The 21-Card Trick

In my previous post, I introduced the relevance of educational magic in today’s world. Here in my second article for Kids Entertainer Hub, I’ll discuss in detail one educational card trick that you can use.

Welcome to the 21-Card Trick, a popular, self-working card trick. And like all self-working card effects, this ‘trick’ has some interesting maths and ideas used in computer science that underlie it.

If you follow a well-defined set of instructions when performing the 21-Card Trick, the ‘magic’ will happen all by itself. The concept behind it can be compared to algorithms that are used to design computer programs. Below is the list of instructions for the trick. Let’s call the procedure an algorithm.

Algorithm

• Have the volunteer shuffle a pack of cards.
• Deal out a row of three cards face up from left to right.
• Repeat this another six times so that there are 21 cards laid out.
• Have the volunteer mentally select one of the cards.
• The volunteer does not tell you the card but points to what pile it is in.
• Collect the pile that DOES NOT have the volunteer’s card.
• Collect the pile that DOES have the volunteer’s card and place this on the first pile.
• Collect the remaining pile and place it on top.
• Repeat steps 2 and 3.
• Ask the volunteer to point to the pile where their card is in.
• Repeat steps 6, 7, and 8.
• Repeat steps 2 and 3.
• Ask the volunteer to point to the pile where their card is in.
• Repeat steps 6, 7, and 8.
• Repeat steps 2 and 3.
• The middle card is the volunteer’s chosen card.

Now what if our algorithm is not correct? Would the trick work? The chances are no. The same goes for the algorithms used in the design of computer programs. An incorrect algorithm equals an incorrect program.

So what do we have to do? Well, we have to test our algorithm and make sure that it works every time. This is exactly the same as testing a computer program. We need to be sure that a computer program works 100 percent of the time. Why? Let’s put it this way: Would you feel safe in a plane if the computer program used to operate the landing gear only worked 99 percent of the time?

Making Sure Our Trick Works

“How many times would we need to test a magic trick to be safe in the knowledge that it works every time?” Professor Peter McOwan once asked.

Answering his own question, the professor said, “To be really certain, it looks like we would have to try it out with every possible set of 21 cards, in all possible starting positions, checking for every card the person might have thought of or selected. To try all these possible combinations would be hugely impractical and would take an impossibly long time. Similarly, testing programs exhaustively like this is not practical and that is why we get bugs in computer programs.”

Although we cannot (and do not need to) test every possible combination, we can use logic to prove that a ‘trick’ works every time. We can create a test and simulate the procedure using a series of diagrams, which is provided in the 21-Card Trick teaching resource.

Get the 21-Card Trick teaching resource at www.flummix.com.

We can highlight all the possible card locations at each stage in the routine by colouring in the diagram until the final phase where the selected card is in the middle of the middle pile.

What we find is that the 21-Card Trick will always have a magical outcome if we follow the instructions correctly. We have used logic to prove that our algorithm is correct. And just like a magic trick with a double hit ending, we have also provided an amazing exercise in developing skills in computational thinking. Now that’s educational magic in action.