Class 6 Maths Chapter 3 NCERT Solutions Hinglish mein: Number Play

Ganita Prakash (Reprint 2026-27) ke Chapter 3, Number Play, ke har sawaal ke jawab: in-text sawaal, har Figure it Out, puzzles, number-pattern sums aur estimation ke kaam. Page numbers book se milte hain, aur jawab chapter ke saath chhape NCERT ke solutions se milaaye gaye hain; jahan hamaara jawab alag hai, wahan wajah bataayi hai. Kai sawaalon ke ek se zyada sahi jawab hain, isliye hamaare jawab udaharan hain. Short notes: Chapter 3 notes.

Hamaare aas-paas numbers (page 55)

Paanch jagah jahan numbers use hote hain: samay bataana, calendar ki dates, paise ginna, test ke marks, aur lambaai aur wazan naapna. Aur bhi: phone numbers, bus numbers, page numbers, game ke score aur dukaan ke daam.

3.1 Numbers jaankaari dete hain (pages 55–56)

Har bachcha bataata hai ki uske kitne padosi usse lambe hain.

1. Nahi. Kinaare waale bachche ka sirf ek padosi hai, isliye wo 0 ya 1 bol sakta hai, 2 kabhi nahi.
2. Sirf tab jab saare bachche ek hi lambaai ke hon. Lambaai alag ho to sabse chhote bachche ka kam se kam ek lamba padosi hoga, aur wo 1 ya 2 bolega.
3. Haan. Agar bachche lambaai ke kram mein khade hon, to beech ke padosi sab 1 bolte hain.
4. Haan. Sabse chhote se sabse lambe ke kram mein khade ho jao: har bachche ka ek lamba padosi hai (1 bolta hai), aur kinaare pe khada sabse lamba 0 bolta hai.
5. Nahi. Sabse lambe bachche ka koi lamba padosi nahi, isliye kisi ko 0 bolna hi padega.
6. Haan. Jaise lambaai ka kram sabse lamba, chhota, sabse chhota, thoda lamba, doosra sabse lamba (5, 3, 1, 2, 4 jaisa) ho to 0, 1, 2, 1, 0 milta hai.
7. Zyada se zyada 2 bachche 2 bol sakte hain. Kinaare waale 2 nahi bol sakte, aur do padosi dono 2 nahi bol sakte (dono ko ek-doosre se chhota hona padega), isliye sirf doosri aur chauthi jagah pe. Udaharan: lambaai 5, 1, 4, 2, 3 se 0, 2, 0, 2, 0 milta hai.

3.2 Supercells (pages 57–59)

Supercell ka number apne saare padosi cells ke numbers se bada hota hai.

1. 6828, 670, 9435, 3780, 3708, 7308, 8000, 5583, 52 mein supercells hain 6828, 9435 aur 8000.

2. Rangeen cells doosra, chautha (1258) aur nauvaan hain. Ek jawab: 5346, 8000, 1000, 1258, 1100, 2000, 3000, 9635, 9999. Jaanch: 8000, 5346 aur 1000 se bada; 1258, 1000 aur 1100 se bada; 9999, 9635 se bada; aur baaki har cell ka koi bada padosi hai.

3 aur 4. Zyada se zyada supercells ke liye har doosra cell bada rakho: 300, 120, 450, 160, 520, 140, 610, 180, 700. Isme 300, 450, 520, 610 aur 700 supercells hain, yaani 5.

5. Row mein n cells hon to zyada se zyada supercells n ka aadha, upar ki taraf round karke:

Row mein cells	Zyada se zyada supercells
1 ya 2	1
3 ya 4	2
5 ya 6	3
7 ya 8	4
9 ya 10	5

Tareeka: pehle cell ko supercell banao aur phir har doosre cell ko (bada, chhota, bada, chhota, …).

6. Nahi. Sabse bade number waala cell apne saare padosiyon se bada hota hai, isliye kam se kam ek supercell hamesha hoga.

