Mathmagic

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.

Markdown

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italics

**bold** or __bold__

bold


- bulleted
- list

bulleted
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1. numbered
2. list

numbered
list

Note: you must add a full line of space before and after lists for them to show up correctly

paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

example link

> This is a quote

This is a quote

    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"

# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"

Math

Appears as

Remember to wrap math in $ ... $ or \[ ... \] to ensure proper formatting.

2 \times 3

2 \times 3

2^{34}

2^{34}

a_{i-1}

a_{i-1}

\frac{2}{3}

\frac{2}{3}

\sqrt{2}

\sqrt{2}

\sum_{i=1}^3

\sum_{i=1}^3

\sin \theta

\sin \theta

\boxed{123}

\boxed{123}

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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, mathematical codes 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].

Mursalin Habib - 7 years, 6 months ago

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.

Bruce Wayne - 7 years, 6 months ago

One can refer this.

Bhargav Das - 7 years, 6 months ago

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

Yong See Foo - 7 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$