01-05-2006, 05:21 AM
I hearby declare vspickelen the winner of this challenge. Special thanks goes to Agamemnus for helping me explain it 
Vspickelen, nicely done. That's the same solution I thought of. Not exactly the same but based on the same principles.
Sterling: (WARNING: spoilers ahead!)
No, the volunteer chooses five cards but Alice gets to decide which card to make the guessed card. She also doesn't need to hide the other suited (signal) card. It just makes it more difficult for the audience to figure out the trick. (BTW, what he meant by "hide" the other card is that by the sum of the shown cards Bob would be able to determine the location of the same-suited card. For example, if the sum of the four cards divided by four has a remainder of 0, then make the signal card the first card. If the remainder is 1, then make it the second, etc.)
She could, for example, order the cards so that the guessed card always has the same suit as the first card. It's still a bit tricky to solve since now there are only three cards to make a permutation with. (WARNING: more spoilers! Stop here if you want to solve the rest of the problem on your own.) Three cards could only represent six combinations and there are twelve possible cards to guess from. But Alice can choose which of the two suited cards is the guessed card. Now she just orders them so that the following is true:
card1's suit = card5's suit
and
(card1's value + the number shown by the combination [1 through 6]) MOD 13 = card5's value
(To keep things simple, values could be assigned like: A=1, 2=2, 3=3,.... ,J=11, Q=12, and K=0)
Voila!
Vspickelen, nicely done. That's the same solution I thought of. Not exactly the same but based on the same principles.
Sterling: (WARNING: spoilers ahead!)
No, the volunteer chooses five cards but Alice gets to decide which card to make the guessed card. She also doesn't need to hide the other suited (signal) card. It just makes it more difficult for the audience to figure out the trick. (BTW, what he meant by "hide" the other card is that by the sum of the shown cards Bob would be able to determine the location of the same-suited card. For example, if the sum of the four cards divided by four has a remainder of 0, then make the signal card the first card. If the remainder is 1, then make it the second, etc.)
She could, for example, order the cards so that the guessed card always has the same suit as the first card. It's still a bit tricky to solve since now there are only three cards to make a permutation with. (WARNING: more spoilers! Stop here if you want to solve the rest of the problem on your own.) Three cards could only represent six combinations and there are twelve possible cards to guess from. But Alice can choose which of the two suited cards is the guessed card. Now she just orders them so that the following is true:
card1's suit = card5's suit
and
(card1's value + the number shown by the combination [1 through 6]) MOD 13 = card5's value
(To keep things simple, values could be assigned like: A=1, 2=2, 3=3,.... ,J=11, Q=12, and K=0)
Voila!
Quote:You can even do this with up to 124 unique cards. (in the deck):o Wow. I didn't know that. Since there wasn't any information left over after my solution, I assumed 52 was the max. That get's me thinking...
hat were we arguing about again?