Hi - i've just watched a youtube magic card trick - { Math magic card trick!! - YouTube } - although I understand the math involved - i'm stuck trying to define a 'general rule' or formula to describe the exercise. Can anyone please help or advise ?

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- March 6th 2013, 11:03 AMGlynAnyone good with 'general rules' ?
Hi - i've just watched a youtube magic card trick - { Math magic card trick!! - YouTube } - although I understand the math involved - i'm stuck trying to define a 'general rule' or formula to describe the exercise. Can anyone please help or advise ?

- March 7th 2013, 05:00 AMjackkariesRe: Anyone good with 'general rules' ?

I just join this forum and I really appreciate your work. This trick is awesome and I will try this one as soon as possible .

lists - March 7th 2013, 06:49 AMHallsofIvyRe: Anyone good with 'general rules' ?
As a general rule, there are no "general rules".

- March 7th 2013, 07:00 AMGlynRe: Anyone good with 'general rules' ?
Many thanks ! I just wondered, with both 52 and 10 being limiting factors in the exercise, whether there was an expression that could be used to describe the use of the exercise.

- March 7th 2013, 10:13 AMBobPRe: Anyone good with 'general rules' ?
I'm not sure what is meant by a ' general rule ', but if it's simply the maths behind this trick, that's pretty easy.

First note that if you know the bottom card of a pile, then you know how many cards there are in the pile, simply subtract from 11.

If for example the bottom card is a 4, then you count 4,5,6,7,8,9,10. That's 7 cards and equals 11 - 4.

Suppose then that the bottom cards of the three chosen piles are a, b and c.

The total number of cards in the three piles will be (11 - a) + (11 - b) + (11 - c) = 33 - (a + b + c), in which case the number of remaining cards will be 52 - {33 - (a + b + c)} = 19 + (a + b + c).

Subract 19 and you are left with (a + b + c), the sum of the bottom cards in the three piles. - March 7th 2013, 05:44 PMGlynRe: Anyone good with 'general rules' ?
Many thanks. I simply wondered if there were a more succinct expression than 52 = 19 + remainder stack + stacks a+b+c.

- March 8th 2013, 01:17 AMBobPRe: Anyone good with 'general rules' ?
I'm still not sure what it is that are looking for. It's easy enough to extend this to multiple packs, multiple stacks and a different top number (<=13), but it would seem that you are always going to arrive at some formula of this type.

- March 9th 2013, 04:21 AMGlynRe: Anyone good with 'general rules' ?
Thank you for the reply - I have resolved the math - just wondered if there were any suggestions about encapsulating this exercise in a simple and engaging algebraic model for teaching children