Sliding Puzzle Kaise Solve Karein: 3x3, 4x4 aur 5x5 Step by Step

Sliding puzzle solve karne ke liye top row poori karein, phir uske neeche waali row, aur aise hi chalte rahein jab tak sirf do rows na bachein; un do rows ko left se ek-ek column karke poora karein, aur aakhri 2×2 square khud solve ho jaata hai jab aap khaali jagah ko uske chaaron taraf ghumaate hain. Aapko bas ek trick chahiye, har row aur column ki aakhri do tiles ke liye: woh ek-ek karke nahi, balki ek stacked pair ki tarah saath mein jaati hain.

Poora method bas itna hi hai, aur yeh 3×3, 4×4 aur 5×5 teeno par ek jaisa chalta hai. Neeche ise move by move samjhaaya gaya hai, saath mein woh parity check jo batata hai ki board solve ho bhi sakta hai ya nahi, aur Klotski aur car-escape puzzles ka alag plan, jahan pieces alag-alag size ke hote hain. Try karne ke liye board chahiye, to yahan ek khelein: hamara free Sliding Puzzle browser mein 3x3, 4x4 aur 5x5 mein chalta hai, aur uska har shuffle solvable hota hai.

Rules: ek khaali square, aur aadhe shuffles kabhi solve nahi ho sakte

Sliding tile puzzle numbered tiles ka ek square frame hota hai jismein ek jagah khaali hoti hai. Khaali jagah ke bagal ki koi bhi tile aap usmein slide kar sakte hain, aur goal hai tiles ko order mein laana, left se right aur upar se neeche, aur khaali jagah neeche right corner mein. 3×3 version 8-puzzle hai, 4×4 15-puzzle aur 5×5 24-puzzle: naam is baat se ki unmein kitni tiles hain.

Tiles nikaal kar random tareeke se wapas laga dein, to jitne arrangements ban sakte hain unmein se theek aadhe kabhi solve nahi honge. Slide karne se ek chhupi hui ginti kabhi nahi badalti jise parity kehte hain, aur ise aap pencil se check kar sakte hain. Tiles ko left se right, upar se neeche padhein, khaali jagah chhod kar, aur har woh pair ginein jismein bada number chhote se pehle aata hai. Aisa har pair ek inversion hai.

• Odd width (3×3, 5×5): puzzle tabhi solvable hai jab inversions ki ginti even ho.
• Even width (4×4): khaali jagah jis row mein hai woh bhi jodein, rows ko upar se 1 se 4 tak gin kar. Puzzle tabhi solvable hai jab yeh total even ho. (Rows neeche se ginein to total odd chahiye. Rule wahi, bas ulta.)

Ek 3×3 example dekhte hain. Board lein 1 3 _ / 4 2 5 / 7 8 6, khaali jagah upar right mein. Padhne par milta hai 1, 3, 4, 2, 5, 7, 8, 6. Inversions hain: 3 ka 2 se pehle aana, 4 ka 2 se pehle, 7 ka 6 se pehle aur 8 ka 6 se pehle. Yeh chaar hain, yaani even, to board solve ho sakta hai. Isme chaar moves lagti hain: 3 ko right, 2 ko upar, 5 ko left aur 6 ko upar slide karein. Ab ek solved board lein aur 7 aur 8 ki jagah badal dein. Yeh ek inversion hai, odd, aur slides ka koi bhi sequence ise kabhi theek nahi karega.

Isi jaal ke 4×4 version ne 15-puzzle ko mashhoor kiya. 1880 mein United States mein iska craze chal raha tha, aur puzzle writer Sam Loyd ne baad mein daava kiya ki unhone $1,000 ka prize rakha tha, us insaan ke liye jo 14 aur 15 ki jagah badle hue solved board se shuru karke unhe theek kar de. Ek inversion, plus row 4 mein khaali jagah, total 5: odd, yaani impossible. Prize ke paise kabhi khatre mein the hi nahi. Koi bhi theek se bana digital puzzle solved board se legal moves karke khud ko shuffle karta hai, isliye aapki screen waale puzzle ka solution zaroor hai. Jis puzzle ko kisi bhai-behen ne khol kar wapas jod diya ho, uska shaayad na ho.

3×3 (8-puzzle) chaar stages mein solve hota hai

Rows upar se gini jaati hain aur columns left se. “Lock” ka matlab hai ki uske baad khaali jagah kabhi un squares se nahi guzregi.