7. Sabse bada number hamesha supercell hai. Sabse chhota number kabhi supercell nahi ho sakta, kyunki uske padosi bade hote hain.

8. Doosre sabse bade ko sabse bade ke paas rakho: 1, 3, 2, 9, 8, 4, 5, 7, 6. Yahan 8, 9 ke paas hai, isliye supercell nahi.

9. Haan, mumkin hai: 2, 1, 5, 3, 9, 8, 4, 7, 6. Doosra sabse chhota, 2, kinaare pe 1 ke paas hai, isliye supercell hai, jabki doosra sabse bada, 8, 9 ke paas hai aur supercell nahi.

10. Sample variations: 9 cells aise bharo ki theek 3 supercells hon; row aise bharo ki doosra sabse chhota supercell ho par teesra sabse bada na ho; 3 × 3 grid mein theek 4 supercells banao.

Grid tables. Book ki Table 1 mein rangeen cells 7500, 9870, 8632 aur 6034 supercells hain. Dhyaan do ki 5785 (neeche left) bhi apne dono padosiyon, 4580 aur 1944, se bada hai, isliye niyam ke hisaab se wo bhi supercell hai, bhale hi book ne use rang nahi kiya.

Table 2, 1, 0, 6, 3 aur 9 se bane numbers se bharne ka ek tareeka (rangeen cells pe ★):

Row	Column 1	Column 2	Column 3	Column 4
1	96,310 ★	96,301	36,109	63,910 ★
2	90,613	13,609	60,319 ★	19,306
3	30,196	10,639	60,193	31,690
4	10,369	10,963 ★	10,693	93,160 ★

• Upar-left cell 96,310 hi ho sakta hai, 96,301 se bada akela arrangement. Ye table ka sabse bada number hai.
• 10,963 ke padosi usse chhote hone chahiye, isliye wo 10,369, 10,396, 10,639, 10,693 aur 10,936 mein se aate hain.
• Is table mein sabse chhota even number 19,306 hai aur 50,000 se bada sabse chhota number 60,193 hai. Doosre sahi tareekon se sabse chhota even number badal sakta hai; jaise NCERT ki answer key 10,396 use karti hai.

3.3 Number line pe patterns (page 59)

Figure it Out. Do likhe hue nishaan batate hain ki nishaanon ke beech kitna fark hai:

• a. 2010 aur 2020 do nishaan door hain, isliye nishaan 5-5 badhte hain: 1990, 1995, 2000, 2005, 2010, 2015, 2020, 2025, 2030, 2035. Sabse chhota 1990, sabse bada 2035.
• b. Nishaan 1-1 badhte hain: 9993, 9994, 9995, 9996, 9997, 9998, 9999, 10,000, 10,001, 10,002. Sabse chhota 9993, sabse bada 10,002.
• c. Nishaan 1-1 badhte hain: 15,077, 15,078, 15,079, 15,080, 15,081, 15,082, 15,083, 15,084, 15,085, 15,086. Sabse chhota 15,077, sabse bada 15,086.
• d. Nishaan 1000-1000 badhte hain: 83,705, 84,705, 85,705, 86,705, 87,705, 88,705, 89,705, 90,705, 91,705, 92,705. Sabse chhota 83,705, sabse bada 92,705.

3.4 Digits se khel (pages 60–61)

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)

1. Digit sum 14. Aur numbers: 77, 95, 149, 239, 707, 1157, 2525. Digit sum 14 waala sabse chhota number 59 hai (1-digit number sirf 9 tak jaata hai, aur 2-digit mein tens digit kam se kam 5 chahiye). Sabse bada 5-digit 95,000 hai. Digit sum 14 waala koi sabse bada number nahi: 95, 950, 9,500, 95,000, 9,50,000, zero jodte jao aur number badhta jaata hai.

2. 40 se 70 tak digit sums.

