Wednesday, May 14, 2025

Class 8 NCERT bridge course Answers Activity W6.4 Pretty Palindromic Patterns

 Activity W 6.4 Pretty Palindromic Patterns 

 Engaging students in these puzzles will make them more observant about numbers. 

Pretty Palindromic Patterns 



Procedure 

The numbers that can be read the same from left to right and from right to left are called palindromes or palindromic numbers. 

Part I: Forming Palindromes from Given Digits

Given digits: 3, 4, 5

Palindromes you can form:

  • 2-digit: 33, 44, 55

  • 3-digit: 343, 454, 353, 535, 445, 544, 333, 444, 555

  • 5-digit: 34543, 35453, 34343, 44444, etc.

 The game challenge:

  • ❗ Most palindromes formed → Winner

  • ❗ Longest palindrome formed → Winner

For example, 232, 444, 54645, etc. 

1. Students may be asked to write all palindromes using certain number of digits.

 For example, using the digits 3, 4, 5 we can form palindromes 343, 454, 34543, 333, etc. 

Students may form as many palindromes using the given digits. 

2. A game can be played, based on this. 

 The one who forms maximum number of palindromes using the given digits will be the winner. 

Or 

The one who forms the longest palindrome will be the winner, etc.

Procedure 

1. Students may write a 2-digit number and reverse the order of the digits. 

Add these two numbers. 

Part II: Reverse and Add Process

2. They may check whether the addition is a palindrome. 

If not, continue the process of reversing the digits and adding them. 

3. They may check, if they get a palindrome at some stage or not. 

For example, 

Example 1:

  • Start with: 36 → 36 + 63 = 99 

  •  Palindrome in 1 step

36 + 63 = 99 (a palindrome!) 

Example 2:

  • Start with: 39 → 39 + 93 = 132

  • 132 + 231 = 363 

  • Palindrome in 2 steps

39 + 93 = 132 (not a palindrome) 

132 + 231 = 363 (a Palindrome!) 

Example 3:

  • Start with: 89

    • 89 + 98 = 187

    • 187 + 781 = 968

    • 968 + 869 = 1837

    • 1837 + 7381 = 9218

    • 9218 + 8129 = 17347

    • 17347 + 74371 = 91718

    • 91718 + 81719 = 173437

    • 173437 + 734371 = 907808

    • 907808 + 808709 = 1716517 

    •  Palindrome (10 steps!)

4. Students may be asked to do this for different numbers. 

Students may explore and tell, for which numbers it took only one step, few steps or large number of steps. 

5. Students may explore whether reversing and adding numbers repeatedly, starting with a 2-digit number, always give a palindrome? 

Do All Numbers Reach a Palindrome?

  •  For 2-digit numbers, almost all lead to a palindrome within a few steps.

  • For some large numbers (like 196), it’s unknown if they ever reach a palindrome — this is an unsolved math mystery.

Observation: Most numbers do reach a palindrome, but some take many steps

III. Procedure

 tth th h t u 

Write the number in words: 

I am a 5-digit palindrome. 

 I am an odd number. 

 My ‘t’ digit is double of my ‘u’ digit. 

 My ‘h’ digit is double of my ‘t’ digit. 

 Who am I? _________________ 

Since it’s a palindrome, its structure is:

less
A B C B A (tthth = palindrome structure)

Let’s use:

  • A = 1 (odd)

  • u = 1 → t = 2 × 1 = 2

  • t = 2 → h = 2 × 2 = 4

So we have:

  • u = 1

  • t = 2

  • h = 4

Therefore, the number is:
→ A B C B A → 1 2 4 2 1 

Answer: 12421

 Teacher/students may create more such puzzles and give others to solve.

Palindromic Puzzles for Students

Puzzle 1:

I am a 3-digit palindrome.
I am less than 500.
My middle digit is the smallest possible odd number.
Who am I?
Answer: 101, 303, etc. (Middle digit = 1, smallest odd)

Puzzle 2:

I am a 4-digit palindrome.
The sum of my digits is 22.
My outer digits are the same and even.
What could I be?
Answer: 2662 (2 + 6 + 6 + 2 = 16), 4774, 6446 (check sums)

 Puzzle 3:

Form the longest 7-digit palindrome using only two digits: 2 and 5.
Answer: 2552552 or 2225222, etc.

 Puzzle 4:

Start with 65. Reverse and add.
Continue the process until you get a palindrome.
How many steps does it take?
65 + 56 = 121 ✅ 1 step only!

Puzzle 5:

I am a 5-digit palindrome.
The sum of all my digits is 25.
My digits include only 3 different digits.
What could I be?
Answer: 35853, 46964, etc.




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