Palindrome numbers kya hain?

Palindrome kya hai?

66, 848, 575, 797 aur 1111 ko dekho. Har ek ko left se right aur phir right se left padho: same number milta hai. Aise numbers ko palindromes ya palindromic numbers kehte hain. Ye shabd un words ke liye bhi use hota hai jo dono taraf se same padhe jaate hain, jaise ‘madam’ aur ‘level’.

Ek jhatpat test: number ko ulta likho. Agar kuch na badle, to wo palindrome hai. 4554 ulta bhi 4554 hai, isliye palindrome; 4545 ulta 5454 hai, isliye nahi.

1, 2 aur 3 se saare 3-digit palindromes

3-digit palindrome ka pehla aur aakhri digit same hota hai. Sirf 1, 2 aur 3 se pehla digit (jo aakhri bhi tay karta hai) 3 tarah se aur beech ka digit 3 tarah se chun sakte hain, isliye 3 × 3 = 9 palindromes bante hain:

Pehla aur aakhri digit	Palindromes
1	111, 121, 131
2	212, 222, 232
3	313, 323, 333

Reverse and add

Koi 2-digit number lo. Usme uska ulta jodo. Agar jawab palindrome hai to ruko; nahi to jawab ko ulta karke phir jodo.

• 25 + 52 = 77, ek hi step mein palindrome.
• 19 + 91 = 110; 110 ka ulta 011, yaani 11, aur 110 + 11 = 121.
• 68 + 86 = 154, 154 + 451 = 605, 605 + 506 = 1111.

Kya har 2-digit number palindrome tak pahunchta hai? Haan. Kuch ko der lagti hai: 79 ko 6 steps (44,044 pe khatam), aur 89 ko 24 steps lagte hain, jo 8,813,200,023,188 pe khatam hota hai. 3-digit numbers ke liye jawab kisi ko nahi pata: 196 se shuru karke shaayad kabhi palindrome nahi banta, par ise kisi ne prove nahi kiya.

Palindrome puzzle

“Main ek 5-digit palindrome hoon. Main odd hoon. Mera tens digit mere units digit ka double hai, aur mera hundreds digit mere tens digit ka double hai.”

Units digit ko u kaho. Tens digit 2u aur hundreds digit 4u hai, aur 4u ek hi digit hona chahiye, isliye u 1 ya 2 hai. Number odd hai, isliye u = 1, yaani tens 2 aur hundreds 4. Palindrome mein ten-thousands digit units ke barabar (1) aur thousands digit tens ke barabar (2) hota hai. Number hai 12,421, twelve thousand four hundred twenty-one.

Sabse chhota aur sabse bada 5-digit palindrome

Sabse chhota 5-digit palindrome 10,001 aur sabse bada 99,999 hai.

• Jod: 10,001 + 99,999 = 1,10,000
• Fark: 99,999 − 10,001 = 89,998

Ghadi pe palindromes

1:21 jaise likhi jaane waali 12-ghante ki ghadi pe koi time palindrome hai agar wo ulta bhi same padha jaaye. 1 se 9 tak har ghante mein chhah hain: jaise 1:01, 1:11, 1:21, 1:31, 1:41 aur 1:51. Do-digit ghanton mein sirf teen: 10:01, 11:11 aur 12:21. Kul milaakar 57 palindromic times.

Agar abhi 10:01 hai, to agla palindromic time 11:11 hai, 70 minute baad, aur uske baad 12:21, 10:01 se 140 minute baad.

Palindromic dates

Meghana ka janamdin 11/02/2011, 11022011 likhne pe dono taraf se same padha jaata hai. Saal 2000 se, dd/mm/yyyy mein, aisi sirf aath dates aayi 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. Saari February mein hain, kyunki 20 se shuru hone waale saal ke liye mahina 02 chahiye. Agli date 03/02/2030 hogi.

Palindromes numbers mein chhupa sirf ek pattern hai. Doosre ke liye padho Kaprekar routine aur 6174. Textbook ke sawaalon ke liye dekho Chapter 3 ke NCERT solutions; poore chapter ke liye Chapter 3 ke notes.