01-03-2006, 04:19 PM
I still don't see how it's possible (I don't want to ruin it by looking up a solution). This is the best I can think of:
Let say the cards in the deck have been assigned numbers 1 to 52.
Volunteer randomly picks 5 cards.
Alice always shows the 4 lowest numbered cards to Bob. This way Bob knows the fifth card is higher than the highest card he's show. The worst case scenario is the first 4 cards get picked - then there are still 48 possibilities. Best case scenario is #51 and #52 getting picked - Bob is shown #51 and knows the fifth has to be #52.
Alice doesn't have to show them to Bob in the same order they were picked, right? Maybe it could mean something different to Bob depending on whether he's first shown the highest of the 4, or the lowest of the 4, etc.
4 * 3 * 2 * 1 = 24 different ways to order the 4 cards. So in the worst case scenario this could cut it down to 48 / 24 = 2 possibilites.
And that's where I get stuck. Can I have a hint?
Let say the cards in the deck have been assigned numbers 1 to 52.
Volunteer randomly picks 5 cards.
Alice always shows the 4 lowest numbered cards to Bob. This way Bob knows the fifth card is higher than the highest card he's show. The worst case scenario is the first 4 cards get picked - then there are still 48 possibilities. Best case scenario is #51 and #52 getting picked - Bob is shown #51 and knows the fifth has to be #52.
Alice doesn't have to show them to Bob in the same order they were picked, right? Maybe it could mean something different to Bob depending on whether he's first shown the highest of the 4, or the lowest of the 4, etc.
4 * 3 * 2 * 1 = 24 different ways to order the 4 cards. So in the worst case scenario this could cut it down to 48 / 24 = 2 possibilites.
And that's where I get stuck. Can I have a hint?