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| 26 MAY 2004 at 7:50am |
GreySorcerer Apprentice
Posts : 251
Joined: 3 SEP 2003
Status : Online | Judging by some of the other posts, there's a few math geniuses in here. Can anyone offer the mathematical explanation of a card trick that has puzzled me for years?
Here it is in its simplest form:
- Start with a full deck of 52 playing cards.
- Build a pile of cards face-up on the table. The total number of cards you'll put in the pile is determined by the value of the first card (13 - card value = number of additional cards added). For example, if the first card is a 10, you'd put three cards on top of it. If the first card is a 7, you'd add another six cards to it. You cannot begin the pile with a face card.
- Build two more piles of cards following the same rule, for a total of three piles.
- Turn each of the three piles face down.
- Flip over the top card on two of the piles and add their values, then add 10.
- Remove that amount of cards from your pile of undealt cards.
- Count the number of cards remaining in the deck. That number will equal the value of the overturned card in the third pile.
If I didn't explain that clearly enough, here's a working example:
Pile 1: 9, X, X, X, X
Pile 2: 7, X, X, X, X, X, X
Pile 3: 8, X, X, X, X, X
34 cards remain in the deck
9 + 7 = 16
16 + 10 = 26
34 - 26 = 8
It doesn't matter which two cards you add together. The end result always equals the value of the third.
Why?
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| 26 MAY 2004 at 1:57pm |
ElfstoneGuild Master
Posts : 5892
Joined: 4 NOV 2002
Status : Online | Let's define the cards as x, y and z.
Now, you start with placing x on the table and add 13-x cards on top, that means you put 1+(13-x) cards in a pile, or simply 14-x cards.
You do the same with y and z, thus you receive
14-x + 14-y + 14-z = P <=> 42 - x - y - z = P
where P is the amount of cards in all 3 piles together.
Example:
x=9, y=7, z=8
-> 42 - 9 - 7 - 8 = 18 cards in the piles
This means you will get the amount of cards in the deck (D) by
D = 52 - P
<=>
D = 52 - (42 - x - y - z)
<=>
D = 10 + x + y + z
Example:
52 - 18 = 34 = 10 + 9 + 7 + 8
Now formulate your question in an equation.
x + y + 10 is what you calculate. Then you substract this from the number of cards in the deck, which we already called D.
You get:
D - (x + y + 10) = z
If you can't see it already, substitute D with the above equation:
10 + x + y + z - (x + y + 10) = z
<=>
10 + x + y + z - x - y - 10 = z
<=> z = z
Example:
34 - (9 + 7 + 10) = 34 - 26 = 8 = z
There you are.
[b]playing[/b]: Destination Treasure Island (done in two sittings, but it's nice), Syberia (ho-hum), Dracula: Last Sanctuary (on hold)&&[b]reading[/b]: even more study papers&&[b]listening to[/b]: [url=http://www.last.fm/user/Brax82/]this and that[/url], plus [url=http://www.musicovery.com/]Musicovery[/url]&&[b]TV favorites[/b]: (currently) Pushing Daisies, Chuck, Journeyman (cancelled! grrr...), Heroes&& all-time) 24, Stargate SG1, X-Files, Lost, House
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| 27 MAY 2004 at 9:16pm |
GreySorcerer Apprentice
Posts : 251
Joined: 3 SEP 2003
Status : Online | Originally Posted By Elfstone (26 MAY 2004 1:57pm)
There you are.
It took me a while to comprehend all of that, but it makes sense to me.
Thanks.
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| 31 MAY 2004 at 8:08am |
KamisoriXSchattenjger
Posts : 1700
Joined: 15 MAY 2004
Status : Online | these crazy germans again
[IMG]http://img269.imageshack.us/img269/971/kamisig94ct.gif[/IMG]&&&&If the Earth would be a Sphere, and not a Disc, I wouldn't be so afraid to fall of the Edge...
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| 31 MAY 2004 at 12:41pm |
ElfstoneGuild Master
Posts : 5892
Joined: 4 NOV 2002
Status : Online | Whassup? [smiley=boggled.gif]
[b]playing[/b]: Destination Treasure Island (done in two sittings, but it's nice), Syberia (ho-hum), Dracula: Last Sanctuary (on hold)&&[b]reading[/b]: even more study papers&&[b]listening to[/b]: [url=http://www.last.fm/user/Brax82/]this and that[/url], plus [url=http://www.musicovery.com/]Musicovery[/url]&&[b]TV favorites[/b]: (currently) Pushing Daisies, Chuck, Journeyman (cancelled! grrr...), Heroes&& all-time) 24, Stargate SG1, X-Files, Lost, House
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| 5 JUN 2004 at 3:40pm |
| Deleted User | Neverthless, a rather fascinating card trick! Never heard about it before...
The seemingly magic thing is the value of the third card. But that's because it's easy to forget that it's actually the number of cards in the third pile that's interesting.
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