Class 6 Maths · Chapter 3
Short answer:
Class 6 Maths Chapter 3 "Number Play" (Ganita Prakash, NEP-aligned rationalised syllabus) students ko numbers ke saath discovery-based activities karwata hai — Kaprekar constant (6174), palindrome numbers, supercells aur triangular number patterns. Koi heavy formula nahi, sirf logical exploration.
Chapter 3 poore Class 6 Maths Ganita Prakash ki sabse interesting aur discovery-wali unit hai. Yahan koi bhi complex formula ya theorem nahi hai — sab kuch numbers ke saath 'khelne' se seekha jaata hai. NCERT ka naya rationalised syllabus (2026-27 session) is chapter ko early stage pe rakhta hai taaki students ko pattern-recognition ka mazaa aaye, before woh Chapter 5 Prime Time ya The Other Side of Zero jaise deeper concepts tak pahunchein.
Is chapter me hum Kaprekar constant, palindrome numbers, supercells (spreadsheet-style grids), aur successive number sums jaisi activities karte hain. Ye poori foundation aage ke chapters ki understanding ko strong banati hai.
Chapter 3 Summary — 5 Minute Revision
Chapter 3 "Number Play" NCERT Class 6 Maths Ganita Prakash ka ek discovery-driven chapter hai jisme students Kaprekar constant (6174), palindrome numbers, supercells aur number sequence patterns explore karte hain. Ye chapter formula-heavy nahi hai — iska focus pattern-recognition, logical reasoning aur numbers ke saath curiosity-based khelna hai.
Is chapter ki activities aage ke chapters ki neev banti hain, jaise number theory aur number-line based topics — dono is early number-sense practice pe based hain.
Overall, ye chapter is tarah design kiya gaya hai ki students ko formal formula sikhaye bina bhi strong number-sense aur pattern-observation ki practice mil jaaye, jo aage ke sabhi chapters ke liye foundation ka kaam karti hai.
In-Text Questions — Solutions
3.1 In-text: Kya har 4-digit number Kaprekar process me 6174 pe pahunchta hai? 1000 number try karo.
1000 lo. Digits: 1,0,0,0
Descending = 1000, Ascending = 0001
1000 − 1 = 999 → arrange karke: 0999
9990 − 999 = 8991
9981 − 1899 = 8082
8820 − 288 = 8532
8532 − 2358 = 6174
Answer: Haan, kuch zyaada steps lagne ke baad bhi 1000 se shuru karke hum 6174 pe pahunch jaate hain. Sirf woh numbers jinke sab digits same hon (jaise 1111, 2222) ye process kaam nahi karta kyunki descending − ascending = 0 ho jaata hai.
3.2 In-text: 2-digit palindrome numbers ki total ginti batao.
2-digit palindrome woh number hote hain jinke dono digits same hon: 11, 22, 33, 44, 55, 66, 77, 88, 99
Total 2-digit palindrome numbers = 9
Pattern: aisa number hamesha 11 × single-digit ka multiple hota hai (11×1=11, 11×2=22, ...11×9=99).
3.3 In-text: Successive odd numbers ka sum karke pattern dhoondo — 1, 1+3, 1+3+5.
1 = 1 = 1²
1+3 = 4 = 2²
1+3+5 = 9 = 3²
1+3+5+7 = 16 = 4²
Pattern: Pehle n odd numbers ka sum hamesha n² (perfect square) hota hai. Ye interesting connection hai square numbers aur odd numbers ke beech.
Exercise Questions — Solutions (Q1–Q4)
3.1 Q1. Kaprekar Constant process ka use karke 4-digit number 6174 mile ya nahi, number 3524 se shuru karke check karo.
Step 1: 3524 ke digits ko descending aur ascending order me arrange karo.
Descending = 5432, Ascending = 2345
5432 − 2345 = 3087
Step 2: 3087 ke digits (0,3,8,7) ko phir arrange karo.
