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NCERT Solutions for Class 6 Maths Chapter 3 Excercise 3.12 Number Play

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NCERT Solutions for Class 6 Excercise 3.12 Maths FREE PDF Download

Chapter 3.12 Games and Winning Strategies from Class 6 Maths explores different mathematical strategies that can be applied to games. The chapter helps students understand the logic and reasoning behind winning strategies through fun and engaging games. By learning these techniques, students enhance their problem-solving skills and improve their mathematical thinking. The chapter also introduces the concept of patterns and how they can be used to predict outcomes in various games.

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Table of Content
1. NCERT Solutions for Class 6 Excercise 3.12 Maths FREE PDF Download
2. Glance on Class 6 Number Play Ex 3.12 Number Play
3. Access NCERT Solutions for Class 6 Maths Ex 3.12 Number Play
    3.13.12 Games and Winning Strategies 
4. Benefits of NCERT Solutions for Class 6 Maths Ex 3.12
5. Class 6 Maths Chapter 3: Exercises Breakdown
6. Important Study Material Links for Maths Chapter 3 Class 6
7. Conclusion
8. Chapter-wise NCERT Solutions Class 6 Maths
9. Related Important Links for Class 6  Maths 
FAQs


Our Class 6 Maths NCERT Solutions PDF breaks the lesson into easy-to-understand explanations, making learning fun and interactive. Students will develop essential language skills with engaging activities and exercises. Check out the revised CBSE Class 6 Maths  Syllabus and start practising the Maths Class 6 Chapter 3.


Glance on Class 6 Number Play Ex 3.12 Number Play

  • Understanding the logic of games.

  • Recognizing patterns to predict outcomes.

  • Exploring winning strategies through mathematical thinking.

  • Application of reasoning in simple games.

  • Problem-solving using game theory.

Access NCERT Solutions for Class 6 Maths Ex 3.12 Number Play

3.12 Games and Winning Strategies 

Figure it Out (Page No. 72 – 73)

Question 1. This grid has only one supercell (number greater than all its neighbours). If you exchange two digits of one of the numbers, there will be 4 supercells. Figure out which digits to swap.


16,200

39,344

29,765

23,609

62,871

45,306

19,381

50,319

38,408



Solution:
If we swap first and last digit of central number 62,871, we get the desired result.


16,200

39,344

29,765

23,609

21,876

45,306

19,381

50,319

38,408



Question 2. How many rounds does your year of birth take to recall the Kaprekar constant?
Solution: If your year of birth is 2000
Step 1: Now from digits of number 2000
Here largest number = 2000
and smallest number = 0002
Let’s subtract them = 2000 – 0002 = 1998


Step 2: Now from digits of number 1998
Here largest number = 9981
and smallest number = 1899
Let’s subtract them = 9981 – 1899 = 8082


Step 3: Now from digits of number 8082
Here largest number = 8820
and smallest number = 0288
Let’s subtract them = 8820 – 0288 = 8532


Step 4: Now from digits of number 8532
Here largest number = 8532
and smallest number = 2358

Let’s subtract them = 8532 – 2358 = 6174


which is a Kaprekar constant.
Hence it took 4 rounds to reach the Kaprekar constant from 2000.


Question 3. We are the group of 5-digit numbers between 35,000 and 75,000 such that all of our digits are odd. Who is the largest number in our group? Who is the smallest number in our group? Who among us is the closest to 50,000?
Solution

The largest number with all odd digits (different) = 73951
The largest number with all odd digits (repetitive) = 73999
The smallest number (non repetitive) = 35,179
The smallest number (repetitive) = 57111
Closest to 50,000 (in case of non-repetition) = 49751
Closest to 50,000 (in case of repetition) = 49999


Question 4. Estimate the number of holidays you get in a year including weekends, festivals and vacation. Then try to get an exact number and see how close your estimate is.
Solution:
Will be done by students.


Question 5. Estimate the number of litres a mug, a bucket and an overhead tank can hold.
Solution:
Will be done by students


Question 6. Write one 5-digit number and two 3-digit numbers such that their sum is 18,670. ‘
Solution:
5 digit number = 1 8 0 0 0
3 digit number = 6 7 0
Sum = 1 8 000 + 670 = 18670


Question 7. Choose a number between 210 and 390. Create a number pattern similar to those shown in Section 3.9 that will sum up to this number.


Choose a number between 210 and 390. Create a number pattern similar to those shown in Section 3.9 that will sum up to this number


Solution:
Sum of No. = 5 × 1 = 5
+ 10 × 3 = 30
+ 15 × 5 = 75
+ 20 × 7 = 140 = 250
which lies between 210 and 390.


Question 8. Recall the sequence of Powers of 2 from Chapter 1, Table 1. Why is the Collatz conjecture correct for all the starting numbers in this sequence?
Solution: The square of power of 2 is :
1,2,4, 8, 16, 32, 64

Let’s take the number’ 64 as per Collatz Conjecture


  • 64 is even, divide by 2 = 32

  • 32 is even, divide by 2 = 16

  • 16 is even, divide by 2 = 8

  • 8 is even, divide by 2 = 4

  • 4 is even, divide by 2 = 2

  • 2 is even, divide by 2 = 1


Hence Collatz conjecture is correct in all numbers in the power of 2 sequence.
As it is power of 2, and in Collatz Conjecture even number is divided by 2 in each step.


