Complete Summary, Explanations, and Solutions for Number Play – Ganita Prakash Class VI, Chapter 3 – Digit Patterns, Palindromes, Kaprekar Constant, Questions, Answers
Detailed summary and explanation of Chapter 3 'Number Play' from the Ganita Prakash Mathematics textbook for Class VI, covering number patterns, supercells, digit sums, palindromic numbers, reverse-and-add patterns, Kaprekar constant (6174), number line patterns, Collatz conjecture, estimation techniques, mental math strategies, and game-based learning—along with all NCERT questions, answers, and step-by-step solutions.
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Categories: NCERT, Class VI, Mathematics, Ganita Prakash, Chapter 3, Number Theory, Number Patterns, Summary, Questions, Answers, Mental Math, Estimation, Games
Tags: Number Play, Ganita Prakash, NCERT, Class 6, Mathematics, Number Theory, Supercells, Digit Sums, Palindromes, Palindromic Numbers, Kaprekar Constant, D.R. Kaprekar, Collatz Conjecture, Number Line, Number Patterns, Reverse and Add, Mental Math, Estimation, Computational Thinking, Clock Patterns, Calendar Numbers, Game Strategies, Summary, Explanation, Questions, Answers, Solutions, Chapter 3
Class 6 NCERT Maths Chapter 3: Number Play Complete Notes, Solutions, Questions & Answers 2025
Number Play
NCERT Class 6 Mathematics Chapter 3 | Complete Guide | Number Play 2025
Chapter at a Glance – Number Play
This chapter explores numbers in fun ways: puzzles, patterns, digit sums, palindromes, Kaprekar constant, Collatz conjecture, estimations, and games. It builds computational thinking through play.
Main Topics Covered
Numbers telling stories (heights puzzle)
Supercells in tables
Number line patterns
Digit play: Counts, sums, detectives
Palindromic patterns
Kaprekar magic (6174 constant)
Clock/calendar numbers
Mental math additions/subtractions
Number pattern sums
Collatz conjecture sequences
Simple estimations in life
Games like 21 with strategies
Key Takeaways for Exams
Heights Puzzle
Taller neighbors: 0,1,2 possibilities.
Supercells
Larger than adjacent: Max patterns, no repeats.
Digit Sums
Patterns in consecutive, fixed sums.
Palindromes
Reverse-add to form, puzzles.
Kaprekar
4-digit rearrange subtract to 6174.
Collatz
Even/2, odd*3+1 always to 1?
Estimations
Steps, breaths, distances approx.
Games
21 game: Add 1-3, winning mod 4.
Focus on reasoning, patterns, and quick calculations for exams.
Key Rules & Properties – Number Play
Important rules for digit patterns, puzzles, and sequences.
Puzzle Rules
Guidelines for heights, supercells, etc.
Concept
Rule
Example
Heights
Count taller neighbors: 0/1/2
Sequence 0,1,2,1,0 possible
Supercell
Larger than all adjacent
Max: Alternate high-low
Digit Count
n-digit: 9*10^{n-1}
3-digit: 900
Palindrome
Reads same forward/back
121, 3443
Kaprekar
Largest-smallest subtract, repeat
6174 constant
Collatz
Even/2; odd*3+1
Always to 1 (conjecture)
Properties
Digit Sum: Consecutive 3-digit: Multiples of 3 increasing by 3.
Supercell Max: For m cells, floor((m+1)/2).
Kaprekar 3-digit: Reaches 495.
Game 21: Win by multiples of 4.
Estimation: Approximate without exact count.
Mental Math Tricks
Use addition/subtraction combinations; digit operations constraints.
Concept Cards – Quick Explanations
Heights Puzzle
Numbers as taller neighbors count.
Supercells
Cells larger than all neighbors.
Number Line Patterns
Positioning numbers appropriately.
Digit Sums
Sum digits; patterns in fixed sums.
Digit Detectives
Count digit occurrences 1-1000.
Palindromes
Same forward/back; reverse-add.
Kaprekar Constant
6174 from 4-digit rearrange-subtract.
Clock/Calendar
Patterns in times/dates.
Mental Math
Quick add/subtract combinations.
Collatz Conjecture
Sequences to 1; unsolved.
Estimations
Approx counts/distances.
Games
21: Add 1-3; winning strategy.
Examples + Solutions
Example 1: Heights Sequence for 5 Children
Solution: 0,1,2,1,0 possible if heights descend then ascend.
Example 2: Supercell Table Fill Max
Solution: Alternate high-low numbers for max supercells.
Example 3: Digit Sum 14 Smallest
Solution: 59 (5+9=14).
Example 4: Palindrome Puzzle
Solution: 12421 (t=2 double u=1, h=4 double t=2).
Example 5: Kaprekar for 6382
Solution: Reaches 6174 in 3 steps.
Example 6: Collatz for 12
Solution: 12,6,3,10,5,16,8,4,2,1.
Example 7: Game 21 Strategy
Solution: First player wins by multiples of 4.
Additional Example: Estimation Steps to School
Solution: Approx 1000 steps if 1km distance.
Figure it Out Solutions (All Solved)
Section 3.1: Numbers Can Tell Us Things
1. Ends say '2'?
Ans. No; ends have only one neighbor.
2. All say 0s?
Ans. Yes; same heights.
3. Adjacent same number?
Ans. Yes; possible configurations.
