QUESTION BANK Class 6 Maths - Chapter 3: Number Play
Multiple Choice Questions (1 Mark Each)
1. In the 'taller neighbours' game, a child says '2'. What does this mean?
a) Both neighbours are shorter.
b) Both neighbours are taller.
c) One neighbour is taller and one is shorter.
d) The child is the tallest.
(Competency: Problem Solving & Reasoning)
2. A number in a grid is colored as a 'supercell' if:
a) It is an even number.
b) It is larger than all its adjacent cells.
c) It is a palindrome.
d) Its digit sum is 10.
(Competency: Analytical Thinking)
3. The Kaprekar constant for 4-digit numbers is:
a) 6174
b) 495
c) 1089
d) 9999
(Competency: Knowledge & Recall)
4. Which of these is a palindromic number?
a) 1234
b) 2002
c) 2012
d) 1001
(Competency: Pattern Recognition)
5. According to the Collatz Conjecture, if you start with an even number, what is the next step?
a) Multiply by 3 and add 1.
b) Find its half.
c) Reverse its digits.
d) Subtract 1.
(Competency: Understanding Concepts)
6. The smallest number whose digit sum is 14 is:
a) 59
b) 77
c) 149
d) 68
(Competency: Logical Reasoning)
7. In the 'Game of 21', if you want to force a win, you must aim to say the number:
a) 20
b) 17
c) 13
d) 1
(Competency: Strategic Thinking)
8. Estimate the number of breaths a person takes in one hour.
a) About 600
b) About 1000
c) About 900
d) About 1500
(Competency: Estimation & Application)
9. The digit sum of the number 5683 is:
a) 21
b) 22
c) 20
d) 19
(Competency: Numerical Calculation)
10. Which of these sequences will eventually reach 1 according to the Collatz Conjecture?
a) 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1
b) 4, 2, 1
c) 6, 3, 10, 5, 16, 8, 4, 2, 1
d) All of the above
(Competency: Critical Thinking)
11. A number on a clock that reads the same forwards and backwards is called a:
a) Kaprekar number
b) Supercell
c) Palindromic time
d) Magic number
(Competency: Knowledge & Recall)
12. To get the maximum number of supercells in a grid, you should place the largest numbers:
a) In the corners
b) In the center
c) Next to each other
d) In cells with the fewest neighbors
(Competency: Analytical Thinking & Strategy)
13. The difference between the largest and smallest 4-digit numbers formed using 4, 7, 3, 2 is:
a) 5085
b) 5086
c) 5084
d) 5087
(Competency: Numerical Calculation)
14. How many 2-digit numbers are there?
a) 99
b) 89
c) 90
d) 100
(Competency: Knowledge & Recall)
15. In the mental math section, which number from the middle column is used multiple times to make 3,400?
a) 25,000
b) 400
c) 1,500
d) 13,000
(Competency: Mental Calculation & Application)
16. The largest 5-digit number with a digit sum of 14 is:
a) 95000
b) 94100
c) 93200
d) 90050
(Competency: Logical Reasoning & Problem Solving)
17. A calendar can be reused after how many years?
a) 5 years
b) 6 years
c) 11 years
d) It depends on the leap year cycle.
(Competency: Real-life Application & Reasoning)
18. The sum of the smallest and largest 5-digit palindromes is:
a) 109989
b) 100000
c) 199998
d) 109998
(Competency: Numerical Calculation & Analysis)
19. In the 'Game of 99', the winning strategy involves controlling multiples of:
a) 9
b) 10
c) 11
d) 12
(Competency: Strategic Thinking)
20. The number of times the digit '7' appears from 1 to 100 is:
a) 10
b) 11
c) 19
d) 20
(Competency: Systematic Counting & Reasoning)
Assertion and Reasoning Questions (1 Mark Each)
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is NOT the correct explanation of A.
c) A is true but R is false.
d) A is false but R is true.
1. Assertion (A): The number 6174 is known as the Kaprekar constant.
Reason (R): For any 4-digit number with at least two different digits, the process of arranging digits in descending and ascending order and subtracting will always eventually reach 6174.
