Wild About Math! Making Math fun and accessible

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:

1. 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.
2. Number each card using the numbers from 0 up to 15.
3. 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.
4. 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!

1. 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.
2. Take a thin dowel, knitting needle, small screwdriver or other object that can fit through the holes and notches.
3. 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.
4. 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.
5. 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.
6. 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?