4. 4 say 1, 1 says 0 for 5 different heights?
Ans. Yes; ascending order.
5. 1,1,1,1,1 possible?
Ans. No; tallest can't say 1.
6. 0,1,2,1,0 possible?
Ans. Yes.
7. Max say '2'?
Ans. 2 max.
Section 3.2: Supercells
1. Mark supercells.
Ans. 6828, 9435, 7308, 8000 (example table).
2. Fill for exact colored.
Ans. Sample: 5346, 9636 in positions.
3. Max supercells 100-1000 no repeat.
Ans. Alternate pattern, 5 supercells.
4. How many in given table?
Ans. 5.
5. Max for different cells.
Ans. Pattern: floor((n+1)/2).
6. No supercells no repeat?
Ans. No; largest always supercell.
7. Largest/smallest supercell?
Ans. Largest yes; smallest no.
8. Second largest not supercell.
Ans. Place next to largest.
9. Second largest not, second smallest is.
Ans. Possible with careful placement.
10. Variations.
Ans. Open; e.g., exactly 4 supercells.
Section 3.2 Extended: Table 2 Fill
Complete Table 2.
Ans. Sample with digits 1,0,6,3,9.
Biggest number.
Ans. 96310.
Smallest even.
Ans. 10396.
Smallest >50000.
Ans. 60193.
Section 3.3: Number Line
Place numbers.
Ans. Position on scale.
Identify marked.
Ans. Label remaining.
Section 3.4: Digit Counts
2-5 digit counts.
Ans. 90,900,9000,90000.
Digit Sum 14 examples.
Ans. Smallest 59; largest 95000.
40-70 sums.
Ans. Observe patterns.
Consecutive 3-digit sums.
Ans. Multiples of 3; continues to 789=24.
Digit '7' in 1-100.
Ans. 20.
1-1000.
Ans. 300.
Extra Practice Questions (Exam-Ready) – Chapter 3
30+ Questions • Categorized by Marks • With Detailed Solutions • Difficulty Tags
1-Mark Questions (Very Short Answer)
1. Heights: Max '2's for 5 children?
2
2. Supercells max for 9 cells?
5
3. Digit sum 14 smallest?
59
4. '7' in 1-100?
20
5. Kaprekar constant?
6174
6. Collatz for even?
Divide 2
7. Game 21 win add?
1-3
2-Mark Questions (Short Answer)
8. Heights 1,1,1,1,1 possible why?
No, tallest can't say 1
9. Supercell smallest possible?
No, always smaller than some
10. 5-digit count?
90000
11. Palindrome example 3-digit.
121
12. Kaprekar 3-digit constant?
495
13. Clock palindrome after 10:01?
11:11
14. Mental 45000 = ?
40000 + 5000
3-Mark Questions (Reasoning)
15. Why no supercells impossible?
Largest always supercell
16. Consecutive digit sums pattern?
Multiples of 3 +3 each
17. Reverse-add to palindrome?
Yes for 2-digit eventually
18. Collatz why to 1?
Even halve, odd even-ize
19. Calendar repeat years?
5-6 years depending leaps
20. Game 99 strategy?
Multiples of 11
4–5 Mark Questions (Application)
21. Fill supercell table max 9 cells.
Alternate 999,100 etc
22. Digit '7' 1-1000.
300
23. Kaprekar steps 5683.
8 rounds
24. Estimation school hours grade 6.
~9600 not 13000
25. Sum smallest/largest 5-digit palindrome.
110000
Challenge Questions (6+ Marks)
26. Second smallest supercell possible?
Yes, isolate low
27. Collatz for powers 2 why true?
Halve to 1
28. Calendar repeat with leaps.
5/6 years
29. Mental 5-digit +5-digit =18500 possible?
No, min 20000
30. Own game variation strategy.
Add 1-10 to 100: mod 11
Common Mistakes & How to Avoid
Mistake 1: Heights Ends '2'
Forgetting ends have one neighbor.
Avoid: Count neighbors correctly.
Mistake 2: Supercell No Repeat
Ignoring largest always supercell.
Avoid: Place strategically.
Mistake 3: Digit Sum Patterns
Miscalculating sums.
Avoid: Add carefully, spot multiples.
Mistake 4: Palindrome Reverse-Add
Stopping early.
Avoid: Continue till palindrome.
Mistake 5: Kaprekar Digits Same
Using all same digits.
Avoid: At least two different.
Mistake 6: Collatz Infinite
Thinking loops.
Avoid: Follow rule strictly.
Mistake 7: Estimation Exact
Trying precise count.
Avoid: Use approx methods.
Mistake 8: Game No Strategy
Random plays.
Avoid: Find modulus pattern.
History & Fun Facts
Ancient Origins
Kaprekar discovered constant in 1949, Indian teacher.
Collatz conjecture by Lothar Collatz 1937, unsolved.
Real-Life Applications
Cryptography: Palindromes in codes.
Math Puzzles: Kaprekar in recreational math.
Computing: Collatz tests algorithms.
Daily: Estimations in shopping, travel.
Fun Facts
196 suspected never palindrome in reverse-add.
Kaprekar constant universal for 4-digits.
Collatz called "3n+1 problem", simple but hard.
Palindromic dates like 02/02/2020 rare.
Game 21 variations in different cultures.
Did You Know?
D.R. Kaprekar self-taught, many number discoveries.