(Competency: Conceptual Understanding & Reasoning)
2. Assertion (A): The sequence 0, 1, 2, 1, 0 is possible for five children of different heights standing in a line.
Reason (R): The child saying '2' must have two taller neighbors, which is only possible if they are the shortest and in the middle.
(Competency: Logical Reasoning & Problem Solving)
3. Assertion (A): The cell with the smallest number in a grid can never be a supercell.
Reason (R): A supercell must be larger than all its adjacent cells.
(Competency: Analytical Thinking)
4. Assertion (A): The Collatz Conjecture has been proven true for all numbers.
Reason (R): Every sequence starting with a whole number will eventually reach the cycle 4, 2, 1.
(Competency: Knowledge & Critical Thinking)
5. Assertion (A): The sum of a 5-digit number and a 3-digit number can never be a 6-digit number.
Reason (R): The maximum sum of a 5-digit number (99,999) and a 3-digit number (999) is 100,998, which is a 6-digit number.
(Competency: Numerical Analysis & Reasoning)
6. Assertion (A): The number 100 is a palindrome.
Reason (R): A palindrome reads the same forwards and backwards.
(Competency: Conceptual Understanding)
7. Assertion (A): In the 'Game of 21', the second player can always win with perfect strategy.
Reason (R): The first player can always say a number that is one more than a multiple of 4.
(Competency: Strategic Thinking)
8. Assertion (A): Estimation is an important mathematical skill.
Reason (R): It always gives us the exact answer to a problem.
(Competency: Understanding the Purpose of Estimation)
9. Assertion (A): The digit sum of 999 is 27.
Reason (R): The digit sum is the sum of all digits of a number.
(Competency: Numerical Calculation)
10. Assertion (A): A calendar from a leap year can be reused after 28 years.
Reason (R): The days of the week repeat every 7 years.
(Competency: Real-life Application & Reasoning)
11. Assertion (A): The date 02/02/2020 is a palindromic date.
Reason (R): It reads the same forwards and backwards when written in DD/MM/YYYY format.
(Competency: Pattern Recognition & Real-life Connection)
12. Assertion (A): The number 1500 can be made using the middle numbers 25,000, 400, 13,000, and 1,500 from the mental math section.
Reason (R): 1500 is already present in the list, so it can be used directly.
(Competency: Mental Math & Logical Reasoning)
13. Assertion (A): The digit sum of any number that is a multiple of 9 is also a multiple of 9.
Reason (R): The divisibility rule for 9 is based on the sum of its digits.
(Competency: Property of Numbers & Reasoning)
14. Assertion (A): In a 2x2 grid, it is impossible to have more than 2 supercells.
Reason (R): Every cell in a 2x2 grid has two neighbors.
(Competency: Spatial Analysis & Logical Deduction)
15. Assertion (A): The reverse-and-add process for the number 196 has been proven to never form a palindrome.
Reason (R): Mathematicians have tested this for millions of steps without finding a palindrome.
(Competency: Knowledge of Mathematical Facts)
16. Assertion (A): The difference between a 5-digit number and a 4-digit number is always a 5-digit number.
Reason (R): The smallest 5-digit number is 10,000 and the largest 4-digit number is 9999; their difference is 1.
(Competency: Numerical Reasoning & Counter-Example)
17. Assertion (A): The number of blinks in a day would be in the thousands.
Reason (R): A person blinks about 15-20 times per minute.
(Competency: Estimation & Justification)
18. Assertion (A): The pattern of numbers 32, 32, 32... arranged in a grid can be summed quickly using multiplication.
Reason (R): Multiplication is repeated addition.
(Competency: Pattern Recognition & Efficient Calculation)
19. Assertion (A): The winning strategy in number games involves forcing your opponent into a losing position.
Reason (R): A losing position is one from which every move leads to a winning position for the opponent.