1. Tile 1 ko ghar laayein. Khaali jagah ko ghuma kar 1 ko top-left corner mein laayein. Use lock karein.
2. Tiles 2 aur 3 ek stacked pair ki tarah. 2 ko top-right corner mein rakhein (3 ka square, uska apna nahi) aur 3 ko theek uske neeche, row 2, column 3 mein. Khaali jagah ko row 2 ke raaste top-middle square tak laayein, corner se kabhi nahi. 2 ko left slide karein, phir 3 ko upar. Top row ho gayi. Use lock karein.
3. Tiles 4 aur 7 ek stacked pair ki tarah, side mein. 7 ko 4 ke square (row 2, column 1) mein rakhein aur 4 ko theek uske right mein, centre mein. Khaali jagah ko bottom row ke saath-saath bottom-left corner tak laayein. 7 ko neeche slide karein, phir 4 ko left. Left column ho gaya. Use lock karein.
4. Tiles 5, 6 aur 8: ghumaayein. Ab bacha hai ek 2×2 square, teen tiles aur khaali jagah. Khaali jagah ko ek hi direction mein uske chaaron taraf ghumaayein aur teeno tiles tab tak ghoomti rehti hain jab tak apni jagah na baith jaayein. Sahi direction mein kabhi chhe se zyada moves nahi lagti; agar pehle chakkar se kuch na bane, to ulti direction mein ghumaayein.

Stacked pair kyun? Agar aap 2 ko pehle ghar rakh dein, to 3 ka corner tak pahunchne ka akela raasta 2 ke square se hokar jaata hai, to 3 ko rakhte hi 2 bahar ho jaata hai. Dono ko pehle stack karke ghumaane se dono do slides mein baith jaate hain. Zyaadatar log is baat par yakeen karne se pehle ek-ek waala tareeka kai baar try karte hain. Hamne zyaadatar logon se zyada baar try kiya.

4×4 (15-puzzle): do rows, do columns, phir ek rotation

15-puzzle mein plan wahi hai, bas ek stage zyada. Row 1 (tiles 1 se 4) aur row 2 (5 se 8) ko rows ki tarah solve karein, phir neeche ki do rows ko column by column: 9 aur 13, phir 10 aur 14, phir aakhri 2×2 mein 11, 12 aur 15 ko ghuma kar ghar laayein. Har row mein pehli do tiles aasaan hain; unhe ek-ek karke ghar le jaayein. Trick sirf aakhri pair ke liye chahiye.

Row ki aakhri do tiles, move by move

Yeh rahi row 1 ke liye, jahan tiles 1 aur 2 pehle se ghar par aur locked hain.

1. Pehle tile 4 ko raaste se hataayein. Agar 4 row 1 ya row 2 mein hai, to use row 3 ya usse neeche le jaayein. Isse woh step 2 mein bhatak kar galat square mein nahi pahunchegi.
2. Tile 3 ko top-right corner mein rakhein (row 1, column 4), jo 4 ka square hai, 3 ka nahi.
3. Tile 4 ko theek uske neeche waale square mein laayein (row 2, column 4), sirf rows 2 se 4 ki tiles hila kar, taaki 3 corner mein hi rahe.
4. Khaali jagah ko row 2, column 3 mein laayein, tile 4 ke bagal mein, phir se row 1 ko chhue bina. Phir row 1, column 3 mein jo bhi tile hai use neeche khaali jagah mein slide karein. Ab khaali jagah 3 ke square mein hai, 3 uske right mein hai aur 4 teen ke neeche.
5. 3 ko left slide karein. 4 ko upar slide karein. Row 1 poori. Use lock karein.

Row 2 bhi aise hi chalti hai: 5 aur 6 ek-ek karke jaate hain, phir 7 row 2, column 4 mein, 8 uske neeche row 3, column 4 mein, khaali jagah row 2, column 3 mein, aur wahi do slides: 7 left, 8 upar.

Neeche ki do rows, ek-ek column karke

Rows 1 aur 2 lock hone ke baad chaar-chaar ki do rows bachti hain: upar 9, 10, 11, 12 aur neeche 13, 14, 15 aur khaali jagah. Yahan rows kaam nahi karengi kyunki tiles park karne ke liye koi extra row nahi hai, isliye aap columns mein aage badhte hain, wahi pair trick side mein ghuma kar.

