Important Questions Class 6 Maths Chapter 3 Number Play

Number play means using numbers to notice patterns, solve puzzles, estimate quantities and build strategies. A digit sum, palindrome, number line or game rule can reveal how numbers behave in different situations.

Strong number sense grows when students stop treating numbers as only calculation tools. Important Questions Class 6 Maths Chapter 3 helps students prepare Number Play from the 2026 NCERT Ganita Prakash syllabus through pattern-based and reasoning-based questions. The chapter tests supercells, number lines, digit sums, palindromic numbers, Kaprekar’s constant, mental maths, estimation, Collatz sequences and winning strategies. CBSE school exams may frame these as puzzles, “always sometimes never” questions, short reasoning answers and quick calculation tasks. The NCERT chapter highlights that numbers can convey information, reveal patterns, support estimation and help build strategies.

Key Takeaways

• Supercell: A cell becomes a supercell when its number is greater than all adjacent neighbouring cells.
• Digit Sum: The digit sum of a number is found by adding all its digits.
• Palindrome: A palindromic number reads the same from left to right and right to left.
• Kaprekar Constant: The 4-digit Kaprekar process reaches 6174 for numbers with at least two different digits.

Important Questions Class 6 Maths Chapter 3 Structure 2026

Class 6 Maths Chapter 3 Important Questions with Answers

Number Play does not reward memorisation alone. These class 6 maths chapter 3 important questions check whether students can explain a pattern, test a rule and justify an answer.

1. Where do we use numbers in daily life?

We use numbers to count, measure, compare, record and organise information.

1. Time uses numbers for hours and minutes.
2. Money uses numbers for rupees and paise.
3. Marks, dates, height and distance also use numbers.

Final Answer: Numbers help in counting, time, money, measurement and records.

2. What does Number Play in Class 6 Maths teach?

Number Play teaches students to find patterns, estimate values, solve puzzles and build strategies.

1. It uses number lines, digits and palindromes.
2. It includes Kaprekar’s constant and Collatz sequences.
3. It connects maths with games and estimation.

Final Answer: Number Play develops number sense and reasoning.

3. Why are reasoning questions important in Number Play?

Reasoning questions are important because many answers need explanation, not only calculation.

1. Students must say why a sequence is possible.
2. They must justify whether a statement is always true.
3. This supports CBSE-style answer writing.

Final Answer: Reasoning shows how a student thinks with numbers.

4. What are five situations where numbers are used?

Numbers are used in time, calendars, marks, money and measurement.

1. Time shows hours and minutes.
2. Calendars show dates and years.
3. Measurement uses length, weight and distance.

Final Answer: Time, calendars, marks, money and measurement use numbers.

Class 6 Maths Chapter 3 Number Play Questions on Taller Neighbours

The taller-neighbour activity looks simple, but it trains logical arrangement. Students must check positions, end points and neighbouring heights before answering.

5. Can children standing at the ends say 2 in the taller-neighbour game?

No, children standing at the ends cannot say 2.

1. An end child has only one neighbour.
2. To say 2, a child needs two taller neighbours.
3. Therefore, an end child cannot say 2.

Final Answer: No

6. Can all children say only 0 in the taller-neighbour game?

Yes, all children can say 0 if all children have the same height.

1. A child says 0 when no neighbour is taller.
2. Equal-height neighbours are not taller.
3. Therefore, all can say 0.

Final Answer: Yes, if all have the same height

7. Can two children standing next to each other say the same number?

Yes, two children standing next to each other can say the same number.

1. Their taller-neighbour counts may match.
2. Position and height arrangement decide the count.
3. Same counts can appear side by side.

Final Answer: Yes

8. Can five children of different heights stand so that four say 1 and one says 0?

Yes, they can stand in ascending order of height.

1. Each child except one can have one taller neighbour.
2. The tallest child can say 0.
3. The arrangement depends on height order.