Numbers	Digit sums
40–49	4, 5, 6, 7, 8, 9, 10, 11, 12, 13
50–59	5, 6, 7, 8, 9, 10, 11, 12, 13, 14
60–69	6, 7, 8, 9, 10, 11, 12, 13, 14, 15
70	7

Har das mein digit sum 1-1 badhta hai; agle das pe jaate hi (49 se 50) 8 ghat jaata hai; aur har naya das pichhle se 1 zyada se shuru hota hai.

3. Lagaataar digits. 123 → 6, 234 → 9, 345 → 12, 456 → 15, 567 → 18, 678 → 21, 789 → 24. Sums 3-3 badhte hain aur har sum beech ke digit ka 3 guna hai. List 789 pe ruk jaati hai, kyunki badhte digits waale aise sirf saat numbers hain, par niyam ghatte digits waalon pe bhi chalta hai, jaise 210 (3) aur 987 (24).

Digit Detectives. 1 se 100 tak digit 7 20 baar likha jaata hai: ones place mein 10 baar aur 70 se 79 mein 10 baar (77 do baar ginta hai). 1 se 1000 tak 300 baar: ones, tens aur hundreds, har jagah 100 baar.

3.5 Sundar palindromic patterns (pages 61–62)

1, 2 aur 3 se 3-digit palindromes: 111, 121, 131, 212, 222, 232, 313, 323, 333.

Reverse and add. Jaise 57 + 75 = 132, 132 + 231 = 363; aur 68 + 86 = 154, 154 + 451 = 605, 605 + 506 = 1111. Kisi bhi 2-digit number se shuru karo, hamesha palindrome milta hai, bhale hi 89 aur 98 ko 24 steps lagein. 3-digit numbers ke liye kisi ko nahi pata; 196 se shaayad kabhi nahi banta. Aur padho palindrome numbers kya hain mein.

Puzzle time. Number hai 12,421: twelve thousand four hundred twenty-one. Units digit odd hona chahiye, aur 4 × units ek digit hona chahiye, isliye units 1, tens 2, hundreds 4, aur palindrome 2 aur 1 dohraata hai.

3.6 Kaprekar ka jaadui number (pages 62–63)

Alag-alag 4-digit numbers sab 6174 tak pahunchte hain. Jaise 2026: 5994, 5355, 1998, 8082, 8532, 6174.

3-digit numbers 495 tak pahunchte hain, jo dohraata hai (954 − 459 = 495). Udaharan: 321 → 321 − 123 = 198 → 981 − 189 = 792 → 972 − 279 = 693 → 963 − 369 = 594 → 954 − 459 = 495. Aur padho Kaprekar routine aur 6174 mein.

3.7 Ghadi aur calendar ke numbers (pages 64–65)

12-ghante ki ghadi pe times:

• Saare digits same (jaise 4:44): 1:11, 2:22, 3:33, 4:44, 5:55 aur 11:11.
• Ghanta minute mein dohraaya (jaise 10:10): 1:01, 2:02, …, 9:09 (01:01 se 09:09 likhkar), 10:10, 11:11 aur 12:12.
• Palindromes (jaise 12:21): 10:01, 11:11 aur 12:21, aur 1:21 jaisi ghadi pe 1 se 9 tak har ghante ke chhah (1:01, 1:11, 1:21, 1:31, 1:41, 1:51, …, 9:59): kul 57.

Manish (20/12/2012) jaisi dates, jisme din aur mahina saal ke roop mein dohraate hain: 20/01/2001, 20/02/2002, …, 20/11/2011, aur pehle 19/01/1901 se 19/12/1912.

Meghana (11/02/2011) jaisi dates, jo dono taraf se same padhi jaati hain: 2000 se aath hain: 10/02/2001, 20/02/2002, 01/02/2010, 11/02/2011, 21/02/2012, 02/02/2020, 12/02/2021 aur 22/02/2022. (NCERT ki key 01/02/2001 aur 02/02/2002 deti hai, par ye ulta padhne pe same nahi: 01022001 ka ulta 10022010 hai.)

