NCERT Solutions for Class 6 Maths Chapter 3 - Number Play Exercise 3.5

Exercise 3.5

1. What pattern do you see in these numbers: 66, 848, 575, 797, 1111?

These numbers read the same from left to right and from right to left. 

Ans: The pattern in these numbers is that they are palindromes. A palindromic number reads the same from left to right as it does from right to left.

For example:

• 66 reads the same forward and backward.

• 848 is the same when reversed.

• 575 is identical when read from either direction.

• 797 reads the same both ways.

• 1111 is the same forwards and backwards.

2. Write all possible 3-digit palindromes using these digits. 

Ans: Using the digits 1, 2, and 3, the possible 3-digit palindromes are:

1. 111

2. 121

3. 131

4. 222

5. 232

6. 333

3. Will reversing and adding numbers repeatedly, starting with a 2-digit number, always give a palindrome? Explore and find out.

Ans: Choose a 2-digit number (e.g., 47).

1. Reverse the digits of the number (e.g., 47 becomes 74).

2. Add the original number and the reversed number (e.g., 47 + 74 = 121).

3. Check if the result is a palindrome (e.g., 121 is a palindrome).

4. If not a palindrome, repeat the process with the new number (e.g., for 121, reversing it gives 121, and 121 + 121 = 242, which is a palindrome).

Exploration Examples:

1. Number: 23

• Reverse: 32

• Add: 23 + 32 = 55 (Palindrome)

2. Number: 56

• Reverse: 65

• Add: 56 + 65 = 121 (Palindrome)

3. Number: 87

• Reverse: 78

• Add: 87 + 78 = 165

• Reverse: 561

• Add: 165 + 561 = 726 (Palindrome)

Reversing and adding numbers does not always immediately give a palindrome, but with repeated steps, it often leads to one. This process is a fun way to see how numbers can transform into palindromes over time!

Puzzle time

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? _________________

Ans: Form of the Palindrome: The number is in the format tth, th, h, t and u are digits.

1. Odd Number: The last digit (u) must be odd, so possible values for u are 1, 3, 5, 7, or 9.

2. Constraints:

• t = 2u (The ‘t’ digit is double the ‘u’ digit)

• h = 2t (The ‘h’ digit is double the ‘t’ digit)

3. Testing Values:

• If u = 1:

• t = 2 * 1 = 2

• h = 2 * 2 = 4

The number is 22422, which is a valid palindrome and fits all constraints.

• If u = 3:

• t = 2 * 3 = 6

• h = 2 * 6 = 12 (Not valid because h must be a single digit.)

• If u = 5:

• t = 2 * 5 = 10 (Not valid because t must be a single digit.)

• If u = 7:

• t = 2 * 7 = 14 (Not valid because t must be a single digit.)

• If u = 9:

• t = 2 * 9 = 18 (Not valid because t must be a single digit.)
  The only valid 5-digit palindrome is 22422.

Class 6 Maths Chapter 3: Exercises Breakdown

Benefits of NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 Number Play

• They provide detailed explanations and step-by-step solutions, helping students grasp complex concepts easily.

• They offer a variety of practice problems to reinforce understanding and application of number patterns and sequences.

• They ensure alignment with the CBSE Class 6 Maths syllabus, covering all required topics effectively.

• They help in developing critical thinking and problem-solving skills by working through palindromic patterns and sequences.

• They allow students to check their answers and understand the correct methods, improving their learning and confidence.

• They are available as a free PDF download, making it easy for students to access and use for study and revision anytime, anywhere.

Important Study Material Links for Class 6 Maths Chapter 3 - Number Play

Conclusion

NCERT Solutions for Class 6 Maths Chapter 3 Exercise 3.5 "Number Play" is a great help for students. They provide clear and easy-to-follow explanations for solving problems related to number patterns and sequences. By working through these exercises, students can improve their understanding of palindromes and other number concepts in line with the CBSE syllabus. These solutions make it easier for students to practice and get better at problem-solving, which improves their confidence. The solutions are available as a free PDF download, making it convenient for students to study and revise whenever they need to.

Chapter-Specific NCERT Solutions for Class 6 Maths

Given below are the chapter-wise NCERT Solutions for Class 6 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Maths Class 6

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.