Descending = 8730, Ascending = 0378
8730 − 378 = 8352
Step 3:
Descending = 8532, Ascending = 2358
8532 − 2358 = 6174
Answer: 3 steps me hume Kaprekar constant 6174 mil jaata hai. Isse aage koi bhi 4-digit number (jisme sab digits same na ho) isi process se ghoome-ghoome kar hamesha 6174 pe hi pahunchta hai.
3.2 Q2. 1 se 100 tak ke numbers me kitne palindrome numbers hain? Unki list banao.
Palindrome number woh hota hai jo aage se padho ya peeche se, same lagta hai — jaise 11, 22, 121.
1 se 9 tak: sab single-digit numbers palindrome hote hain (1,2,3,4,5,6,7,8,9) → 9 numbers.
10 se 99 tak: jinke dono digits same hon — 11, 22, 33, 44, 55, 66, 77, 88, 99 → 9 numbers.
100: palindrome nahi hai (1-0-0 reverse me 0-0-1).
Total palindrome numbers (1–100) = 9 + 9 = 18
List: 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99
3.3 Q3. Kisi bhi 3-digit number ke saath uska reverse number jodne par jo pattern banta hai, use 528 aur uske reverse se verify karo. Kya ye hamesha palindrome deta hai?
528 ka reverse = 825
528 + 825 = 1353 (palindrome nahi)
Agar phir se reverse jode: 1353 + 3531 = 4884 → ye palindrome hai.
Answer: Har number palindrome nahi deta pehle step me, lekin 'reverse-and-add' process ko kai baar repeat karne se zyaadatar numbers eventually palindrome ban jaate hain. Kuch special numbers (jaise 196) ye pattern follow nahi karte aur unhe Lychrel-type numbers kaha jaata hai — ye NCERT ke Number Play chapter ka discovery-based activity hai, koi fixed rule nahi.
3.4 Q4. Successive numbers ka sum lekar patterns dhoondo: 1+2, 1+2+3, 1+2+3+4 ka result kis shape ke numbers banate hain?
1+2 = 3
1+2+3 = 6
1+2+3+4 = 10
1+2+3+4+5 = 15
Ye numbers (1, 3, 6, 10, 15, ...) Triangular Numbers kehlaate hain — inhe dots se triangle shape me arrange kar sakte hain.
Pattern rule: n-tak ka sum = n(n+1)/2
Verify: n=4 → 4×5/2 = 10 ✓ (matches 1+2+3+4)
Important Equations — Ek Nazar Me
| Concept | Rule / Formula | Example |
|---|---|---|
| Kaprekar Constant | 4-digit number ke digits ko descending − ascending order me arrange karke repeat subtract karo | Kisi bhi number se shuru karke 6174 tak pahunchna |
| Palindrome Number | Aage se padho ya peeche se — same rehta hai | 121, 1331, 55 |
| Triangular Numbers | Sum of first n natural numbers = n(n+1)/2 | 1+2+3+4 = 4×5/2 = 10 |
| Supercell (spreadsheet pattern) | Woh cell jiski value uske sabhi neighbouring cells se badi ho | Grid me largest-neighbour check karna |
| Reverse-and-Add pattern | Number + uska reverse = naya number (kai baar palindrome deta hai) | 528 + 825 = 1353; 1353+3531=4884 |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Kaprekar constant nikalte waqt digits ko galat order me arrange karna — hamesha pehle descending phir ascending order banao, phir subtract karo.
- 4-digit number ke saare digits same hone par (jaise 1111) process apply karna — is case me descending − ascending = 0 aata hai, ye edge case hai jise students miss kar dete hain.
- Subtraction ke baad jo number aata hai usme leading zero ko ignore karna — jaise 999 ko 4-digit banate waqt 0999 likhna zaroori hai, warna next step galat ho jaata hai.