Kya calendar dobaara use ho sakta hai? Haan, jab saal hafte ke same din se shuru ho aur same type (leap ya nahi) ka ho. Jo saal leap year nahi, uska calendar 6 ya 11 saal baad lautta hai: 2025 ka 2031 mein aur 2026 ka 2037 mein. Leap year ka calendar 28 saal baad: 2024 ka 2052 mein. (NCERT ki key ka niyam ‘5 ya 6 saal baad’ hamesha nahi chalta; 2026 iska udaharan hai.)

Figure it Out

1. Udaharan (yahan 4-digit numbers hain, isliye aage zero nahi):

• a. Digits 9, 8, 1, 0: 9810 − 1089 = 8721, 5085 se zyada.
• b. Digits 5, 4, 3, 2: 5432 − 2345 = 3087, 5085 se kam.
• c. Digits 9, 8, 7, 6: 9876 + 6789 = 16,665, 9779 se zyada.
• d. Digits 4, 3, 2, 1: 4321 + 1234 = 5555, 9779 se kam.

2. Sabse chhota 5-digit palindrome 10,001, sabse bada 99,999. Jod 1,10,000; fark 89,998.

3. 10:01 se agla palindromic time 11:11 hai, 70 minute baad; uske baad 12:21, 10:01 se 140 minute baad.

4. Zero ko aage rakhkar 5683 ko 7 rounds lagte hain: 8653 − 3568 = 5085, 8550 − 0558 = 7992, 9972 − 2799 = 7173, 7731 − 1377 = 6354, 6543 − 3456 = 3087, 8730 − 0378 = 8352, 8532 − 2358 = 6174. NCERT ki answer key 5, 0, 8, 5 se sabse chhota 5058 likhti hai aur isliye 8 rounds ginti hai; dono 6174 pe pahunchte hain.

3.8 Mental maths (pages 65–67)

Side ke numbers banaana (beech ka har number kai baar use ho sakta hai):

Number	Ek tareeka
38,800	25,000 + 13,000 + 400 + 400
3,400	1,500 + 1,500 + 400
28,000	25,000 + 1,500 + 1,500
63,000	60,000 + 1,500 + 1,500
61,600	60,000 + 400 + 400 + 400 + 400
19,500	13,000 + 1,500 × 3 + 400 × 5
31,000	25,000 + 1,500 × 4
20,900	13,000 + 1,500 × 5 + 400

1,000? Nahi. Beech mein 1,000 se chhota sirf 400 hai, aur 400, 800, 1,200 mein 1,000 chhoot jaata hai. 14,000 = 1,500 × 8 + 400 × 5; 15,000 = 13,000 + 400 × 5; 16,000 = 13,000 + 1,500 × 2. Baaki har hazaar ban jaata hai, isliye sirf 1,000 nahi banta.

Jodna aur ghataana: 45,000 = 40,000 + 12,000 − 7,000; 5,900 = 7,000 − 800 − 300; 17,500 = 12,000 + 7,000 − 1,500; 21,400 = 12,000 + 7,000 + 800 + 800 + 800.

Figure it Out 1.

Case	Udaharan
5-digit + 5-digit, jod 90,250 se zyada	50,000 + 45,000 = 95,000
5-digit + 3-digit, 6-digit jod	99,500 + 600 = 1,00,100
4-digit + 4-digit, 6-digit jod	Mumkin nahi: 9,999 + 9,999 = 19,998 sirf 5-digit hai
5-digit + 5-digit, 6-digit jod	60,000 + 50,000 = 1,10,000
5-digit + 5-digit = 18,500	Mumkin nahi: sabse chhota jod 10,000 + 10,000 = 20,000
5-digit − 5-digit, fark 56,503 se kam	60,000 − 20,000 = 40,000
5-digit − 3-digit, 4-digit fark	10,500 − 900 = 9,600
5-digit − 4-digit, 4-digit fark	15,000 − 7,000 = 8,000
5-digit − 5-digit, 3-digit fark	20,500 − 20,000 = 500
5-digit − 5-digit = 91,500	Mumkin nahi: sabse bada fark 99,999 − 10,000 = 89,999

Figure it Out 2. Hamesha, kabhi-kabhi, kabhi nahi?

