This isn't nearly as impressive as captain's flying aces, but it sure looks magical. Takes two people who know what's going on. call them A and B
1) A gets 5 different audience members to randomly select any card from the same deck. B is outside of the room.
2) B comes into the room, and A puts 4 of the cards on the table face up. B then announces the 5th card.
-how: since there are 5 cards and 4 four suits, there must be a repeated suit in the cards. the first of the 4 cards layed down indicates the suit (and something else which will be explained later) the next 3 indicate which card of that suit it is. the following explanation gets a little sticky.
-how to determine which card value?
seemingly useless piece of information #1: there are 13 cards in every suit; if you write the numbers 1 through 13 in a circle, any two of them can be at most 6 numbers apart. (1 and 13 are only 1 apart in the circle)
seemingly useless piece of information #2: you can order any 3 items in exactly 6 ways. those 6 ways are (in order): abc, acb, bac, bca, cab, cba
call the 4 cards person A puts down 1 2 3 4 (tricky!). i've already said card 1 indicates the suit of card 5. lets use V to represent the value of card 1, and W to represent the value of card 5. since the distance between V and W can be at most 6 (in the circular drawing), cards 2 3 4 can communicate that distance.
time for an example. say the 5 cards picked are 2c 7c jd 9s 5h. the clubs are the repeated suit, with a distance of 5 between 2 and 7. so card 1 is 2c.
cards 2 3 4 must say 'add 5 to the 2 of clubs.' using seemingly useless piece of info #2, we order cards 2 3 4 in the 5th possible way of ordering 3 items: cab. since cards 2 3 4 are chosen from values jack (11), 9, and 5, this order #5 is cab which corresponds to 11-5-9, since a=5, b=9, c=11.
so card 1 is 2 of clubs.
cards 2 3 4 are jd, 9s, 5h. this ordering says: "add 5 to the 2 of clubs".
therefore, card 5 is the 7 of clubs.
why is the 2 of clubs the first card, and not the 7 of clubs? because to get from 7 to 2 (in our circle of 13), you have to add 8. you cannot specify 8 using my 6-orders method, so the 2 comes first.
if our 5 cards are jc, jd, 2c, 9s, 5h, we again have clubs repeating, but this time to get from the 2c to jc, we must add 9. therefore, the jack of clubs (club 11) is card 1, and we must add 4 to get from the jack of clubs to the 2 of clubs. so we put cards 2 3 4 into the 4th listed order: bca. our choices are jd, 9s, 5h (11, 9, 5). a is 5. b is 9, c is 11. co bca is 9-11-5.
questions?
1) A gets 5 different audience members to randomly select any card from the same deck. B is outside of the room.
2) B comes into the room, and A puts 4 of the cards on the table face up. B then announces the 5th card.
-how: since there are 5 cards and 4 four suits, there must be a repeated suit in the cards. the first of the 4 cards layed down indicates the suit (and something else which will be explained later) the next 3 indicate which card of that suit it is. the following explanation gets a little sticky.
-how to determine which card value?
seemingly useless piece of information #1: there are 13 cards in every suit; if you write the numbers 1 through 13 in a circle, any two of them can be at most 6 numbers apart. (1 and 13 are only 1 apart in the circle)
seemingly useless piece of information #2: you can order any 3 items in exactly 6 ways. those 6 ways are (in order): abc, acb, bac, bca, cab, cba
call the 4 cards person A puts down 1 2 3 4 (tricky!). i've already said card 1 indicates the suit of card 5. lets use V to represent the value of card 1, and W to represent the value of card 5. since the distance between V and W can be at most 6 (in the circular drawing), cards 2 3 4 can communicate that distance.
time for an example. say the 5 cards picked are 2c 7c jd 9s 5h. the clubs are the repeated suit, with a distance of 5 between 2 and 7. so card 1 is 2c.
cards 2 3 4 must say 'add 5 to the 2 of clubs.' using seemingly useless piece of info #2, we order cards 2 3 4 in the 5th possible way of ordering 3 items: cab. since cards 2 3 4 are chosen from values jack (11), 9, and 5, this order #5 is cab which corresponds to 11-5-9, since a=5, b=9, c=11.
so card 1 is 2 of clubs.
cards 2 3 4 are jd, 9s, 5h. this ordering says: "add 5 to the 2 of clubs".
therefore, card 5 is the 7 of clubs.
why is the 2 of clubs the first card, and not the 7 of clubs? because to get from 7 to 2 (in our circle of 13), you have to add 8. you cannot specify 8 using my 6-orders method, so the 2 comes first.
if our 5 cards are jc, jd, 2c, 9s, 5h, we again have clubs repeating, but this time to get from the 2c to jc, we must add 9. therefore, the jack of clubs (club 11) is card 1, and we must add 4 to get from the jack of clubs to the 2 of clubs. so we put cards 2 3 4 into the 4th listed order: bca. our choices are jd, 9s, 5h (11, 9, 5). a is 5. b is 9, c is 11. co bca is 9-11-5.
questions?
