Class 6 NCERT bridge course Answers Activity W1.5 The Reversing Digits Magic Trick

 Activity W1.5  The Reversing Digits Magic Trick

Ask the students to write a two-digit number whose digits are not the same.

 Let them reverse the number and subtract the smaller from the larger. 

 Ask them to repeat the process with the obtained answer till they reach a one-digit number. 

 Teacher may predict the one-digit number. 

 Let them sit in group and observe their calculations and identify the patterns in the intermediate answers.

 They may be asked to identify the two-digit numbers which will lead to a one-digit number in one step.

 Motivate them to play this trick with their family members and other friends.

Activity W1.5 – The Reversing Digits Magic Trick

“Subtract and Reveal the Secret!”

Objective:

To discover number patterns through reversing and subtracting digits of 2-digit numbers.

Instructions:

1. Think of any two-digit number (digits should not be the same).

2. Reverse the digits to form another number.

3. Subtract the smaller number from the larger one.

4. If the result is not a one-digit number, repeat the process:

   • Reverse it

   • Subtract again

5. Continue until you reach a one-digit number.

6. Your teacher or friend will predict the final number!

Example 1:

• Start with: 73

• Reverse: 37

• Subtract: 73 – 37 = 36

• Reverse 36 → 63

• Subtract: 63 – 36 = 27

• Reverse 27 → 72

• Subtract: 72 – 27 = 45

• Reverse 45 → 54

• Subtract: 54 – 45 =  9

 Final one-digit number is 9

Example 2:

• Start with: 52

• Reverse: 25

• Subtract: 52 – 25 = 27

• Reverse: 72

• Subtract: 72 – 27 = 45

• Reverse: 54

• Subtract: 54 – 45 =  9

What’s the Pattern?

No matter which number you start with (as long as digits are different), you'll eventually end up with 9!

This is because of divisibility and digit difference:

• The difference between a number and its reverse is always divisible by 9.

• Eventually, all such differences reduce to 9.

Group Activity Suggestions:

• Try it with different starting numbers.

• Record how many steps it takes to reach 9.

• Find which numbers reach 9 in just one step (like 91 – 19 = 72 → 72 – 27 = 45 → ... = 9).

• Predict the number when your friend plays the trick!

Challenge:

Try with 3-digit numbers or explore what happens if the digits are the same. Does the trick still work?

Image: Flow of the Reversing Digits Trick

(Note: If you'd like a specific new image illustrating this exact flowchart — 73 → 37 → 36 → 63 → ... → 9 — just let me know and I’ll generate one for this activity.)