Completely rightI 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.
Funny Forwards
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Greenday
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samwise
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When you lay the cards out I assume you lay them out vertically?Completely rightI 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.![]()
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Greenday
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Nah you lay them horizontallyWhen you lay the cards out I assume you lay them out vertically?Completely rightI 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.![]()
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samwise
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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
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
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samwise
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Sorry, I mean lay them horizontally but deal them verticially.Nah you lay them horizontallyWhen you lay the cards out I assume you lay them out vertically?
Completely right![]()
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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!
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samwise
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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 likeNot if you picked that card as the row its in would go in the middle so any card that's picked will change places
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
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Greenday
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Greenday
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samwise
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Alex LS
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9.9999r - 0.9999r does not equal 9.0 but 8.9999rand I seemed to have proved 1 = 0.999r which it isn't? What gives?
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samwise
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Alex LS
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See? This is the problem when you start dealing with recurring decimals. Infinity is a pain to work with.
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samwise
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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.See? This is the problem when you start dealing with recurring decimals. Infinity is a pain to work with.
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