A simple and amazing Magic Trick using Binary Numbers.

Here is the long-awaited magic trick, I was talking about in my last blog on Binary Numbers. Let us learn this simple amazing magic trick using binary numbers.

I assume you all have practiced the conversion of Decimal Numbers to Binary, and Binary Numbers to Decimal. If you haven’t, I strongly recommend you to, do so. A clear understanding of the Binary Number system and its conversion is a must-know thing, for this trick.

Prerequisites for the Binary Numbers Magic Trick.

Before we perform this trick, we need 4 cards.

Behind these cards, we write some specific numbers, like this:

Let’s play

Now pick a family member or friend from your audience and ask him/her to guess a number, between 0 and 15.

Once they have guessed their number, show them the cards, one by one, sequentially, starting from Card 1. While showing them the cards, ask them if their guessed number is present on that particular card or not.

Note down their answers in Yes (the number is present) or No, against each card. Based on their answers, you can calculate their guessed number. Magic!

How does this magic trick work?

As you observe the numbers in the cards, you can easily figure out that numbers 0, 1, 2, 4, 8, and 15, can be easily identified, because:

If the guessed number is,

1. If not found in any cards, then the number is 0.
2. Found on every card, then the number is 15.
3. If found on any one of the cards, and not on any other, then if the number is:
   • Card 1, then the guessed number is 1
   • Card 2, then the guessed number is 2
   • Card 3, then the guessed number is 4
   • Card 4, then the guessed number is 8

But that is too many things to remember, and what about other numbers? Not so easy to guess, right?

It is, only if you know the trick! Let us discuss an example

Assume, I am playing with you, and you guessed a number, say 12. Thus, my reply to the question, that the number is present in the cards will be as follows:

Present in Card 1? No
Present in Card 2? No
Present in Card 3? Yes
Present in Card 4? Yes

Note: Refer to the cards, given above.

Now just replace the Yes with 1, and No with 0.

Calculation

Rest you know, what to do. Just convert the Binary to Decimal.
So the guessed number has to be:

(1100)₂ = 1×2³ + 1×2² + 0x2¹ + 0x2⁰
= 8 + 4 + 0 + 0
= (12)₁₀

Woohoo! That’s the guessed number!

Now, go ahead, and play the trick with your friends and family. Don’t forget to practice it a few times, before you perform.

For best performance, try to remember the answers and do the conversion in mind, rather than doing it on paper.

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