## Topology trickery

Here's a very clever topology trick!

More information at Division by Zero.

Hat tip to Multiplication by Infinity.

## 12 cent Math trick

Here's a very interesting and simple trick to impress your friends. It's simple enough to do that even the little ones, if they can count to 12, can do this trick. There's no sleight of hand or any other difficult manipulation to do. In fact, once you know the very simple steps, the trick is pretty automatic.

The trick is based on some very simple algebra but I've found that even though I understand how the trick works it's still eerie to see it work.

I got this trick from Shecky's great Math-Frolic Blog. The trick was developed by Alfred Posamentier, a prolific writer of Math books. While Posamentier is not as well known as Martin Gardner or Cliff Pickover, his books are equally engaging.

I rewrote Posamentier's trick so that it could be performed as a bar trick so that maybe Scam School will pick up the idea and produce a video of it.

Here's my version of the trick:

The scamster hands the victim 12 pennies and then blindfolds himself. The victim is instructed to place the coins on the table such that exactly five of them are heads up. The scamster tells the victim that he can, without removing the blindfold, separate the 12 pennies into two groups, and turn over some pennies so that each group will have exactly the same number of coins heads up. Fumbling around because he can't see, the scamster moves the 12 pennies close together into a group and then somehow picks some of the pennies and moves them to another group. He then turns some coins over and, voila, both groups have the same number of heads up pennies.

How can the scamster know how to separate the coins into two piles? How does he know which coins to turn over? How can he do this all blind-folded? See if you can figure out the trick on your own then head on over to Shecky's blog for Posamentier's solution.

## Terrific Tic Tac Toe Trick

Here's an eerie Tic Tac Toe trick to totally impress your friends. You play a game of Tic Tac Toe with a friend. The game ends in a draw. You pull out a piece of paper (or napkin) that you drew in advance that shows exactly what the ending board would look like. How did you know? Did you control their mind and force them to make the moves you wanted them to?

This great trick is attributed to the late Martin Gardner. It is a great one for kids to learn because it will teach them some things about logical thinking. Hat tip to @grey_matter2 for the trick.

## Math magic with the number 9

9 is a most interesting number. I'm sure that's largely because 9 is 1 less than 10 and most of us have 10 fingers (or digits) and we do arithmetic in a base 10 system. I've seen an amazing number of math tricks that take advantage of something called "digital roots", which is closely related to the idea of "casting out nines." I want to introduce you to these two concepts and share some fun Math tricks you can do with this "9 stuff."

The digital root of a number, and this only makes sense for whole numbers, is what you get when you add up all of its digits. So, the digital root of 112 is 1+1+2, or 4. The digital root for 1234 is 1+2+3+4, which is 10. Now, when you're computing digital roots you only want a single digit so in the case of 1234, you add up its digits to get 10 then add 1+0 to get 1. So, 1 is the digital root of 1234.

## How does Arthur Benjamin square 5 digit numbers in his head?

Last month I blogged about mathemagician Arthur Benjamin and his amazing mental Math feats. Benjamin is a master of doing arithmetic in his head with lots of digits involved. In particular, he's able to square a 5-digit number without writing down partial results. How does he do it? I picked up a copy of Benjamin's Secrets of Mental Math to learn how. Here are the steps Benjamin provides for squaring 46,792.

1. First, Benjamin breaks the number into 46,000 + 792.

2. Then he does a little algebra. If a=46,000 and b=792, then (a+b)^2 = a^2 + 2ab + b^2 = (46,000)^2 + 2(46,000)(792) + 792^2.

3. This simplifies a bit to 1,000,000(46^2) + 2,000(46)(792) + 792^2.

4. Then Benjamin sets out to do the middle product: 2,000(46)(792).

## Impressive Math magic with 16 index cards

Here is one of my very favorite Math tricks that's sure to impress your friends (and yourself the first time you try it). I learned this trick over 30 years ago and amazingly enough I still remember it.

Take 16 index cards and prepare them as follows:

- Make a diagonal cut at the top left of each card as illustrated. This is to keep all the cards oriented the same way because they're going to get mixed up for this trick.
- Number each card using the numbers from 0 up to 15.
- Using a hole punch cut 4 holes in each card as shown in the card numbered 0 in the illustration. It's important that the holes line up from one card to the next. In other words, when you are holding all 16 cards in your hand you should see four holes that go through the whole set of cards.
- Using a pair of scissors cut notches in each of the cards, except for card 0, so that each card matches the corresponding illustration according to is number.

Now for the fun part!

- Have the person you're wanting to impress shuffle all the cards so that they're in a random order. Hold the cards face up, with the numbers showing. After shuffling check that the diagonal cut goes all the way through all 16 cards. That's how you know the cards are all oriented the same way.
- Take a thin dowel, knitting needle, small screwdriver or other object that can fit through the holes and notches.
- Hold the stack of cards in one hand. Put the needle through the rightmost hole (or notch) with your other hand and pull the dowel away from the stack of cards. Some of the cards will come with the dowel - those that have holes in that rightmost hole - and some won't.
- Take the cards that came up with the dowel and put them in the front (top) of the stack in the order they came in when the dowel pulled them away.
- Proceed to the second hole from the right. Using the dowel again, push it through the hole and pull the dowel away from the stack. Take the cards that came with the dowel (these will have holes in the second-to-right position) and put them on the top of the stack, in the order they came in when the dowel pulled them away.
- Repeat with the second-to-left hole and finally with the leftmost hole.

Now, look at the stack of cards. What do you see? They're in order!

Can you explain how this happened?

If you know about computer programming can you relate this trick to the binary number system and to how computers can sort things?

## Amazing Math trick with paper, scissors, and tape

Here's something fun, not too heavy on the Math unless you want it to be, and quite remarkable to those who haven't seen this before. You're going to create a Moebius strip, and variations on it, and surprise yourself and others when you see what you get when you cut the Moebius strip in various ways. A Moebius strip is a strip of paper that you tape together at both ends, but before you do, you make a half twist in the strip. Your Moebius strip should look like the one in the picture from Wikipedia.

Here's the first thing you can do that'll be interesting. Take a pen and draw a line along the strip lengthwise, starting anywhere you want to start on the strip. What happens? You end up back where you started, right? That's the first interesting discovery - the Moebius strip has only one side.