1. Column 1 (tiles 9 aur 13). 13 ko 9 ke square (row 3, column 1) mein rakhein aur 9 ko theek uske right mein (row 3, column 2). Khaali jagah ko row 4 ke saath-saath row 4, column 1 tak laayein. 13 ko neeche slide karein, phir 9 ko left. Column lock karein.
2. Column 2 (tiles 10 aur 14). Ek column aage wahi dobara: 14 row 3, column 2 mein, 10 row 3, column 3 mein, khaali jagah row 4, column 2 mein. 14 neeche, 10 left. Lock karein.
3. Aakhri 2×2 (11, 12 aur 15). Khaali jagah ko square ke chaaron taraf ghumaayein jab tak teeno baith na jaayein, bilkul 3×3 ki tarah. Shuffle legal tha, to baith jaayengi.

Yeh method bharosemand hai, chhota nahi. Sabse chhota raasta dhoondhne waale computer ko kisi bhi 15-puzzle par 80 se zyada single-tile moves kabhi nahi chahiye, aur sirf 17 positions ko poori 80 lagti hain. Row by row usse zyada moves leta hai, lekin ise aap bina ruke, bina soche kar sakte hain, aur insaan ke liye yeh move count se kahin zyada maayne rakhta hai.

5×5 (24-puzzle) ek 4×4 hai, ek extra row aur column ke saath

Har bada board chheel kar apne se ek chhote board tak laaya ja sakta hai. 5×5 par row 1 solve karein (tiles 1 se 5, jismein 4 aur 5 stacked pair hain), phir uske neeche ka left column (6, 11, 16 aur 21, jismein 16 aur 21 side waala pair hain: 21 ko 16 ke square mein, 16 uske right mein, khaali jagah neeche, phir 21 ko neeche aur 16 ko left slide karein). Dono lock karein, aur jo bachta hai woh tiles 7 se 10, 12 se 15, 17 se 20 aur 22 se 24 ka ek 4×4 hai. Use bilkul upar ki tarah solve karein, bas numbers ko 1 se 15 ki jagah positions ki tarah padhein.

Aap row by row row 3 tak bhi chal sakte hain aur phir neeche ki do rows columns mein kar sakte hain; dono raaste usi 2×2 rotation par khatam hote hain. 5×5 ke lagbhag 7.76×10²⁴ reachable arrangements hain, aur abhi tak koi pakka nahi kar paaya ki unmein se kisi ko zyada se zyada kitni moves chahiye. Hamein mile sabse naye bounds, 2016 ke, ise 152 aur 205 single-tile moves ke beech kahin rakhte hain.

Klotski aur car-escape puzzles ke liye alag method chahiye

Row by row tabhi chalta hai jab har piece ek hi size ka ho. Klotski, aur sliding-block puzzles ki poori family jiska woh hissa hai, alag-alag shapes ke pieces milaati hai, aur poori karne ko koi row hoti hi nahi kyunki kisi piece ka numbered ghar nahi hota. Sirf ek piece maayne rakhta hai: jise aap bahar nikaalna chahte hain.

Classic Klotski starting position ek 4×5 tray hai jismein das pieces hain: top middle mein ek bada 2×2 block, uske neeche leta hua ek 2×1 block, uske neeche do chhote 1×1 squares, aur dono side mein do khade 1×2 blocks, sabse neeche ek 1×1 square ke saath. Do khaali squares bottom middle mein saath-saath hote hain. Goal hai 2×2 block ko bottom middle tak laana aur frame ke gap se bahar nikaalna. China mein yahi puzzle Huarong Dao kehlaata hai, jahan bada block warlord Cao Cao hai jo bhaag raha hai. Thodi si lakdi ke liye kaafi badi kahani.

