pick a number between 1 and 21

Guri Bee

2 min read

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17-10-2024

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The Mind-Reading Game: Picking a Number Between 1 and 21

Have you ever played a game where someone seems to guess your thoughts? There's a classic trick that utilizes a bit of math magic to make you feel like a mind reader. The game involves picking a number between 1 and 21, and the "mind reader" can seemingly deduce your choice with remarkable accuracy.

Here's how it works:

1. The Setup: Ask someone to pick a number between 1 and 21, but to keep it secret.

2. The Magic: Perform a series of simple calculations:

   • Step 1: Have them multiply their chosen number by 3.
   • Step 2: Add 3 to the result.
   • Step 3: Multiply the new sum by 3 again.

3. The Reveal: Now, ask them to tell you the final result. You can quickly calculate their original number using this formula:

   (Final Result - 9) / 9 = Original Number

Why Does It Work?

This trick relies on a clever manipulation of mathematical operations. Let's break it down:

• Multiplying by 3: This is the key step. It creates a unique pattern that allows us to easily reverse the process.
• Adding 3: This ensures that the final result is always a multiple of 3.
• Dividing by 9: This effectively cancels out the multiplications by 3 and isolates the original number.

A Practical Example:

Let's say someone picks the number 7. Here's how the calculations play out:

1. 7 x 3 = 21
2. 21 + 3 = 24
3. 24 x 3 = 72

Now, using the formula:

(72 - 9) / 9 = 63 / 9 = 7

The original number, 7, is revealed!

Beyond the Trick:

While this game may seem like a mind-reading feat, it's actually based on simple mathematical principles. It's a great way to demonstrate the power of algebra and how equations can be manipulated to solve for unknown variables. The trick also highlights how seemingly complex calculations can be reversed with the right approach.

The Next Time You Play:

Try this trick out on your friends and family. You'll be amazed at how easily you can seem to "read" their minds. Remember, it's just a bit of fun and a clever demonstration of how mathematics can be used to create intriguing illusions.

Note: This explanation is based on the information found in a GitHub repository discussing mathematical puzzles. The code and explanations are freely available for learning and exploration.