• a. Sirf kabhi-kabhi sach: 20,000 + 30,000 = 50,000, par 60,000 + 50,000 = 1,10,000.
• b. Sirf kabhi-kabhi sach: 1,000 + 10 = 1,010, par 9,999 + 99 = 10,098.
• c. Kabhi nahi: sabse bada jod, 9,999 + 99 = 10,098, sirf 5 digits ka hai.
• d. Sirf kabhi-kabhi sach: 90,000 − 10,000 = 80,000, par 12,000 − 10,000 = 2,000.
• e. Kabhi nahi: sabse chhota fark, 10,000 − 99 = 9,901, phir bhi 4 digits ka hai.

3.9 Number patterns se khel (pages 67–68)

Same numbers ko group karo aur ek-ek jodne ki jagah guna karo. (NCERT ki key ye sums nahi deti; humne figures gine.)

• a. Baarah 40 aur das 50: 480 + 500 = 980.
• b. 64 squares; 20 gehre squares mein 5 dots aur 44 mein 1 dot: 100 + 44 = 144.
• c. Battees 32 aur solah 64: 1,024 + 1,024 = 2,048.
• d. 35 dice faces, 18 mein 4 dots aur 17 mein 3: 72 + 51 = 123.
• e. 15, 25 aur 35 har ek baais baar: 22 × 75 = 1,650.
• f. Beech mein 1,000, chaar 500, aath 250 aur atthaarah 125: 1,000 + 2,000 + 2,000 + 2,250 = 7,250.

3.10 Collatz conjecture (pages 68–69)

Aur sequences: 6: 6, 3, 10, 5, 16, 8, 4, 2, 1. 9: 9, 28, 14, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. Jo bhi sequence aazmaao, 1 tak pahunchti hai.

Kya tum ispe bharosa karte ho? Bharosa karna theek hai, kyunki ab tak jaancha har number 1 tak pahuncha hai, par kisi ne ise prove nahi kiya, isliye pakka nahi keh sakte. NCERT ki key kehti hai ki hum ‘pakka 1 tak pahunchenge’, par ye ek proof hota, aur aisa koi proof nahi hai: isiliye book ise unsolved rahasya kehti hai. Aur padho Collatz conjecture kya hai mein.

3.11 Aasaan estimation (pages 69–71)

Andaaze alag-alag hote hain; zaroori hai samajhdaar tareeka. Aur padho estimation kaise karein mein.

1. Kadam (ek kadam lagbhag aadha metre): classroom ke darwaaze tak lagbhag 10 se 20; 100 m ground ke aar-paar lagbhag 200; classroom se school gate tak shaayad 100 se 300; 1 km door ghar tak lagbhag 2,000.

2. Palkein aur saansein: minute mein lagbhag 15 se 20 baar palak, ghante mein 1,000, jaagte din mein 15,000 se zyada; minute mein lagbhag 20 saansein, ghante mein 1,200, din mein lagbhag 30,000.

3. Cheezein: kuch hazaar: 100 g packet mein chaawal ke daane, school ki deewar ki eentein; das hazaar se zyada: 5 kg bore mein chaawal ke daane, sir ke baal.

