A friend of mine taught me a good magic (math) trick that can be performed with cards. It involves simple math. No sleight of hand is involved in this trick which makes it possible for anyone to perform it.

**Requirements: **

2 mathemagicians, an ordinary deck of cards (discard the jokers and you should be left with 52 cards), spectators (of course )

**The Act:**

**The Pledge**: The first magician comes on stage and the second magician leaves the stage. Assure the spectators that the two magicians will NEVER EVER exchange information in any form other than the cards. (And yes, we are gonna stick to that rule)The first magician hands over the deck of cards to one of the spectators and tells him/her to shuffle it as many times as he/she wants. The spectator is then asked to choose any 5 cards of his/her choice and then hands those 5 cards to the magician. The magician then shows these 5 cards to the entire audience. (NOTE: At this point everyone, including the first magician, knows what those 5 cards are. Only the second magician is unaware of the 5 cards chosen)

The magician then carefully gives that spectator, one of those 5 cards and keeps with himself the rest (4 cards).

**The Turn**: He then places the ORDERED set of 4 cards on the table and leaves the stage.**The Prestige**: The second magician (who had no idea till now as to which cards the spectator had chosen) comes up on the stage, looks at the cards and then magically announces the fifth card to leave the audience speechless.

Can you work out how this can be performed?

**Here are some rules:**

The mathmagicians are smart and have pre-decided their strategy to work the fifth card.

No tampering of the deck of cards, in any form (folding, scratching, marking etc), is allowed.

Once the acts starts, the mathmagicians never come into contact with each other.

**Working solution of the trick will be revealed on December 6th at 6:00 pm GMT.**

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## Comments

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TopNewestIf one is familiar with Tournament of Towns, they can refer to 1998 (Tournament 19) Spring A-Level Senior Problem 6.

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One can refer this.

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I'm not sure why you want to tell people how this is done.

This effect is called Cheney's Five Card Trick. It is a perfect example of how you can use mathematical codes to communicate and create astounding results. The magicians communicate in codes,

mathematicalcodes to communicate with each other. The magicians use simple tools like 'the pigeonhole principle', 'modular arithmetic' and 'permutation codes' to make this work.I'm not going into all the details [which you can probably find out through a Google search].

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This exercise is just for fun. And as you said, this uses simple tools like pigeonhole principle, modular arithmetic and permutation codes. It is a fun way to use math in your daily life. Nothing more...nothing less.

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