{"id":963,"date":"2026-02-22T15:16:26","date_gmt":"2026-02-22T15:16:26","guid":{"rendered":"https:\/\/shatranj.art\/?page_id=963"},"modified":"2026-02-23T11:10:10","modified_gmt":"2026-02-23T11:10:10","slug":"poster-17","status":"publish","type":"page","link":"https:\/\/shatranj.art\/ha\/exhibit\/poster-17\/","title":{"rendered":"fosta 17"},"content":{"rendered":"
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Yawon Dare na \u0198ararrawa<\/b><\/h2>

Zurfin Tarihi:<\/b> Yawon Doki wata jerin lissafi ce inda doki ke ziyartar kowanne murabba'i a kan allo na catur sau \u0257aya kawai. Wannan kalubale ne na dabaru kuma matsala ce ta gargajiya a cikin lissafin nisha\u0257i.<\/span><\/p>

\u00a0<\/p>

Asali:<\/b><\/p>

Wannan matsala ba sabuwar ganowa ba ce. Mafi tsofaffin mafita da aka sani sun samo asali ne tun \u0199arni na 9, daga manyan masana daga Bagadaza kamar Al-Adli da As-Suli. Bugu da \u0199ari, a cikin adabin Indiya na \u0199arni na 9, mawakin Kashmiri Rudrata ya nuna wannan kyawun lissafi a cikin aikinsa Kavyalankara, inda ya rubuta wata wa\u0199a wadda ta bi jerin zagayen zakaran catur.<\/p>

\u00a0<\/p>

Adabin Yamma:<\/b><\/p>

A \u0199arni na 13, Sarki Alfonso X na Castile ya gabatar da dabaru masu rikitarwa bisa ga motsin zakaran soja a cikin shahararren littafinsa Libro de los Juegos (Littafin Wasanni). Duk da haka, ginshikin lissafi na zamani na wannan matsala an kafa shi a shekarar 1759 ta Leonhard Euler, inda bincikensa yanzu ake ganinsa a matsayin \u0257aya daga cikin ginshi\u0199ai na Ka'idar Graf.<\/p>

\u00a0<\/p>

Halaye:<\/b><\/p>

Yawon shakatawa mai rufewa (mai komawa ciki):<\/b> Idan doki ya tsaya a murabba'i daidai tafiyar doki \u0257aya daga murabba'in farawa, hakan yana ba shi damar fara zagayen nan take.<\/p>

\u00a0<\/p>

Yawon bude ido:<\/b><\/p>

Idan zakaran ya ziyarci dukkan murabba'ai amma ya \u0199are a murabba'i da ba zai iya isa wurin farawa da motsi guda ba.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Matsalar Sarauniya Takwas: Dijkstra da Haihuwar Shirye-shiryen Tsari<\/b><\/h2>

An gabatar da shi ta Max Bezzel a shekarar 1848 kuma ya ja hankalin manyan masana kamar Carl Friedrich Gauss; an mayar da wannan matsalar zuwa \u201cmanifesto na shirye-shirye\u201d a shekarun 1970 ta hannun \u0257aya daga cikin kakannin kimiyyar kwamfuta ta zamani, Edsger W. Dijkstra.<\/p>

Alakar Dijkstra da DFS<\/b><\/h3>

A cikin muhimmin aikinsa, <\/span>Bayanan lura kan shirye-shirye mai tsari<\/span><\/i> (1972), Dijkstra ya yi amfani da Matsalar Sarauniya Takwas don nuna yadda za a gina wani algorithm cikin tsari ta hanyar wani tsari da ya kira \u201cingantawa mataki-mataki.\u201d<\/span><\/p>

  • DFS da Backtracking: Dijkstra ya bayyana hanyar saka sarauniya a layi \u0257aya sannan a sauka zuwa layin na gaba (Depth-First Search \u2013 DFS) da kuma komawa mataki na baya don gwada wata dama bayan kaiwa ga makale (Backtracking) a matsayin mafi tsarkin misali na shirye-shiryen tsari.<\/li><\/ul>