- Palindrome check karte waqt sirf number ko dekh kar guess lagana, actual reverse likh kar compare nahi karna — hamesha digit-by-digit reverse likh kar match karo.
- Triangular number pattern me formula n(n+1)/2 lagate waqt n ki value galat lena — jaise 1+2+3+4 ke liye n=4 hoga, n=5 nahi.
- Successive odd numbers ka sum karte waqt beech ka koi odd number skip kar dena — jaise 1+3+7 (5 miss ho gaya), jisse square number pattern match nahi karta.
Board-Style Important Questions
- Kisi bhi 4-digit number (jisme digits same na ho) ko lekar Kaprekar constant process dikhao aur 6174 tak pahuncho.
- 1 se 200 tak ke sabhi 3-digit palindrome numbers ki list banao aur unki total ginti batao.
- Successive natural numbers ka sum (1 se n tak) triangular number pattern banata hai — n=6 tak ka sum nikalo aur formula se verify karo.
- Ek number aur uske reverse ka sum lekar dikhao ki kaunse numbers ek hi step me palindrome ban jaate hain aur kaunse nahi.
- Spreadsheet grid me supercells identify karne ka rule likho aur ek 3x3 grid example se dikhao.
- Pehle 5 odd numbers ka sum lekar dikhao ki ye kis perfect square number ke barabar hai, aur pattern ka general rule likho.
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths Chapter 3 Number Play me kya-kya topics cover hote hain?
Ganita Prakash ke Chapter 3 'Number Play' me supercells, patterns in a spreadsheet, Kaprekar constant (6174), palindrome numbers, number sequences aur puzzles jaise mazedaar activities cover hoti hain. Ye chapter students ko numbers ke saath khelte hue pattern-recognition aur logical reasoning sikhata hai — koi bhi heavy formula nahi hai, sab kuch exploration-based hai.
Kaprekar Constant kya hota hai aur ye chapter me kyun important hai?
Kaprekar Constant number 6174 hai. Koi bhi 4-digit number (jisme sab digits same na ho) lo, digits ko descending aur ascending order me arrange karke subtract karo, aur ye process repeat karo — chahe kuch bhi number ho, kuch hi steps me tumhe hamesha 6174 mil jaayega. Ye chapter ka signature discovery hai jo students ko patterns ki power dikhata hai.
NCERT Class 6 Maths Ganita Prakash PDF 2026-27 session ke liye kahan se download karein?
Official Ganita Prakash textbook PDF ncert.nic.in ki website se free download ho sakti hai — 'Publications' section me jaake Class 6 Mathematics select karo. 2026-27 session ke liye rationalised syllabus wali latest edition hi use karo, kyunki purani 14-chapter 'Mathematics' book ab replace ho chuki hai.
Chapter 1 'Patterns in Mathematics' aur Chapter 3 'Number Play' me kya connection hai?
NCERT Class 6 Maths Ganita Prakash chapter 1 patterns in mathematics solutions me students number patterns (odd, even, square, triangular numbers) seekhte hain — aur Chapter 3 'Number Play' usi foundation ko aage badhaate hue Kaprekar constant, palindromes jaise deeper number puzzles explore karta hai. Dono chapters conceptually connected hain.
Kya Number Play chapter me exam ke liye important questions aate hain?
Ji haan, Kaprekar constant process, palindrome numbers identify karna, aur successive number sums (triangular numbers) jaise questions frequently poochhe jaate hain kyunki ye chapter ki core concepts hain. In-text aur exercise dono jagah ke examples achhi tarah practice karna helpful hota hai.
Number Play chapter kis class level ke liye designed hai aur difficulty level kaisa hai?
Ye Class 6 ka introductory-level chapter hai jo purely activity aur discovery-based hai — koi complex formula nahi. Difficulty easy-to-moderate hai, isliye students ko pattern-observation aur simple arithmetic (addition, subtraction) ki practice chahiye, advanced calculation ki nahi.
Class 6 Maths — Saare Chapters
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