### Card Tricks

Snowstorms, earthquakes, terrorism attempts... What could be better this time of the year than cuddling up near the fireplace with your family and friends and enjoying some captivating card tricks. These tricks are fun, surprisingly easy and impressive. What is even more fascinating, however, is how you can use math to explain how they work.

You need 21 playing cards (pick any cards from the pile), and one person to choose and remember one of the cards. You, of course, will guess which one was picked.

1. Put all 21 cards into 3 columns by placing one card in each column, then a second card in each column, etc. till each column has 7. Ask the person to tell you which column his/her card is in. Also, ask this person to think about their card while you look straight into her/his eyes, pretending to have mind-reading capabilities.

2. Collapse the columns back into a deck, one on top of another. But make sure that the column that the person just pointed to is in the middle. Do not mix up cards in the columns.

3. Repeat steps (1) and (2), saying that you are getting closer.

4. Repeat only step 1). The middle card in the column that person pointed to would be the card he/she originally picked.

You are doing magic, and all thanks to math. How does it work?

Let's rewind. You place the cards in three columns and your participant points to the column where his card is.

You then gather all the cards back into one deck, placing the column that the person pointed to in the middle of your pile. You know that the card he picked is somewhere between the 8th and 14th cards in your deck.

When you divide the cards into columns again, the 1st card goes in the 1st column, 2nd card in 2nd, 3rd in 3rd, 4th card in 1st column, 5th in 2nd, 6th in 3rd, etc. Then the column in which the selected card is will occupy places 8-14 in the figure below. The first two and the last two cards in each column definitely do not hold the picked card. The picked card is somewhere in the middle of one of the columns: one of the three middle cards in the central column or one of the two “middle” cards in the left or right columns. All these possible locations of the picked card are colored orange on the illustration below.

Then the person points to the column where his card is now:

You gather the cards into a pile again, making sure to put the column the person pointed to in the middle. The picked card is in position 10, 11, or 12. More specifically, if it was in the first column, it would be in the positions 11 or 12, central column – positions 10, 11 or 12, right column – positions 10 or 11. But you don't need to keep track of all these details or remember any specific cards. All you do is spread the cards into three columns, gather them, spread, gather and spread again. Math does the magic for you.

When you place the cards into columns for the third and last time, cards 10, 11 and 12 are now each middle cards in a different pile. The picked card is one of them.

As soon as the person points to one of the columns, you know that the picked card is the middle card in this column.

Trick 2: Magic Words Card Trick
In this super-trick you can guess not one, but a pair of cards! And you can do it simultaneously for many different players. Choose 20 cards and lay them out in pairs.

Ask every player to remember one pair. Gather all the cards, without mixing up the pairs. Then spread out all 20 cards in 4 rows of 5 cards each, using special magic words, ask every player to tell you which rows his/her cards are in, and … guess them!

Did I leave anything out? Of course – the magic words.

You use them to put the cards into 4 rows of 5 cards each. These magic words are your key to this puzzle. You need to learn them. But do not reveal them to your audience.

Here are the magic words in English:

Russian version of magic words:
НАУКА
УМЕЕТ
МНОГО
ГИТИК

Notice that every letter is present twice in this magic word collection, and there are 20 letters total. So, we have 10 pairs of same letters and 10 pairs of cards. Imagine these magic words laid out in front of you on a table just like on the image above. Take your cards and place the first pair of cards where the two letter Bs are, in the top row. Next pair goes where the letter I is, in the first and second rows. Third pair where the letter Ls are. Continue with the rest of the letters and card pairs. It does not matter which pair corresponds to which letter. The only important thing is to make both cards in each pair fill the spot of the same letter.

Notice that any two rows have only one letter in common. Therefore, when your opponent points to the rows his cards are in, you recollect the magic words that you used to spread the cards and think which letter is in common for these two rows (or one row if both picked cards are in one row). Once you know what letter it is, you just point to the cards that are placed in this letter's spots.

Enjoy! These precious fun moments of surprise and discovery stay in our memories. One day your kids will entertain their friends and kids with these puzzles. Just as I did, learning them from my father.

1. This game is interesting, other than playing some basic games I've never played some serious card games forget about puzzles but this one looks like a scrabble as well. Thanks for sharing!

2. Looks like a lot of fun. I'm thinking of trying out this new game with my folks this weekend. One thing is sure this game is going to keep us home all day...!!

