# Mathemagic - Magic with Cards

By Sam Wheeler Friday, September 19, 2014

Hello and welcome to another edition of Mathemagic. If you joined us last week you may have been trying to solve the puzzle and some of you may have solved it yourselves, check out the solution in the first trick.

## Card sense

Do you remember the coin trick from last week where you separate the coins into two piles each with the same number of coins facing heads up? You can do exactly the same with a deck of playing cards, but with an interesting addition:

1) Remove 20 playing cards from a deck, turn them face up and ask your friend to shuffle the face up pile into the face down pile.

2) Now take the deck and close your eyes. Remove 20 cards from random places in the deck and place them into a separate pile.

3) Now turn the whole pile you separated over and announce that each pile now has the same number of face up cards.

You can take this even further: If you take a full deck of cards (without jokers), shuffle it thoroughly and split the deck exactly in half (26 in each pile) then the number of red cards in one pile is exactly equal to the number of black cards in the other pile. This will always work as long as the deck is a full deck with no missing or extra cards. If one pile has 10 black cards then the other 16 cards must be red. The other pile must contain the only other red cards in the deck, so it will contain 10 red cards and 16 black cards. You could perform that as a trick by itself, simply separate the cards randomly into two piles with twenty six in each and state that you have separated them in such a way that the number of red cards in the left hand pile is equal to the number of black cards in the right hand pile.

If you don’t cut the deck exactly in half then you get a slightly different result. For example if you take 20 cards in one pile and 32 in the other then you can state that the larger pile contains exactly 6 more black cards than the number of red cards in the small pile. To calculate the difference between the two colours in each pile subtract the number in the small pile from 26.

Now if we return to the ‘Card Sense’ trick. After your friend has checked that the 2 piles contain an equal number of face up cards you continue:

6) Hold your hands over each pile and state that the large pile has exactly 6 more red cards than the number of black cards in the small pile.

7) Ask your friend to count (out loud) the number of black cards in the small pile.

8) In your mind add 6 to the number of black cards and say that if you are correct there will be 6 more red cards in the large pile, tell them how many that will be exactly.

## Truth or lies

1) Have your friend shuffle the cards and remove any 9 cards they like.

2) Ask them to deal out the 9 cards into 3 piles of 3 cards

3) Ask them to pick up any pile and to choose any card from that pile.

4) They should place their chosen card on top of one of the remaining piles and then place the other remaining pile on top of their card.

5) Then they should place the 2 cards remaining from the original pile on top of the combined piles.

6) Their card is now lost. Explain to them that in this game you will ask them some questions and they can either lie or tell the truth.

7) Tell them to start by spelling “lie” by dealing one card to the table for each letter. Dealing into a face down pile. They should then place the remaining cards on top of the dealt pile.

8) Ask them what the value of their card was – remind them that they can lie or tell the truth. Then ask them to spell the value they named and to deal one card for each letter they named. They should place the remainder on top of the dealt pile.

9) Now ask them to spell “of” and deal one card for each letter they name. Drop the remainder on top of the dealt pile.

10) Ask for the name of their cards suit – remind them that they can lie or tell the truth. Then ask them to spell the name of their suit, dealing one card for each letter and to drop the remainder on top.

11) Name the card they spelt and ask them if they were being honest. Now ask them for the real name of their card.

12) Now finally ask them to spell “truth”, dealing one card to the table for each letter, but this time they must not drop the remainder on top.

13) Ask them to turn over the last card they dealt (the letter “h” from “truth”) and it will be their chosen card!

## How does this work?

When the card is returned to the packet it will be sixth from the top. Spelling “lie” means it will be third from the top. Any playing card value you spell will result in the card ending seventh from the top. Spelling “of” will place the card fifth from the top. Any suit you spell will end with the card fifth from the top. Now when you spell “truth” the selection will appear as you spell the last letter.

So it doesn’t matter if they lie about their card or tell the truth you will always be able to find their card. Do the whole trick again but this time when you place the selected card down you should put it face up (so it is the only face up card in the packet). Now when you are doing the spelling process you will be able to see what happens to the selected card during every step of the trick.

## Card divination

Do you remember the Three Object Divination trick from the first issue of Mathemagic? You can do an even more impressive (and easier) version of this trick by using playing cards:

1) Place three playing cards face down on the table in a row and remember the card in the middle.

2) Turn your back and ask them to peek at any of the cards, remember it and switch the other two (so if they peek at the middle card then they should switch the left card with the right card).

3) Turn back to face them and now ask them to continue switching two cards at a time. As they do this you need to keep track of the middle card, watching where it ends up.

4) Turn over all of the cards. If the card you tracked is the one you remembered at the beginning then that is the one they peeked at. If it isn’t the card you remembered at the beginning then they didn’t peek at the card currently in the middle nor did they think of the card you remembered at the beginning – they must be thinking of the only remaining card.

Simple, easy and really effective.

## Puzzle

Finally I’d like to end with a puzzle, the answer will be posted next week in the next edition of Mathemagic.

Write down any 3 digit number but make sure the digit in the hundreds place is different to the digit in the ones place (e.g. 123).

Reverse your number and write it below your first number (e.g. 321). Now subtract the smaller number from the larger number.

If you tell me the first or last digit in your new number I’ll be able to tell you the other 2 digits in your number – can you work out how?