Class 6 Maths Chapter 3: Number Play (Hinglish Notes)
Ye chapter 5 lines mein
Number Play dikhaata hai ki numbers sirf ginti se kahin zyada kaam karte hain. Wo jaankaari de sakte hain, jaise bachche bataate hain ki unke kitne padosi lambe hain, aur unme patterns chhupe hain: supercells, digit sums, dono taraf se same padhe jaane waale palindromes, aur Kaprekar ka routine, jo kam se kam do alag digits waale har 4-digit number ko 6174 tak le jaata hai. Kuch sawaal poochne mein aasaan par abhi tak unsolved hain, jaise Collatz conjecture. Chapter mein mental maths, estimation aur 21 jaise games ki jeetne waali strategy bhi hai.
Numbers jaankaari dete hain
Hum numbers ko samay, taareekh, paise, marks, naap aur bahut kuch ke liye use karte hain. Chapter ek puzzle se shuru hota hai: alag-alag lambaai ke bachche ek line mein khade hain, aur har bachcha ek number bolta hai. Ye number hai unke kitne padosi unse lambe hain. Do lambe padosi hon to 2, ek ho to 1, aur koi na ho to 0.
Kinaare waale bachche ka sirf ek padosi hota hai, isliye wo kabhi 2 nahi bol sakta. Sabse lamba bachcha hamesha 0 bolta hai, aur alag lambaai ke 5 bachchon mein zyada se zyada 2 hi 2 bol sakte hain.
Supercells
Table ka koi cell supercell hai agar uska number apne saare padosi cells ke numbers se bada ho. Ek row mein padosi left aur right waale cells hain; kinaare waale cell ka sirf ek padosi hota hai.
Sabse bade number waala cell hamesha supercell hota hai, aur sabse chhote number waala kabhi nahi. n cells ki row mein zyada se zyada aadhe cells (upar ki taraf round karke) supercell ho sakte hain: baari-baari se bada, chhota, bada bharo. Grid mein padosi left, right, upar aur neeche waale cells hain. Book ki Table 1 dhyaan se dekho: rangeen cells ke alaawa neeche-left ka 5785 bhi apne dono padosiyon (4580 aur 1944) se bada hai, isliye niyam ke hisaab se wo bhi supercell hai.
Digits aur number line
2180, 2754 aur 9590 jaise numbers ko 1000 se 10,000 ki number line pe rakhne ka matlab hai ye dhoondhna ki wo kin do hazaaron ke beech hain. Digits ke hisaab se numbers ginne pe ek saaf pattern milta hai:
| Digits | Kitne numbers |
|---|---|
| 1 | 9 (1–9) |
| 2 | 90 (10–99) |
| 3 | 900 (100–999) |
| 4 | 9,000 (1000–9999) |
| 5 | 90,000 (10,000–99,999) |
Kisi number ka digit sum uske digits ka jod hai: 68, 176 aur 545 sabka digit sum 14 hai. Digit sum 14 waala sabse chhota number 59 hai, aur sabse bada 5-digit 95,000. Digit Detectives mein Dinesh 1 se 100 tak likhta hai: digit 7 20 baar aata hai, aur 1 se 1000 tak 300 baar.
Palindromes
66, 848, 575, 797 aur 1111 jaise numbers left se right aur right se left same padhe jaate hain. Ye palindromes hain. Kisi 2-digit number mein uska ulta jodo aur dohraao, to hamesha palindrome milta hai: 68 + 86 = 154, 154 + 451 = 605, 605 + 506 = 1111. Aur padho palindrome numbers kya hain mein.
Kaprekar ka jaadui number
Devlali, Maharashtra ke maths teacher D. R. Kaprekar ne 1949 mein ye khoja. Kam se kam do alag digits waala 4-digit number lo. Uske digits se sabse bada aur sabse chhota number banao, aur ghataao. Jawab ke saath dohraao. Tum hamesha 6174 pe pahunchoge, jise Kaprekar constant kehte hain, aur phir wahi dohraata hai, kyunki 7641 − 1467 = 6174. 3-digit numbers ke liye ye routine 495 tak pahunchta hai. Aur padho Kaprekar routine aur 6174 mein.
Ghadi aur calendar ke numbers
Kuch times mein patterns hain: 4:44 (saare digits same), 10:10 (ghante ko minute mein dohraana) aur 12:21 (palindrome). Dates bhi khelti hain: Manish ka janamdin 20/12/2012 digits 2, 0, 1, 2 dohraata hai, aur Meghana ka 11/02/2011 dono taraf se same padha jaata hai. Kisi saal ka calendar lautta bhi hai: jo saal leap year nahi, uska calendar 6 ya 11 saal baad lautta hai (2026 ka calendar 2037 mein), aur leap year ka 28 saal baad.
Mental maths
Diye gaye hisson se koi number banaane ke liye bade, aasaan tukdon mein socho: 38,800 = 25,000 + 13,000 + 400 + 400, aur 3,400 = 1,500 + 1,500 + 400. Kuch jod namumkin hain: 1,000 se chhota hissa sirf 400 ho, to 1,000 nahi ban sakta. Size ke baare mein sochna bhi madad karta hai: 4-digit aur 2-digit ka jod zyada se zyada 9,999 + 99 = 10,098 hai, isliye wo kabhi 6-digit nahi hota, jabki do 5-digit numbers ka jod kabhi-kabhi 6-digit hota hai.
