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Greenday
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Post by Greenday »

I know how to do the magic 21 card trick, the 3 rows of 7 are the important bit, when the person says which row their card is in, gather them into the rows horizontally, one on top of the other so you will have three piles, gather them all together and make sure the pile containing thier card is put in the middle then lay them out again, once again place the pile with their card in the middle, lay them out for a third and final time, do the same again then count out the cards, their card will be the 11th one.
Completely right :D :D :D :D :D
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samwise
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Post by samwise »

I know how to do the magic 21 card trick, the 3 rows of 7 are the important bit, when the person says which row their card is in, gather them into the rows horizontally, one on top of the other so you will have three piles, gather them all together and make sure the pile containing thier card is put in the middle then lay them out again, once again place the pile with their card in the middle, lay them out for a third and final time, do the same again then count out the cards, their card will be the 11th one.
Completely right :D :D :D :D :D
When you lay the cards out I assume you lay them out vertically?

Greenday
Posts: 1480
Joined: Sat Feb 15, 2003 7:54 pm
Location: Gloucestershire

Post by Greenday »

I know how to do the magic 21 card trick, the 3 rows of 7 are the important bit, when the person says which row their card is in, gather them into the rows horizontally, one on top of the other so you will have three piles, gather them all together and make sure the pile containing thier card is put in the middle then lay them out again, once again place the pile with their card in the middle, lay them out for a third and final time, do the same again then count out the cards, their card will be the 11th one.
Completely right :D :D :D :D :D
When you lay the cards out I assume you lay them out vertically?
Nah you lay them horizontally
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samwise
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Location: SE16, London

Post by samwise »

OK, so while on number games this is a very dull-to-look-at problem but has been known to make A-level maths students cry.

A recurring number is where the decimal part goes on forever eg 1/3 when represented as a decimal = 0.3333333333333333 and the 3's go on and on. That means you'll need a short hand to write it, I'll use an "r". So 0.333r = 1/3.

OK, a quick proof ......

if x = 0.333r
10x = 0.333r x 10
10x = 3.333r
9x = 10x - x
9x = 3.333r - 0.333r
9x = 3
x = 3 / 9
x = 1 / 3
x = 0.333r

So x = 0.333r, tell me something we didn't already know! OK now try

x = 0.999r
10x = 0.999r x 10
10x = 9.999r
9x = 10x - x
9x = 9.999r - 0.999r
9x = 9
x = 9 / 9
x = 1

and I seemed to have proved 1 = 0.999r which it isn't? What gives?

Jason

PS Yep, I'm great fun at parties ;)

samwise
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Location: SE16, London

Post by samwise »


Completely right :D :D :D :D :D
When you lay the cards out I assume you lay them out vertically?
Nah you lay them horizontally
Sorry, I mean lay them horizontally but deal them verticially.

If you collect them horizontally and deal them out horizontally then a card that's, say, the 1st in row 2 will remain the 1st card in row 2 all the time and be the 8th card after 3 goes?

It's a good trick though! ;)

Greenday
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Location: Gloucestershire

Post by Greenday »

Not if you picked that card as the row its in would go in the middle so any card that's picked will change places :D
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samwise
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Location: SE16, London

Post by samwise »

Not if you picked that card as the row its in would go in the middle so any card that's picked will change places :D
I must be missing the point somewhere. Row two is in the middle anyway so putting it in the middle isn't going to help? I've got 21 cards like

1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21

I pick card card number 8 and say row 2

row 2 goes in the middle so the deck of 21 has the same order as above? I then deal them horizontally and get the same layout as above? Cheers

Jason

Greenday
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Post by Greenday »

The reason they change is because when you deal the cards you deal them across the rows e.g. the 1st in column 1, then 1st card column 2, then 3rd card in column 3, then 2nd card in column 1 and so on and so
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Greenday
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Post by Greenday »

I think the reason this is confusing is because its arranged slightly differently in real life, so if anyone who's going to Thorpe park wants to see some crap magic tricks i'll be more than happy to show them :D
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samwise
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Post by samwise »

The reason they change is because when you deal the cards you deal them across the rows e.g. the 1st in column 1, then 1st card column 2, then 3rd card in column 3, then 2nd card in column 1 and so on and so
Yep, that's what I meant by dealing vertically rather than horizontally, that works! ;)

Jason

Alex LS
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Post by Alex LS »

and I seemed to have proved 1 = 0.999r which it isn't? What gives?
9.9999r - 0.9999r does not equal 9.0 but 8.9999r
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samwise
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Post by samwise »

and I seemed to have proved 1 = 0.999r which it isn't? What gives?
9.9999r - 0.9999r does not equal 9.0 but 8.9999r
in which case what does 9.999r - 1 equal? It can't be 8.999r otherwise

9.999r - 1 = 8.999r
and
9.999r - 0.999r = 8.999r

therefore 1 = 0.999r again :?: Cheers

Jason

Alex LS
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Post by Alex LS »

See? This is the problem when you start dealing with recurring decimals. Infinity is a pain to work with.
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CB
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Post by CB »

My God! WHY do i keep looking at this topic!!!! :no:
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samwise
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Post by samwise »

See? This is the problem when you start dealing with recurring decimals. Infinity is a pain to work with.
Which is pretty much the right answer! It's not so much the recuring bit that cause the problem but the number 0.9999r and how to represent it.

0.333r can be written as 1/3 but 0.999r is 1 - 1/infinity.

Once you have infinity in an equation the normal rules of "what i do one side of the equals sign I can do the opposite to the other" break down i.e.

10x = infinity
x = infinity / 10
x = infinity

no longer work (10x = x?) as doing +-*/ on infinity always gives infinity.

Alex gets the gold star! :)

Cheers

Jason