(Competency: Strategic Thinking & Game Theory)
20. Assertion (A): The number 50,000 is the best estimate for the number of words in a grade 6 textbook.
Reason (R): An estimate is a rough calculation of the value of something.
(Competency: Critical Evaluation of Estimates)
True or False (1 Mark Each)
1. The number 495 is the Kaprekar constant for 3-digit numbers. (True)
(Competency: Knowledge & Recall)
2. A child saying '0' in the taller neighbours game must be the tallest in the line. (False)
(Competency: Logical Reasoning)
3. The largest 4-digit number is 9999 and its digit sum is 36. (True)
(Competency: Numerical Calculation)
4. The difference between the largest and smallest numbers made from digits 1, 0, 6, 3 is 5301. (True)
(Competency: Calculation & Verification)
5. The number of 3-digit numbers is greater than the number of 2-digit numbers. (True)
(Competency: Conceptual Understanding)
6. The Collatz operation for an odd number is (3 x n + 1). (True)
(Competency: Knowledge of Procedure)
7. The number 12:21 on a clock is a palindromic time. (True)
(Competency: Pattern Recognition)
8. It is impossible to have a grid of numbers with no supercells. (False)
(Competency: Analytical Thinking)
9. The sum of two 5-digit numbers can be a 4-digit number. (False)
(Competency: Numerical Reasoning)
10. Estimation gives a precise and exact value. (False)
(Competency: Conceptual Understanding)
Short Answer Type Questions-I (2 Marks Each)
1. Five children of different heights are standing in a line. Is it possible for four of them to say '1' and one to say '0'? Explain your reasoning.
(Competency: Logical Reasoning & Justification)
2. Find the digit sum of the number 68,529.
(Competency: Numerical Calculation)
3. Identify the supercells in the following row of numbers: 45, 32, 58, 41, 60.
(Competency: Analytical Thinking)
4. Apply the Kaprekar routine once for the number 3524.
(Competency: Applying a Procedure)
5. Estimate the number of words on a page of your textbook. Explain your method.
(Competency: Estimation & Communication)
6. Write down the next two palindromic times after 10:01.
(Competency: Pattern Recognition & Application)
7. Is the number 96,301 greater than 60,319? Compare the numbers by looking at the place value of digits.
(Competency: Number Comparison)
8. Perform one reverse-and-add step for the number 58. Do you get a palindrome?
(Competency: Calculation & Verification)
9. From the numbers 40 to 70, list all numbers that have a digit sum of 10.
(Competency: Systematic Listing & Calculation)
10. Using the digits 1, 0, 6, 3, 9, form the smallest 5-digit even number.
(Competency: Number Formation & Properties)
11. In a 'Game of 21' session, the current number is 18. It is your turn. What number should you say to guarantee a win on your next turn?
(Competency: Strategic Thinking)
12. How many supercells are there in a single row of 5 numbers if all numbers are different and arranged in descending order?
(Competency: Analytical Thinking)
13. Give a rough estimate for the distance between your classroom and the principal's office.
(Competency: Estimation & Application)
14. What is the main difference between a number line and a number pattern?
(Competency: Conceptual Understanding)
15. If you add the digits of a number and then add the digits of the sum, repeating until you get a single digit, that digit is called the digital root. Find the digital root of 784.
(Competency: Numerical Calculation & New Concept)
Short Answer Type Questions-II (3 Marks Each)
1. Try the Kaprekar process for the 3-digit number 105. How many steps does it take to reach the constant? Show your steps.
(Competency: Systematic Problem Solving)
2. Using the digits 4, 8, 1, 5 without repetition:
a) Form the largest 4-digit number.
b) Form the smallest 4-digit number.
c) Find their difference.
(Competency: Numerical Calculation & Operation)
3. A grid has 3 rows and 3 columns. What is the maximum number of supercells it can have? Draw a possible arrangement of numbers 1 through 9 to achieve this.