3. Really like this trick, but it can also be done with only 15 cards to the same effect. I am going to put my video up tomorrow so come check out amazingcardmagic.wordpress.com

4. DUMN man! Some week ago I remembered this trick (trick #1) from my childhood (other 20 years ago) and made youtube video. Pls do not punish me for advert myself:
http://youtu.be/hFMMVNCpcZ8
It is not same - I use 27 cards

Funny - this page it was second page then I choosed find "card tricks".
Nice see your explaned how it works. In wide you can take any count of card and any count of columns, but you will be need find way how to find choosed card.

5. This comment has been removed by the author.

6. Very nice ideas. Thanks for sharing

7. It seems to be fun activity for my children. You elaborated the complete post in very detail and easy & simple language. Great job! Kudos to you!

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10. There's another way of doing the 2nd trick without splitting them in pairs, forgot how it goes though, been about 15 years since I've tried

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12. This trick is great and I have seen it done multiple ways, the way I enjoy doing it is with 4 rows of 4 and then using a magicians force at the end to complicate things. It makes it much more interesting for the spectator plus it is much harder to work out.

My name is Richard and I am from Kids Magic, where we offer courses for great tutorials just like this one in video format. http://www.cardtricksforkids.com

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35. Trick 1: I CAN READ YOU MIND

You need 21 playing cards (pick any cards from the pile), and one person to choose and remember one of the cards.
You, of course, will guess which one was picked.

(1) Put all 21 cards into 3 columns by placing one card in each column, then a second card in each column, etc. till each column has 7.

Ask the person to tell you which column his/her card is in. Also, ask this person to think about their card while you look straight
into her/his eyes, pretending to have mind-reading capabilities.

(2) Collapse the columns back into a deck, one on top of another. But make sure that the column that the person just pointed to is in the middle.
Do not mix up cards in the columns.

(3) Repeat steps (1) and (2), saying that you are getting closer.

(4) Repeat only step 1). The MIDDLE card in the column that person pointed to would be the card he/she originally picked.
-----------------------------------------------------

I have made some minor changes in the original document by adding then number (3) and (4) in the above, so that I can reference them in the
following dialogue.

I have performed a thorough MATHEMATICAL ANALYSIS of this card trick, with the intention of writing a computer program that will perform the same
'mind reading' trick for any NUMBER (let this number be called M) of cards (since there are only 51 cards in a deck, we will need to use UNIQUELY
generated RANDOM numbers, when M is greater than 51).

NOTE these observations from the card trick with 21 cards:
(a) There are 21 cards split onto 3 groups of 7 cards. We will represent these numbers by M=21, N=3 and K=7
(b) Note that N and K are ODD numbers (any ODD number multiplied by an ODD number will give an ODD number)
(c) The MIDDLE card of the 21 cards is given by the formula, (M+1)/2 which equals 11

In the above case, we have:

(a) for any ODD number P, defined by P = 2 * Q + 1, where Q = 1, 2, 3, 4, 5, etc, ie. all integers greater than ZERO
(b) if we restrict the number of GROUPS to 3, then N=3 (or P = 2 * 1 + 1 = 3, ie. we chose Q=1)
(c) if we restrict the number of cards in each Group to K=7 (or P = 2 * 3 + 1 = 7, ie. we chose Q=3)
(d) the number of cards is M = N * K = 3 * 7 = 21
(e) you must distribute the cards into 3 groups, 7 per group as defined in (1),(2) and (3) above
(f) in step (4), the MIDDLE card = ( M + 1 )/2 = (21 + 1)/2 = 11, which is the MIDDLE card of the 21 card deck

Can this procedure work if we swap and make N=7 GROUPS and K=3, 3 cards per GROUP?. The answer is a definite YES.
In fact, the algorithm is TRUE for all integer values of Q greater than ZERO.

For example, you an have N = 11 and K = 15, then M = 11 * 15 = 165 unique random numbers,
you must distribute the Numbers into N=11 Groups with 15 numbers in each Group as described in (1), (2) and (3)
then the MIDDLE card in step (4) is (165+1)/2 = 83.

A computer program can very quickly generate a large set of unique random numbers and display these numbers in GROUPs,
the only time consuming part is the user being able to see when the 'CHOSEN' number is displayed on the screen. Since the
numbers will be displayed in a GROUP, the user need are only indicate to the computer that the CHOSEN number is in the
GROUP most recently displayed. The computer need not display the remaining GROUPs of numbers. The computer can then take
the GROUP containing the CHOSEN number and place it in the 'middle' of the other GROUPs and repeat steps (1), (2) and (3).
Finally the computer can display the MIDDLE (the CHOSEN) number.

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