Question 9. Check if the Collatz Conjecture holds for the starting number 100.
Solution:

  • 100 is even, divide by 2 =50

  • 50 is even, divide by 2 = 25

  • 25 is odd, so multiply by 3 and add 1 → 76

  • 76 is even, divide by 2 = 38

  • 38 is even, divide by 2 = 19

  • 19 is odd, so multiply by 3 and add 1 → 58

  • 58 is even, divide by 2 = 29

  • 29 is odd, so multiply by 3 and add 1 → 88

  • 88 is even, divide by 2 = 44

  • 44 is even, divide by 2 = 22

  • 22 is even, divide by 2 = 11

  • 11 is odd, so multiply by 3 and add 1 → 34

  • 34 is even, divide by 2 = 17 

  • 17 is odd, so multiply by 3 and add 1 → 52

  • 52 is even, divide by 2 = 26

  • 26 is even, divide by 2 = 13

  • 13 is odd, so multiply by 3 and add 1 → 40

  • 40 is even, divide by 2 = 20

  • 20 is even, divide by 2 = 10

  • 10 is even, divide by 2 = 5

  • 5 is odd, so multiply by 3 and add 1 → 16

  • 16 is even, divide by 2 = 8

  • 8 is even, divide by 2 = 4

  • 4 is even, divide by 2 = 2

  • 2 is even, divide by 2 = 1


Yes, the Collatz conjecture holds for the starting number 100. 


Benefits of NCERT Solutions for Class 6 Maths Ex 3.12

  • Enhances problem-solving skills: By learning to analyze game strategies, students improve their ability to solve problems logically.

  • Improves reasoning ability: The chapter sharpens the reasoning skills of students by teaching them to recognize patterns and predict outcomes.

  • Practical application of maths: Students learn how maths can be applied to real-life situations through games.

  • Boosts critical thinking: The chapter encourages critical thinking as students explore various strategies to win games.

 

Class 6 Maths Chapter 3: Exercises Breakdown

Exercise

Topic

Exercise 3.1

Numbers Can Tell Us Things

Exercise 3.2

Supercells

Exercise 3.3

Patterns of Numbers on the Number Line

Exercise 3.4

Playing with Digits

Exercise 3.5

Pretty Palindromic Patterns

Exercise 3.6

The Magic Number of Kaprekar

Exercise 3.7

Clock and Calendar Numbers

Exercise 3.8

Mental Math

Exercise 3.9

Playing with Number Patterns

Exercise 3.10

An Unsolved Mystery — the Collatz Conjecture!

Exercise 3.11

Simple Estimation



Important Study Material Links for Maths Chapter 3 Class 6

S.No.

Important Study Material Links for Chapter 3

1.

Class 6 Number Play Important Questions

2.

Class 6 Number Play Notes

3.

Class 6 Maths Number Play Worksheets



Conclusion

Chapter 3 Excercise 3.12  Games and Winning Strategies from Class 6 Maths is an engaging and interactive way to strengthen mathematical concepts. Students not only enjoy the process of learning but also understand how to apply mathematical reasoning in real-life scenarios. This chapter is instrumental in building logical thinking and problem-solving abilities through fun and strategic games.


Chapter-wise NCERT Solutions Class 6 Maths

After familiarising yourself with the Class 6 Maths  Chapters Question Answers, you can access comprehensive NCERT Solutions from all Class 6 Maths textbook chapters.


S.No

Chapterwise Links for Class 6 Maths NCERT Solutions

1

Chapter 1 Patterns In Mathematics NCERT Solutions 

2

Chapter 2 Lines and Angles NCERT Solutions 

3

Chapter 3 Number Play NCERT Solutions 

4

Chapter 4 Data Handling and Presentation NCERT Solutions 

5

Chapter 5 Prime Time NCERT Solutions 

6

Chapter 6 Perimeter and Area NCERT Solutions 

7

Chapter 7 Fractions NCERT Solutions 

8

Chapter 8 Playing with Constructions NCERT Solutions 

9

Chapter 9 Symmetry NCERT Solutions 

10

Chapter 10 The Other Side of Zero NCERT Solutions 



Related Important Links for Class 6  Maths 

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


FAQs on NCERT Solutions for Class 6 Maths Chapter 3 Excercise 3.12 Number Play

1. What is the main focus of Exercise 3.12 Games and Winning Strategies?

The exercise focuses on teaching students how to use logical thinking and mathematical strategies to win games.

2. How can recognizing patterns help in games as mentioned in Exercise 3.12 of Chapter 3?

Recognizing patterns helps predict outcomes and formulate winning strategies in games.

3. What is the importance of applying maths in games as discussed in Exercise 3.12 Games and Winning Strategies?

Applying maths in games helps students understand practical uses of mathematical reasoning and improves their problem-solving skills.

4. Can learning winning strategies improve the mathematical thinking of Excercise 3.12?

Yes, learning winning strategies enhances mathematical thinking by encouraging logical reasoning and pattern recognition.

5. What are some examples of games used in Chapter 3 Exercise 3.12 to teach strategies?

The exercise includes simple games like NIM, Tic-Tac-Toe, and puzzles to teach winning strategies.

6. Why is problem-solving an essential skill mentioned in Exercise 3.12 of Chapter 3?

Problem-solving is essential as it helps students develop logical thinking and find solutions using mathematical strategies.

7. How does Number Play Exercise 3.12 improve critical thinking in students?

The exercise improves critical thinking by challenging students to explore various game strategies and predict winning moves.

8. What role does reasoning play in winning games as per Chapter 3 Exercise 3.12?

Reasoning is crucial as it helps students understand the logic behind moves and apply strategies to win games.

9. Does Exercise 3.12 of Chapter 3 include any real-life applications of game strategies?

Yes, the exercise helps students see how game strategies can be applied to solve real-life problems using mathematical reasoning.

10. How does Vedantu's NCERT Solutions for Class 6 Maths help with Exercise 3.12 of Chapter 3?

Vedantu's NCERT Solutions offer step-by-step explanations and strategies to help students easily understand and apply winning techniques in games.