Final Answer: Yes

9. Is the sequence 1, 1, 1, 1, 1 possible for five children of different heights?

No, the sequence 1, 1, 1, 1, 1 is not possible.

1. An end child has only one neighbour.
2. The tallest child cannot have a taller neighbour.
3. So every child cannot say 1.

Final Answer: No

10. Is the sequence 0, 1, 2, 1, 0 possible?

Yes, the sequence 0, 1, 2, 1, 0 is possible.

1. The middle child can have two taller neighbours.
2. The second and fourth children can have one taller neighbour.
3. The end children can have no taller neighbour.

Final Answer: Yes

Supercells Class 6 Maths Important Questions

Supercell questions are a good test of comparison accuracy. In supercells class 6 maths, students must compare a number only with adjacent neighbours, not with every number in the row.

11. What is a supercell?

A supercell is a cell whose number is greater than all its adjacent cells.

1. In a row, adjacent cells are left and right cells.
2. At an end, a cell has only one adjacent cell.
3. In a grid, neighbours may be left, right, top and bottom.

Final Answer: A supercell is greater than all its neighbours.

12. Why is 626 a supercell in the row 200, 577, 626, 345?

626 is a supercell because it is greater than 577 and 345.

1. 577 is the left neighbour.
2. 345 is the right neighbour.
3. 626 is greater than both.

Final Answer: 626 is a supercell

13. Can the largest number in a supercell table always be a supercell?

Yes, the largest number in a table is always a supercell.

1. No neighbouring number can be greater than it.
2. It will be greater than all adjacent cells.
3. This works in a row or grid.

Final Answer: Yes

14. Can the smallest number in a table be a supercell?

No, the smallest number cannot be a supercell.

1. Every adjacent number will be greater than it.
2. A supercell must be greater than its neighbours.
3. The smallest number cannot satisfy this rule.

Final Answer: No

15. In a row of 9 cells, what is the maximum number of supercells possible?

The maximum number of supercells in 9 cells is 5.

1. Supercells cannot usually sit next to each other in a row.
2. Place larger numbers alternately.
3. The pattern gives positions 1, 3, 5, 7 and 9.

Calculation:
(9 + 1) ÷ 2 = 5

Final Answer: 5 supercells

16. Can a supercell table have no supercell without repeating numbers?

No, it cannot have no supercell if numbers are not repeated.

1. One number must be the largest.
2. The largest number is greater than its neighbours.
3. Therefore, it becomes a supercell.

Final Answer: No

Number Line Class 6 Questions from Number Play

Number line questions check place value, interval reading and estimation together. Students must notice the gap between marks before placing each number.

17. Where will 2180 be placed between 1000 and 3000?

2180 will be placed just after 2000 on the number line.

1. 2180 is greater than 2000.
2. It is less than 3000.
3. It is closer to 2000 than 3000.

Final Answer: Just after 2000

18. Which is smaller: 9590 or 9950?

9590 is smaller than 9950.

1. Both numbers are between 9000 and 10000.
2. Compare the hundreds digit after 9.
3. 5 is less than 9.

Final Answer: 9590

19. Which number is closer to 10000: 9590 or 9950?

9950 is closer to 10000.

1. 10000 − 9950 = 50.
2. 10000 − 9590 = 410.
3. 50 is less than 410.

Final Answer: 9950

20. Arrange 1050, 1500, 2180 and 2754 in increasing order.

The increasing order is 1050, 1500, 2180, 2754.

1. Compare the thousands and hundreds places.
2. 1050 is the smallest.
3. 2754 is the largest in this group.

Final Answer: 1050, 1500, 2180, 2754

21. How do you identify the smallest number on a number line?

The smallest number lies farthest to the left on a number line.

1. Numbers increase from left to right.
2. The leftmost marked value is the smallest.
3. The rightmost marked value is the largest.

Final Answer: The leftmost number is the smallest.

Digit Sum Class 6 Questions with Answers

Digit sum questions are common because they look easy but test place-value thinking. In digit sum class 6, students must add digits, not the place values.