Jawab ka andaaza lagaao

1. 5000 se zyada. Ek page pe lagbhag 200 shabd; 25 pages mein hi 5,000.
2. Ye tumhare school pe nirbhar hai. Ek bus ke students gino aur buses ki ginti se guna karo.
3. Shaayad nahi. Kai jagah ek litre doodh lagbhag ₹55 se ₹70 ka hai, aur 5 logon ke liye teen tarah ke phal aur jodte hain, isliye ₹100 kam hai. Apne yahan ke daam jaancho.
4. Map ke scale se seedhi line mein lagbhag 2,200 km; sadak se zyada.
5. Nahi. Din mein lagbhag 6 ghante × 200 din = saal mein 1,200 ghante; 8 saal bhi 10,000 ghante se kam.
6. Lagbhag 5 km per ghanta se: a. 2 km door jagah, lagbhag 25 minute; b. 250 km door rajdhaani, lagbhag 50 ghante chalna (din mein 8 ghante se lagbhag 6 din); c. dakshin se uttar tak lagbhag 3,200 km, lagbhag 640 ghante (din mein 8 ghante se lagbhag 80 din).
7. Sample sawaal: tumhare school mein kitne students hain? Tumhara parivaar mahine mein kitni chapatiyan khaata hai? Tumhare ghar mein roz kitne litre paani lagta hai?

3.12 Games aur jeetne ki strategy (pages 71–72)

Game 1 (1, 2 ya 3 jodo; 21 tak pahuncho). Pehla khiladi hamesha jeet sakta hai. 21 ka nishaana rakho, aur usse pehle 17, 13, 9, 5 aur 1: har ek agle se 4 kam. Pehle 1 bolo; doosra jo bhi jode, baaki jodkar 4 poora karo.

Game 2 (1 se 10 jodo; 99 tak pahuncho). Khaas numbers 99, 88, 77, …, 22, 11 hain (11 ka fark). Pehle khiladi ko 1 se 10 ke beech bolna hi padta hai, isliye doosra khiladi 11 bolta hai aur phir 22, 33, …, 99 pe tikta hai, aur hamesha jeetta hai.

Apne variations: agar har baari 1 se k tak jod sakte ho, to khaas numbers hain target mein se (k + 1) ke multiples ghata ke. Jaise 1 se 4 jodo aur 30 tak pahuncho: khaas numbers 5, 10, 15, 20, 25, 30, isliye doosra khiladi jeetta hai.

Figure it Out (pages 72–73)

1. Sirf 62,871 supercell hai. 6 aur 1 ki jagah badlo aur 12,876 banao. Tab 39,344, 23,609, 45,306 aur 50,319 har ek apne saare padosiyon se bada ho jaata hai: 4 supercells.

2. Janam-saal 2014 ke liye, zero aage rakhkar: 4210 − 0124 = 4086, 8640 − 0468 = 8172, 8721 − 1278 = 7443, 7443 − 3447 = 3996, 9963 − 3699 = 6264, 6642 − 2466 = 4176, 7641 − 1467 = 6174: 7 rounds. Apna saal aazmaao.

3. Sabse bada 73,999; sabse chhota 35,111; 50,000 ke sabse paas 51,111 (neeche waala sabse paas 39,999 kahin door hai).

4. Sample andaaza: 52 Sunday, lagbhag 12 aur hafte ki chhuttiyan, lagbhag 15 tyohaar aur rashtriya chhuttiyan aur lagbhag 50 din vacations, vacation mein pade Sunday ghata ke: lagbhag 120 se 140 din. Phir school ke calendar pe gino.

5. Mug lagbhag 1 litre, baalti lagbhag 15 se 20 litre, overhead tank lagbhag 500 se 1,000 litre.

6. 17,870 + 400 + 400 = 18,670. Ek aur: 18,000 + 300 + 370.

7. 360 chunkar: 120 ke chaaron taraf aath 30 ka ghera (240 + 120 = 360), ya nau 40 ka 3 × 3 square.

8. 2 ki har power even hai aur uska aadha phir 2 ki power hai, isliye sequence bas aadhi hoti jaati hai: jaise 128, 64, 32, 16, 8, 4, 2, 1. 1 se pehle koi odd number nahi aata.

9. Haan: 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 (25 steps).

10. Khaas numbers 22, 18, 14, 10, 6 aur 2 hain. Pehla khiladi 2 bolta hai (0 mein 2 jodkar) aur phir hamesha total 4 se badhaata hai: 6, 10, 14, 18, 22.

Aur practice ke liye padho palindrome numbers kya hain, Kaprekar routine aur 6174, Collatz conjecture kya hai aur estimation kaise karein.