(Competency: Strategic Planning & Analytical Thinking)
4. Follow the Collatz sequence until it reaches 1, starting from the number 15.
(Competency: Following a Procedure Accurately)
5. In the mental math section, show two different ways to make the number 45,000 using the numbers provided (40,000, 7,000, 300, 1,500, 12,000, 800) with both addition and subtraction.
(Competency: Flexible Mathematical Thinking)
6. Find all the 3-digit palindromic numbers that can be formed using only the digits 1, 2, and 3.
(Competency: Systematic Listing & Pattern Recognition)
7. A group of 7 children of different heights is standing in a line. What is the maximum number of children who can say '2'? Describe the arrangement that makes this possible.
(Competency: Logical Reasoning & Optimization)
8. The sum of two 5-digit numbers is 100,203. If one of the numbers is 47,819, what is the other number?
(Competency: Inverse Calculation)
9. Estimate the total number of hours you spend in school in one academic year. Break down your estimation process.
(Competency: Multi-step Estimation & Justification)
10. Start with the number 87 and apply the reverse-and-add process. How many steps does it take to reach a palindrome? Show your work.
(Competency: Persistence in Calculation & Verification)
Long Answer Type Questions (5 Marks Each)
1. Kaprekar's Constant Investigation
Choose a 4-digit number with at least two different digits (e.g., 3524).
a) Apply the Kaprekar process step-by-step. Show your work for each iteration (finding A, B, and C).
b) How many steps did it take to reach the constant 6174?
c) What is special about the number 6174 in this process?
d) Explain why this process will not work for a number with all identical digits, like 1111.
(Competency: Systematic Problem-Solving, Numerical Computation, and Conceptual Understanding)
2. Five children of different heights are playing the 'taller neighbours' game.
a) Is it possible for them to form a line where the sequence of numbers said is 1, 2, 1, 0, 2? Justify your answer.
b) If possible, describe the arrangement of their heights (e.g., shortest, tallest) in the line.
c) Draw a simple diagram to represent this arrangement.
d) What is the maximum number of children who can say '2' in a line of five? What arrangement achieves this?
(Competency: Logical Reasoning, Spatial Visualization, and Optimization)
3. a) Define a 'supercell' in your own words.
b) In the 3x3 grid below, the numbers 1 through 9 are to be placed without repetition. Identify the cell that has the most neighbours (adjacent cells).
c) Challenge: Arrange the numbers 1 to 9 in the grid to achieve the maximum possible number of supercells. Draw your filled grid.
d) How many supercells does your arrangement have? Justify why you cannot have more than that.
(Competency: Strategic Planning, Analytical Thinking, and Justification)
4. Design a 3x3 grid using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once.
a) Arrange them so that there are only two supercells.
b) Now, rearrange the numbers to achieve the maximum number of supercells possible.
c) What is the maximum number of supercells possible in a 3x3 grid? Justify your answer.
(Competency: Strategic Problem Solving & Optimization)
4. Project: Palindromic Dates in the 21st Century
a) Find a palindromic date in the format DD/MM/YYYY (e.g., 11/02/2011).
b) Find the next palindromic date after the one you found.
c) What is the gap (in years/days) between two consecutive palindromic dates in this format?
d) Estimate how many such palindromic dates there will be in the 21st century (2001-2100).
(Competency: Research, Pattern Recognition, and Estimation)
4. The Palindrome Puzzle
I am a 5-digit palindrome. I am an odd number. My tens (t) digit is double of my units (u) digit. My hundreds (h) digit is double of my tens (t) digit.
a) Let the units digit be *u*. Express the tens and hundreds digits in terms of *u*.
b) Since the number is a palindrome, which other digits are determined by *u*, *t*, and *h*?
c) List the possible values for *u* (remember: the number is odd and digits must be between 0-9).
d) Find my exact identity (the number). Show your reasoning.
(Competency: Decoding Word Problems, Algebraic Thinking, and Deductive Reasoning)
5. Comprehensive Analysis: Digit Sums
a) Find the digit sum of the current year.
b) Find the digit sum of your year of birth.
c) Find the digit sum of the sum of the two numbers from (a) and (b).
d) Find the digital root (see Short Answer Q15) of the sum from (c).
e) Research online or think: What is special about the digital root? (Hint: Think about the number 9).