22. What is the digit sum of 68?

The digit sum of 68 is 14.

1. Add the digits 6 and 8.
2. 6 + 8 = 14.
3. Therefore, 68 has digit sum 14.

Final Answer: 14

23. Write three numbers whose digit sum is 14.

Three numbers with digit sum 14 are 59, 68 and 176.

1. 5 + 9 = 14.
2. 6 + 8 = 14.
3. 1 + 7 + 6 = 14.

Final Answer: 59, 68, 176

24. What is the smallest number whose digit sum is 14?

The smallest number whose digit sum is 14 is 59.

1. A one-digit number cannot have digit sum 14.
2. The smallest two-digit number needs the smallest tens digit.
3. 5 + 9 = 14.

Final Answer: 59

25. What is the largest 5-digit number whose digit sum is 14?

The largest 5-digit number whose digit sum is 14 is 95000.

1. To make the number largest, maximise the leftmost digit.
2. Put 9 in the ten-thousands place.
3. Put 5 in the thousands place.

Calculation:
9 + 5 + 0 + 0 + 0 = 14

Final Answer: 95000

26. What pattern appears in digit sums of 123, 234, 345, 456?

The digit sums form multiples of 3.

1. 123 → 1 + 2 + 3 = 6.
2. 234 → 2 + 3 + 4 = 9.
3. 345 → 3 + 4 + 5 = 12.

Final Answer: Digit sums increase by 3.

27. How many times does the digit 7 occur from 1 to 100?

The digit 7 occurs 20 times from 1 to 100.

1. It appears 10 times in the ones place.
2. It appears 10 times in the tens place.
3. 77 contributes two occurrences.

Final Answer: 20 times

28. How many times does the digit 7 occur from 1 to 1000?

The digit 7 occurs 300 times from 1 to 1000.

1. It appears 100 times in the ones place.
2. It appears 100 times in the tens place.
3. It appears 100 times in the hundreds place.

Final Answer: 300 times

Palindromic Numbers Class 6 Questions

Palindromic number questions train students to read digits from both directions. The chapter uses examples such as 66, 848, 575, 797 and 1111.

29. What is a palindromic number?

A palindromic number reads the same from left to right and right to left.

1. 121 reads the same both ways.
2. 575 also reads the same both ways.
3. Such numbers are called palindromes.

Final Answer: A palindrome has the same forward and reverse reading.

30. Is 848 a palindromic number?

Yes, 848 is a palindromic number.

1. From left to right, it reads 848.
2. From right to left, it also reads 848.
3. The first and last digits match.

Final Answer: Yes

31. Write all 3-digit palindromes using 1, 2 and 3.

The 3-digit palindromes are 111, 121, 131, 212, 222, 232, 313, 323 and 333.

1. The first and last digits must match.
2. The middle digit can be 1, 2 or 3.
3. This gives 9 palindromes.

Final Answer: 111, 121, 131, 212, 222, 232, 313, 323, 333

32. What is the smallest 5-digit palindrome?

The smallest 5-digit palindrome is 10001.

1. A 5-digit number must start with at least 1.
2. The last digit must match the first digit.
3. The middle digits can be 0.

Final Answer: 10001

33. What is the largest 5-digit palindrome?

The largest 5-digit palindrome is 99999.

1. The largest digit is 9.
2. All five places can contain 9.
3. The number reads the same both ways.

Final Answer: 99999

34. What is the sum of the smallest and largest 5-digit palindrome?

The sum is 110000.

1. Smallest 5-digit palindrome = 10001.
2. Largest 5-digit palindrome = 99999.
3. Add both numbers.

Calculation:
10001 + 99999 = 110000

Final Answer: 110000

35. What is the difference between the largest and smallest 5-digit palindrome?

The difference is 89998.

