A Math Magic Trick
This is a great trick just for the sake of performing great tricks. BUT – it is also a great way for teachers and parents to make algebra interesting to kids! For all of you teachers and parents out there looking for teaching tricks that will help kids understand algebra, this is one to put into your “teaching tool chest”! I’ll give you the algebraic explanation of the trick below. Here, I will tell you about the trick and explain how to do it.
You start off with a stack of “Space Mystery” cards (which you can make yourself with our free PDF – the link to that is below), half of which have aliens facing up, and the other have space-only cards facing up.
Performing the Space Mystery magic trick is pretty easy once you know how. You start off with an even number of cards – I would suggest 6 to start off with, and then you can work your way up to whatever number you want, but I would suggest no more than 12.
Set up the set of cards such that half of them are showing the alien side, and the other half are showing the space-only side. Place the cards on the table to demonstrate to your audience that half of the cards are showing the alien side:
Now pick up the cards and shuffle them well:
Place half of the cards on the table in a single row one-by-one:
With the remaining cards in your hand, use slight of hand to flip them. I like to switch them into the other hand while I flip them, making it harder for your audience to detect what you did. Now place the remaining cards on the table in a second row one-by-one. Magically, the number of cards showing the alien side are the same in each row:
As you become more proficient with the trick, you can spiff it up by separating the alien-sided cards from the space-only cards in each row to make the illusion look more striking.
Why does this trick work?
How this math magic trick works can be best explained algebraically. I will use the case where 12 cards are being used. With a little patience as you go through the explanation, you will soon get the “Ah-Ha!” moment:
You start off with 6 alien cards face-up
After the cards are randomized, they are split into 2 stacks of cards, 6 cards each
Let the number of alien cards in stack 1 = A
Then the number of alien cards in stack 2 must = 6-A
Now, with a little thought you can determine the number of space-only cards that remain in stack 2. This turns out to be 6 minus the # of alien cards, or:
6 – (6 – A), which is equal to A
So, if you now flip stack 2, the space-only cards (equal to A) now become alien cards – the same number of alien cards in stack 1!
Here is the free PDF (Space Mystery Printable Cards.pdf) that you can use to print your own cards. I used the Avery white, two-sided, clean edge business cards (Avery #28878) to print them out. These can be purchased at any office supply store – I got mine at Walmart! They came out pretty well – very uniform from card to card.
The Alien Storyline
If you are able to perform a dramatic presentation, here is a storyline I came up with that you can use while doing the trick. You explain to the audience the story behind the aliens:
The Talletians are a race of highly intelligent beings from a star system 32 parsecs from our own system. Throughout their history, they have had an obsession with symmetry. This obsession has led them to rapid advances in science and technology, which in turn gave them an ability to quickly conquer space.
The Talletian obsession with symmetry is evident when they travel through space. When they are in groups, they prefer to travel such that they are present in equal numbers between groups. They do not tolerate broken symmetry.
You can witness this “need” for symmetry yourself. The 12 cards in this pack are identical; one side displays a region of space, and the other side displays a Talletian in that space. Start off by dividing the cards in two groups of six cards each – one with the space side up, and the other with the alien side up. Now shuffle the cards several times to insure a random distribution. Now divide the cards into two piles of 6 cards each. Each pile now has the randomly distributed alien-up cards. Break this randomness by flipping one pile over. Now, if you inspect each card in each pile, you will see that each pile contains the same number of alien-up cards. Symmetry has been made!