Math Class Magic: The Lucas Fan (Binary System)

A classic mathematical "magic trick" designed by French mathematician Édouard Lucas in the 19th century. With these 5 simple strips, you can guess any number between 1 and 31 that a friend thinks of!

It is a fantastic STEM educational tool to introduce children (and adults) to the concept of the Binary System in a fun and interactive way.

🎩 How to Perform the Magic Trick:

1. Ask a friend to think of a number between 1 and 31.
2. Show them the 5 strips one by one.
3. Ask: "Is your number written on this strip?"
4. If they say YES, keep that strip in your hand. If they say NO, put it aside.
5. Once you have checked all 5 strips, look at the Red Numbers at the bottom of the strips they said "YES" to.
6. Sum them up. The total is exactly the number they thought of!

Example:

Your friend thinks of 25.

• Is it on strip 1 (Red 1)? -> YES (Keep it)
• Is it on strip 2 (Red 2)? -> NO
• Is it on strip 3 (Red 4)? -> NO
• Is it on strip 4 (Red 8)? -> YES (Keep it)
• Is it on strip 5 (Red 16)? -> YES (Keep it)
• Calculation: 16 + 8 + 1 = 25. Magic!

🎓 Educational Activity: How does it work?

This tool visualizes how computers "think" using the Binary System (Base 2).

Each strip represents a "Bit" or a power of 2:

• Strip 1 = 2^0 = 1
• Strip 2 = 2^1 = 2
• Strip 3 = 2^2 = 4
• Strip 4 = 2^3 = 8
• Strip 5 = 2^4 = 16

Every number can be broken down into a sum of these powers. The numbers printed on each strip are simply all the numbers that have a "1" in that specific binary position. By collecting the strips, you are physically "turning on the bits" needed to make that number.

Happy Teaching!