1. Largest 5-digit palindrome = 99999.
2. Smallest 5-digit palindrome = 10001.
3. Subtract the smaller from the larger.

Calculation:
99999 − 10001 = 89998

Final Answer: 89998

Reverse and Add Palindrome Class 6 Questions

The reverse-and-add activity builds patience with repeated steps. Students must keep reversing and adding until a palindrome appears.

36. What is the reverse-and-add method?

The reverse-and-add method adds a number to its reverse until a palindrome appears.

1. Start with a 2-digit number.
2. Reverse its digits.
3. Add both numbers.
4. Repeat if the result is not a palindrome.

Final Answer: It is a repeated reverse-and-add process.

37. Use reverse-and-add for 12.

The number 12 gives palindrome 33 in one step.

1. Reverse of 12 is 21.
2. Add 12 and 21.
3. The result is 33.

Calculation:
12 + 21 = 33

Final Answer: 33

38. Use reverse-and-add for 47.

The number 47 gives palindrome 121 in one step.

1. Reverse of 47 is 74.
2. Add 47 and 74.
3. The result is 121.

Calculation:
47 + 74 = 121

Final Answer: 121

39. Solve the 5-digit palindrome puzzle: odd number, t is double u, h is double t.

The number is 12421.

1. A 5-digit palindrome has form t t h t u in the puzzle layout.
2. The units digit is 1.
3. Tens digit is 2 and hundreds digit is 4.

Final Answer: 12421

Kaprekar Constant Class 6 Important Questions

Kaprekar questions often test careful digit arrangement. In Kaprekar constant class 6, one subtraction error can change the full answer.

40. What is Kaprekar’s constant for 4-digit numbers?

Kaprekar’s constant for 4-digit numbers is 6174.

1. Choose a 4-digit number with at least two different digits.
2. Arrange digits to form the largest and smallest numbers.
3. Subtract and repeat the process.

Final Answer: 6174

41. What condition is needed before applying the 4-digit Kaprekar process?

The 4-digit number must have at least two different digits.

1. If all digits are same, subtraction gives 0.
2. Different digits create a non-zero difference.
3. The process then moves towards 6174.

Final Answer: At least two digits must be different.

42. Apply Kaprekar steps to 6382 for one round.

The first round gives 6264.

1. Largest number from digits = 8632.
2. Smallest number from digits = 2368.
3. Subtract the smaller from the larger.

Calculation:
8632 − 2368 = 6264

Final Answer: 6264

43. Continue the Kaprekar process from 6264.

The next result is 4176.

1. Largest number from 6264 is 6642.
2. Smallest number from 6264 is 2466.
3. Subtract 2466 from 6642.

Calculation:
6642 − 2466 = 4176

Final Answer: 4176

44. Continue the Kaprekar process from 4176.

The next result is 6174.

1. Largest number from 4176 is 7641.
2. Smallest number from 4176 is 1467.
3. Subtract 1467 from 7641.

Calculation:
7641 − 1467 = 6174

Final Answer: 6174

45. How many rounds does 5683 take to reach the Kaprekar constant?

5683 takes 8 rounds to reach 6174.

1. Apply largest-minus-smallest digit arrangement each round.
2. Continue until 6174 appears.
3. The sequence reaches 6174 in the eighth round.

Final Answer: 8 rounds

46. What number repeats for the 3-digit Kaprekar process?

495 starts repeating in the 3-digit Kaprekar process.

1. Arrange digits in descending and ascending order.
2. Subtract the smaller number.
3. Repeat until the same number returns.

Final Answer: 495

Clock and Calendar Number Play Class 6 Questions

Clock and calendar questions turn patterns into real-life number reading. These are useful for school exams because students must combine time, dates and palindromes.

47. Is 10:01 a palindromic time?

Yes, 10:01 is a palindromic time.

1. The digits read 1001.
2. 1001 reads the same both ways.
3. Therefore, 10:01 is palindromic.

Final Answer: Yes

48. How many minutes after 10:01 will the next palindromic time occur?

The next palindromic time is 11:11, which comes after 70 minutes.