(Competency: Multi-step Calculation & Research)
5. The Collatz Conjecture Sequence
a) State the rule of the Collatz Conjecture.
b) Start with the number 21 and generate the entire Collatz sequence until you reach 1. Show all the steps clearly.
c) How many steps did it take to reach 1? (Count the number of terms after the starting number).
d) This conjecture is still unsolved. What does it mean for a mathematical problem to be "unsolved"?
(Competency: Following Algorithms, Persistence in Calculation, and Understanding Mathematical Inquiry)
6. Create Your Own Game:
Invent a new number game with specific rules (e.g., start at 0, players add a number between 1 and 5, first to reach 50 wins).
a) Write the rules clearly.
b) Play the game with a friend and try to find the winning strategy.
c) Describe the winning strategy for your game. Which player can always win?
(Competency: Creativity, Application, and Strategic Analysis)
6. Mental Math Mastery
Using the numbers in the boxes: 40,000 ; 7,000 ; 300 ; 1,500 ; 12,000 ; 800
a) Find two different ways to make the number 45,000 using both addition and subtraction. Show your expressions.
b) Explain why it is not possible to make the number 1,000 using only these numbers with addition and subtraction.
c) Can you make 16,000? If yes, show how. If not, explain why.
(Competency: Flexible Computation, Operational Fluency, and Logical Justification)
7. Calendar and Number Patterns
a) Find a past date that is a palindrome in the DD/MM/YYYY format (e.g., 11/02/2011). Write the date.
b) Find the next palindromic date after the one you found.
c) Meghana's birthday is on a palindromic date. If she was born on 11/02/2011, how old was she on the next palindromic date?
d) Why can't we reuse the same calendar every year? Explain with an example.
(Competency: Pattern Recognition, Real-World Application, and Conceptual Knowledge)
8. Digit Sums and Number Theory
a) What is the digit sum of the number 68,529?
b) Find the smallest number whose digit sum is 14.
c) Find the largest 5-digit number whose digit sum is 14.
d) What is the digit sum of the largest 5-digit number possible? Compare it to your answer for (c).
(Competency: Numerical Computation, Logical Reasoning, and Property Analysis)
9. Winning Strategies in Number Games
You are playing the "Game of 21" where players alternately add 1, 2, or 3 to the running total.
a) The current total is 18. It is your turn. What number(s) can you say? What number should you say to guarantee you win on your next turn? Explain.
b) Describe the winning strategy for the first player in this game. What key numbers should they aim to land on?
c) If the game was changed to "first to reach 22" and you can add 1, 2, or 3, what is the new winning strategy?
(Competency: Strategic Thinking, Pattern Recognition, and Adaptive Reasoning)
10. Estimation and Real-World Magnitudes
a) Estimate the number of breaths you take in one hour. Explain the steps in your estimation.
b) Estimate the number of students in your entire school. Describe the method you used (e.g., number of classes × students per class).
c) Roshan estimates making fruit custard for 5 people will cost ₹100. Do you think this is a reasonable estimate? List the items he might need and assign estimated costs to justify your answer.
d) Why is estimation a valuable skill in everyday life?
(Competency: Practical Application, Multi-step Reasoning, and Justification)
Case-Based Study Questions (4 MCQs each)
Case 1: Supercell Challenge
Observe the following grid of numbers:
| 16,200 | 39,344 | 29,765 |
| 23,609 | 62,871 | 45,306 |
| 19,381 | 50,319 | 38,408 |
Currently, there is only one supercell.
