Charlie's card is the negative of the sum of Alice's and Bob's total, mod 7. The only information Alice and Bob have given Charlie is what Charlie already knows: his own card. From this, both Alice and Bob can deduce each other's cards.
(none)
(none)
(none)
The webmaster and author of this Math Help site is Graeme McRae.