1. From 10:01 to 11:01 is 60 minutes.
2. From 11:01 to 11:11 is 10 minutes.
3. Total time = 70 minutes.

Final Answer: 70 minutes

49. What is the palindromic time after 11:11?

The next palindromic time after 11:11 is 12:21.

1. 12:21 gives the digit pattern 1221.
2. 1221 reads the same both ways.
3. It comes after 11:11.

Final Answer: 12:21

50. Give two examples of patterned dates like 20/12/2012.

Two examples are 20/04/2004 and 20/06/2006.

1. The digits repeat in a visible pattern.
2. The date format uses day, month and year.
3. Such dates depend on valid calendar dates.

Final Answer: 20/04/2004 and 20/06/2006

Mental Maths Class 6 and Number Patterns Class 6 Questions

Mental maths in this chapter focuses on making target numbers from given numbers. Students should group repeated values instead of adding one by one.

51. Can 1000 be made using 400, 1500, 13000 and 25000 only by addition?

No, 1000 cannot be made using these numbers only by addition.

1. 400 is the only number smaller than 1000.
2. 1000 is not a multiple of 400.
3. All other numbers are greater than 1000.

Final Answer: No

52. Make 14000 using 1500 and 400.

14000 can be made as 1500 × 8 + 400 × 5.

1. 1500 × 8 = 12000.
2. 400 × 5 = 2000.
3. 12000 + 2000 = 14000.

Final Answer: 14000

53. Is 4-digit + 4-digit = 6-digit possible?

No, 4-digit + 4-digit cannot give a 6-digit sum.

1. Greatest 4-digit number = 9999.
2. 9999 + 9999 = 19998.
3. 19998 is a 5-digit number.

Final Answer: Never possible

54. Is 5-digit + 5-digit = 5-digit always true?

No, it is only sometimes true.

1. 20000 + 30000 = 50000, which is 5-digit.
2. 80000 + 90000 = 170000, which is 6-digit.
3. Therefore, it depends on the numbers.

Final Answer: Sometimes true

55. Is 5-digit − 2-digit = 3-digit ever possible?

No, 5-digit minus 2-digit cannot give a 3-digit number.

1. Smallest 5-digit number = 10000.
2. Greatest 2-digit number = 99.
3. 10000 − 99 = 9901.

Final Answer: Never true

Collatz Conjecture Class 6 Questions

The Collatz rule looks like a classroom pattern, but it connects to an unsolved problem in mathematics. The NCERT chapter explains that mathematicians still do not know whether every whole-number starting point reaches 1.

56. What is the Collatz rule?

The Collatz rule says: halve an even number, and multiply an odd number by 3 and add 1.

1. If the number is even, divide by 2.
2. If the number is odd, calculate 3n + 1.
3. Repeat the rule.

Final Answer: Even: n ÷ 2, odd: 3n + 1.

57. Write the Collatz sequence starting from 12.

The Collatz sequence from 12 reaches 1.

1. 12 is even, so halve it.
2. Continue the rule for each new number.
3. Stop when the sequence reaches 1.

Sequence:
12, 6, 3, 10, 5, 16, 8, 4, 2, 1

Final Answer: 12 reaches 1

58. Check if the Collatz conjecture holds for 100.

The Collatz sequence for 100 reaches 1.

1. Start with 100.
2. Apply the even and odd rules.
3. The sequence ends at 1.

Sequence:
100, 50, 25, 76, 38, 19, 58, 29, 88, 44, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1

Final Answer: Yes

59. Why does the Collatz conjecture work for powers of 2?

It works for powers of 2 because repeated halving eventually gives 1.

1. A power of 2 has only factors of 2.
2. Each Collatz step divides it by 2.
3. The sequence becomes 2, then 1.

Final Answer: Powers of 2 reach 1 by repeated halving.

Estimation Class 6 Maths Questions

Estimation questions check whether an answer is reasonable. Students should state assumptions clearly because CBSE-style estimation answers may have more than one valid method.