    \u0198arfin Janyewa Baya:<\/b><\/p>

    A cewar Dijkstra, wannan hanyar tana wakiltar babban mataki na farko wajen inganta tsarin \u201cgwaji da kuskure\u201d zuwa jerin hujjoji marasa kuskure da wani co<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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    Matsalar Gandun Kudu da Allon Catur: Ci gaban exponential<\/b><\/h3>

    tatsuniya da asali:<\/b><\/p>

    A cewar labarin, lokacin da mai \u0199ir\u0199irar catur, Sissa bin Dahir, ya gabatar da wasan ga Sarkin Indiya, sarkin ya tambaye shi wane lada yake so. Sissa ya yi bu\u0199ata mai sau\u0199i: \u201cIna so a ba ni hatsi \u0257aya na alkama a murabba'in farko na allon catur, biyu a na biyu, hu\u0257u a na uku, kuma a kowane murabba'i na gaba, sau biyu na adadin na baya.\u201d Da farko Sarki ya yi watsi da wannan bu\u0199ata, yana tunanin cewa \u0199wayoyi ka\u0257an ne kawai na alkama; duk da haka, lokacin da aka fara lissafi, sai aka gane cewa babu ma'ajiyar ku\u0257i ko dukkanin alkamar duniya za su wadatar don cika wannan bu\u0199ata.<\/p>

    Rikodin Tarihi: Ibn Khallikan (1256)<\/b><\/p>

    An rubuta shi a karon farko a shekarar 1256 ta hannun mashahurin marubucin tarihin rayuwa da masanin tarihi Ibn Khallikan. Ibn Khallikan ya ha\u0257a wannan lamari cikin aikinsa ba kawai a matsayin labari ba, har ma a matsayin hujja ta yadda lissafi ke fa\u0257a\u0257a iyakokin tunani.<\/p>

    Gaskiyar Lissafi:<\/b><\/p>

    Wannan bu\u0199atar da aka yi don murabba'ai 64 a kan allo na catur ita ce mafi tsarkin misali na ci gaban lissafi (ha\u0253akar exponential). Adadin da ke kowane murabba'i ana \u0199ididdige shi ta amfani da \u0199a'idar lissafi 2n-1<\/sup><\/strong> . Daidaitaccen \u0199ididdiga da ke bayar da jimillar adadin alkama shine kamar haka:<\/span><\/p>

    \u00a0<\/p>

    S =<\/span>


    63<\/span>
    \u2211<\/span>
    i<\/i>=0<\/span>
    <\/span><\/p>

    2i<\/i><\/sup> = 264<\/sup> \u2212 \u0257aya<\/span><\/p><\/div>

    Babban adadin da ya biyo bayan wannan lissafi shi ne:<\/p>

    18,446,744,073,709,551,615<\/b><\/p>

    Me yasa yake da muhimmanci sosai?<\/b><\/p>

    • Matakin girma:<\/b> Wannan adadi ya yi daidai da kusan sau 2,000 na jimillar samar da alkama a duniya a kowace shekara a halin yanzu.\u00a0<\/span><\/li><\/ul>

      Darasi na dabaru:<\/b> Wannan matsala darasi ce ta d\u0101 ta hikima wadda ke koyar da shugabanni da masu tsara dabaru yadda \u0199ananan canje-canje (\u201cninka\u201d) za su iya zama \u0199arfafan da ba za a iya sarrafawa ba a tsawon lokaci.<\/span><\/p><\/div><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"

      The Knight’s Tour Historical Depth: The Knight’s Tour is a mathematical sequence in which a knight visits every single square on a chessboard exactly once. It is both a strategic challenge and a classic problem in recreational mathematics. \u00a0 Origins: This problem is far from a modern discovery. The earliest known solutions date back to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":743,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-963","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/pages\/963","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/comments?post=963"}],"version-history":[{"count":22,"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/pages\/963\/revisions"}],"predecessor-version":[{"id":1443,"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/pages\/963\/revisions\/1443"}],"up":[{"embeddable":true,"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/pages\/743"}],"wp:attachment":[{"href":"https:\/\/shatranj.art\/ha\/wp-json\/wp\/v2\/media?parent=963"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}