1. Pehle target piece ka raasta plan karein. Kuch bhi hilaane se pehle, bade block (ya bhaagti car) ko exit tak jo raasta lena hai, use square by square trace karein.
2. Exit se ulta kaam karein. Us raaste ke agle step ke liye poochein ki kya khaali hona chahiye, kaunsa piece raaste mein hai, aur woh piece kahan ja sakta hai. Phir yahi sawaal us piece ke liye poochein jo uske raaste mein hai. Yahi chain asli puzzle hai.
3. Klotski mein dono khaali jagahon ko saath rakhein. khada 1×2 block side mein tabhi ja sakta hai jab do khaali squares ek ke upar ek hon, leta hua 2×1 block upar ya neeche jaane ke liye do khaali squares saath-saath maangta hai, aur bade block ko hamesha do chahiye. Khaali jagahon ko alag karne se aadhe pieces phas jaate hain.
4. Moves ko hile hue pieces se ginein, squares se nahi. Klotski mein koi piece jahan tak pahunch sake wahan tak slide ho, to woh ek move hai, aur is ginti se classic start ko kam se kam 81 moves chahiye. “Yeh block left wall tak” jaisa plan single steps ki list se kahin aasaani se dimaag mein rehta hai.

Sliding car puzzles, yaani Rush Hour family, ek aur rule jodte hain: har gaadi apni lane mein locked hai, isliye board ke aar-paar leti car sirf left aur right ja sakti hai. Isse ulti chain aur bhi kaam ki ho jaati hai, kyunki har blocker ke rukne ki bas kuch hi jagah hoti hain. Ek baar yeh samajh aa jaaye, to agla kadam hai Rush Hour-style puzzles mein tez kaise banein: yaani move count ghataana, jo ek alag skill hai.

3x3 vs 4x4 vs 5x5 vs Klotski ek nazar mein

Aam galtiyan jo board ko unsolved chhod deti hain

• Row ki aakhri do tiles ek-ek karke rakhna. Doosri hamesha pehli ko bahar nikaal deti hai. Unhe stack karein aur ghumaayein.
• Khaali jagah ko poori ho chuki row mein wapas bhatakne dena. Wahan ka har chakkar kiya-karaaya kaam bigaadta hai. Agar kisi raaste ko iski zaroorat hai, to doosra raasta dhoondhein.
• Neeche ki do rows ko rows ki tarah karna. Tile park karne ki koi jagah nahi hai. Jab do rows bachein, columns par switch karein.
• Aakhri 2×2 ko teen alag tiles samajhna. Yeh ek rotation hai. Ghumaayein, aur agar pehle chakkar se kuch na ho, to ulti taraf ghumaayein.
• Parity galat ginna. Khaali jagah ko tile na ginein, aur 4×4 par khaali jagah ki row jodna na bhoolein.
• Klotski mein do khaali jagahon ko alag karna. Bade blocks ko hilne ke liye dono saath-saath chahiye.

Sliding puzzle online kahan khelein: hamara free 15-puzzle, phir Car Parking

Upar waale method ke liye board hai hamara apna Sliding Puzzle, browser mein free, na download, na sign-up. 3×3, 4×4 ya 5×5 chunein, numbered tiles ya heist picture ke saath, aur har shuffle aapke dekhne se pehle parity ke liye check hota hai, isliye impossible waale aadhe mein se aapko kabhi kuch nahi milta. Undo unlimited hai, aur game har size ke liye aapki best move count aur best time rakhta hai. Iski kami: yeh records aapke browser mein rehte hain, isliye site data clear karne ya private window mein khelne se mit jaate hain.

Klotski aur Rush Hour waali side ke liye Car Parking try karein: ek 6×6 car park, traffic mein ghiri ek gold car, aur har gaadi apni lane mein locked. Ek move ka matlab hai ek gaadi ka nayi jagah park hona, chahe woh kitni bhi door slide hui ho, aur 240 levels mein se har level ka ek par hai, yaani hamare solver ka dhoondha sabse chhota solution, saath mein har level mein teen hints. Yeh row-by-row nahi, exit se ulta chalne waala method practise karata hai. Getaway Garage har swipe ke saath saari gaadiyan ek saath chalata hai aur ek jaisi teen ko clear karta hai, jo use phir se ek alag puzzle bana deta hai. Aur poori kahani chahiye, to hamara traffic jam puzzles ka itihaas 15-puzzle ke craze se shuru hota hai.

Decision rule chhota hai. Agar har piece ek hi size ka hai, to upar se rows poori karein, aakhri do rows ke liye columns par switch karein aur aakhri square ghumaayein. Agar pieces alag-alag hain, to woh ek piece chunein jise bhaagna hai aur exit se ulta plan karein. Pehla tareeka 4×4 Sliding Puzzle par try karein aur doosra Car Parking mein, dono aapke browser mein free.