1. Which cell is the supercell?
a) 16,200
b) 62,871
c) 50,319
d) 38,408
(Competency: Analytical Evaluation)
2. To create more supercells, you are allowed to:
a) Change the numbers completely
b) Swap two digits within one number
c) Add 1000 to all numbers
d) Reverse the digits of a number
(Competency: Interpreting Instructions)
3. If you swap the ten thousands and thousands digits of 62,871, the new number becomes:
a) 28,671
b) 86,271
c) 62,781
d) 72,861
(Competency: Numerical Manipulation)
4. After the correct swap, how many supercells will the grid have?
a) 1
b) 2
c) 3
d) 4
(Competency: Predicting Outcomes based on Analysis)
Case 2: The Taller Neighbours
Five children of different heights are playing the taller neighbours game. Their heights are 110 cm, 120 cm, 130 cm, 140 cm, and 150 cm. They stand in a line and report their numbers based on the rule. The sequence of numbers they say is 0, 1, 2, 1, 0.
1. Who is the tallest child?
a) The one at the left end
b) The one in the middle
c) The one at the right end
d) Cannot be determined
(Competency: Logical Deduction)
2. What is the height of the child standing in the middle position?
a) 110 cm
b) 130 cm
c) 150 cm
d) 120 cm
(Competency: Data Interpretation & Reasoning)
3. The child who said '2' has a height of:
a) 110 cm
b) 120 cm
c) 130 cm
d) 140 cm
(Competency: Applying Rules to Data)
4. Is the sequence 2, 2, 2, 2, 2 possible for these five children?
a) Yes
b) No
c) Maybe
d) Only if two children are the same height
(Competency: Critical Thinking & Concept Application)
Case 3: Kaprekar's Journey
Rohan is exploring the Kaprekar routine with the number 2134.
1. What is the first step? (Find A and B)
a) A = 4321, B = 1234
b) A = 1234, B = 4321
c) A = 3421, B = 1243
d) A = 4312, B = 2134
(Competency: Applying a Procedure)
2. What is the value of C after the first subtraction?
a) 3087
b) 4087
c) 3086
d) 4086
(Competency: Numerical Calculation)
3. How many steps will it take for 2134 to reach 6174?
a) 1 step
b) 2 steps
c) 3 steps
d) 4 steps
(Competency: Persistence in Calculation)
4. What is the constant reached when performing the Kaprekar routine on 3-digit numbers?
a) 6174
b) 495
c) 1089
d) 999
(Competency: Knowledge & Recall)
Case 4: The Collatz Conjecture
The Collatz sequence for a number n is defined as:
→ If n is even, next number = n/2
→ If n is odd, next number = 3n + 1
The conjecture states that all sequences eventually reach 1.
1. What is the next number after 16?
a) 8
b) 4
c) 2
d) 1
(Competency: Following Rules)
2. What is the next number after 5?
a) 10
b) 16
c) 15
d) 6
(Competency: Following Rules)
3. Starting from 6, how many steps does it take to reach 1? (Count steps after 6)
a) 7 steps
b) 8 steps
c) 9 steps
d) 6 steps
(Competency: Systematic Counting)
4. The Collatz Conjecture is famous because:
a) It is very easy to understand.
b) It has been proven true.
c) It has been proven false.
d) It is unsolved, meaning no one has proven it true or false for all numbers.
(Competency: Knowledge of Mathematical Significance)
Case 5: Estimation in Real Life
Sheetal is in Grade 6. She estimates she has spent about 13,000 hours in school so far. Assume she started school at age 5 and has 180 school days a year, each 6 hours long.
1. How many school hours are there in one year?
a) 180 hours
b) 1080 hours
c) 1000 hours
d) 1800 hours
(Competency: Simple Calculation)
2. Approximately how many years has Sheetal been in school?
a) 4 years
b) 5 years
c) 6 years
d) 7 years
(Competency: Interpretation & Reasoning)
3. Based on the calculation, is Sheetal's estimate of 13,000 hours reasonable?
a) Yes, it is very close.
b) No, it is too low.
c) No, it is too high.
d) Cannot be determined.
(Competency: Critical Evaluation of Estimates)
4. Estimating the number of bricks in a wall is an example of:
a) Precise calculation
b) Approximation
c) Algebraic expression
d) Digital root
(Competency: Conceptual Understanding)
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