Dohraaye numbers ke patterns mein ek-ek karke jodne ki jagah guna karo: baarah 40 aur das 50 milkar 480 + 500 = 980.
Ek unsolved rahasya: Collatz conjecture
Koi bhi poorn sankhya lo. Agar even hai to aadha karo; agar odd hai to 3 se guna karke 1 jodo. Dohraao. 1937 mein German mathematician Lothar Collatz ne anumaan lagaaya ki hamesha 1 aayega. Ise kabhi prove nahi kiya gaya, isliye ye ab bhi maths ke sabse mashhoor unsolved sawaalon mein se hai. Aur padho Collatz conjecture kya hai mein.
Aasaan estimation
Aksar exact ginti ki zaroorat nahi hoti. Paromita ki class ke teen sections mein 32, 29 aur 35 bachche hain, kul lagbhag 100. Teen-teen sections waali paanch classes (6 se 10) ke saath wo apne school mein lagbhag 500 students ka andaaza lagaati hai. Aur padho estimation kaise karein mein.
Games aur jeetne ki strategy
21 ke game mein do khiladi baari-baari 1, 2 ya 3 jodte hain, pehle khiladi ke 1, 2 ya 3 se shuru karke, aur jo 21 bole wo jeetta hai. Jeetne waale numbers 21, 17, 13, 9, 5 aur 1 hain, har ek mein 4 ka fark. Pehla khiladi 1 bolta hai, aur doosra jo bhi jode, wo baaki jodkar 4 poora karta hai. Doosre game (1 se 10 jodo, 99 tak pahuncho) mein khaas numbers 11, 22, 33, …, 99 hain, aur doosra khiladi hamesha jeet sakta hai.
Har sawaal ke jawab Chapter 3 ke NCERT solutions mein hain.
Key terms (zaroori shabd)
| Term | Matlab |
|---|---|
| Supercell | Wo cell jiska number apne saare padosi cells ke numbers se bada ho: row mein left aur right waale, aur grid mein upar aur neeche waale bhi. |
| Digit sum | Kisi number ke digits ka jod. 68, 176 aur 545, teeno ka digit sum 14 hai. |
| Palindrome | Aisa number jo left se right aur right se left same padha jaaye, jaise 66, 848 aur 1111; ise palindromic number bhi kehte hain. |
| Reverse-and-add | Number mein uska ulta jodna, baar-baar, jab tak palindrome na aa jaaye, jaise 68 → 154 → 605 → 1111. |
| Kaprekar constant | Number 6174. Kisi 4-digit number ke digits se bane sabse bade number mein se sabse chhota ghataane ko baar-baar karne pe hamesha yahi aata hai. |
| D. R. Kaprekar | Devlali, Maharashtra ke ek sarkaari school ke maths teacher, jinhone 1949 mein 6174 waala routine khoja. |
| Collatz conjecture | Lothar Collatz ka 1937 ka anumaan ki even number ko aadha aur odd number ko 3 × n + 1 karte rehne se hamesha 1 aata hai. Abhi tak koi ise prove nahi kar paaya. |
| Estimate (andaaza) | Jab exact ginti ki zaroorat na ho, tab ek samajhdaar, gol-mol jawab, jaise school mein lagbhag 500 students. |
| Winning strategy | Aisi yojana jisse sahi khelne waala khiladi hamesha jeete, jaise 21 ke game mein 1, 5, 9, 13, 17 aur 21 bolna. |
| Computational thinking | Kisi kaam ke liye numbers ko use karne ke step-by-step tareeke sochna aur banaana, jaise Kaprekar ka routine ya game ki strategy. |
Is chapter ke topics
Practice karo
-
Inme se kaunsa number palindrome hai?
Jawab dekho
Jawab: (b) 4554
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Jis 4-digit number ke saare digits same nahi, uspe Kaprekar routine hamesha kahan khatam hota hai?
Jawab dekho
Jawab: (c) 6174
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Collatz sequence mein 7 ke baad kaunsa number aata hai?
Jawab dekho
Jawab: (b) 22
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3-digit numbers kitne hain?
Jawab dekho
Jawab: (b) 900
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Alag-alag numbers ki row mein kaunsa cell hamesha supercell hota hai?
Jawab dekho
Jawab: (c) Sabse bade number waala cell
Students ke sawal
Class 6 Maths Chapter 3 ke mukhya topics kya hain?
Jaankaari dene waale numbers, supercells, number line pe numbers, digits aur digit sums, palindromes, Kaprekar constant 6174, ghadi aur calendar ke numbers, mental maths, number patterns, Collatz conjecture, estimation, aur games ki jeetne waali strategy.
Kya Number Play naye Ganita Prakash book mein hai?
Haan. Number Play, Class 6 Maths ki textbook Ganita Prakash (Reprint 2026-27) ka Chapter 3 hai. Ye Chapter 2, Lines and Angles, ke baad aata hai.
Chapter 3 mein kitne sawaal hain?
Har section ke apne sawaal aur puzzles hain, aur chapter ke end ke Figure it Out mein 10 aur. Hamaare NCERT solutions page pe in sabke jawab hain, un number-pattern sums ke bhi jo NCERT ki answer key mein nahi hain.
Koi sawal atak gaya?
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