60. Why do we use estimation?

We use estimation when an exact count is not needed or not available.

1. Estimation gives a close idea.
2. It helps plan time, cost and quantity.
3. It depends on reasonable assumptions.

Final Answer: Estimation gives a useful approximate value.

61. Estimate the number of students in a school with five classes and three sections per class.

The school may have about 500 students if each section has about 30 to 35 students.

1. One class has about 3 × 32 = 96 students.
2. Five classes have about 5 × 100 students.
3. So, the estimate is about 500.

Final Answer: About 500 students

62. Is ₹100 enough for milk and three fruits for fruit custard for five people?

₹100 may be too low for a full serving with three fruits and milk.

1. Milk itself may take a large part of the cost.
2. Three fruits add more cost.
3. The estimate depends on quantity and fruit choice.

Final Answer: It may not be enough for a proper serving

63. Estimate the number of school hours for a Class 6 student till now.

A Class 6 student may have spent around 9000 to 10000 school hours.

1. Assume 6 hours per day.
2. Assume 200 school days per year.
3. For about 8 years, 6 × 200 × 8 = 9600 hours.

Final Answer: About 9600 hours

Winning Strategy Number Game Class 6 Questions

Winning strategy questions reward backwards thinking. Students should first identify the numbers that force a win, then plan every move around them.

64. In Game 21, which player can always win?

The first player can always win if they use the correct strategy.

1. The player should first say 1.
2. Then they should reach 5, 9, 13, 17 and 21.
3. These numbers differ by 4.

Final Answer: The first player

65. What is the winning pattern in Game 21?

The winning pattern is 1, 5, 9, 13, 17, 21.

1. Each pair of turns can total 4.
2. If the opponent adds 1, add 3.
3. If the opponent adds 2, add 2.

Final Answer: 1, 5, 9, 13, 17, 21

66. In the game where players add 1 to 3 and must reach 22, what is the winning strategy?

The winning strategy is to reach 2 first, then 6, 10, 14, 18 and 22.

1. The target is 22.
2. Moves are from 1 to 3.
3. Safe numbers differ by 4.

Final Answer: 2, 6, 10, 14, 18, 22

67. What does a winning strategy teach in number games class 6?

A winning strategy teaches students to work backwards from the target number.

1. The target decides safe numbers.
2. The allowed moves decide the gap.
3. The player controls the final move.

Final Answer: Winning strategies use backwards reasoning.

Class 6 Maths Chapter 3 Extra Questions for Practice

These class 6 maths chapter 3 extra questions combine quick calculations with pattern logic. They help students revise Number Play before class tests.

68. How many 2-digit numbers are there?

There are 90 two-digit numbers.

1. The smallest 2-digit number is 10.
2. The largest 2-digit number is 99.
3. Count = 99 − 10 + 1 = 90.

Final Answer: 90

69. How many 3-digit numbers are there?

There are 900 three-digit numbers.

1. The smallest 3-digit number is 100.
2. The largest 3-digit number is 999.
3. Count = 999 − 100 + 1 = 900.

Final Answer: 900

70. Write one 5-digit number and two 3-digit numbers whose sum is 18670.

One answer is 18000, 300 and 370.

1. 18000 is a 5-digit number.
2. 300 and 370 are 3-digit numbers.
3. Their sum is 18670.

Calculation:
18000 + 300 + 370 = 18670

Final Answer: 18000, 300, 370

71. Find the largest 5-digit number between 35000 and 75000 with all odd digits.

The largest number is 73999.

1. The number must be less than 75000.
2. The largest possible ten-thousands digit is 7.
3. The next digit must be 3, then use 9s.

Final Answer: 73999

72. Find the smallest 5-digit number between 35000 and 75000 with all odd digits.

The smallest number is 35111.

1. The number must be at least 35000.
2. Use 3 in the ten-thousands place.
3. Use 5 next, then the smallest odd digits.

Final Answer: 35111

Important Questions Class 6 Maths: