Zurfin Tarihi: Yawon Doki wata jerin lissafi ce inda doki ke ziyartar kowanne murabba'i a kan allo na catur sau ɗaya kawai. Wannan kalubale ne na dabaru kuma matsala ce ta gargajiya a cikin lissafin nishaɗi.
Asali:
Wannan matsala ba sabuwar ganowa ba ce. Mafi tsofaffin mafita da aka sani sun samo asali ne tun ƙarni na 9, daga manyan masana daga Bagadaza kamar Al-Adli da As-Suli. Bugu da ƙari, a cikin adabin Indiya na ƙarni na 9, mawakin Kashmiri Rudrata ya nuna wannan kyawun lissafi a cikin aikinsa Kavyalankara, inda ya rubuta wata waƙa wadda ta bi jerin zagayen zakaran catur.
Adabin Yamma:
A ƙarni 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 ɗaya daga cikin ginshiƙai na Ka'idar Graf.
Halaye:
Yawon shakatawa mai rufewa (mai komawa ciki): Idan doki ya tsaya a murabba'i daidai tafiyar doki ɗaya daga murabba'in farawa, hakan yana ba shi damar fara zagayen nan take.
Yawon bude ido:
Idan zakaran ya ziyarci dukkan murabba'ai amma ya ƙare a murabba'i da ba zai iya isa wurin farawa da motsi guda ba.
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 “manifesto na shirye-shirye” a shekarun 1970 ta hannun ɗaya daga cikin kakannin kimiyyar kwamfuta ta zamani, Edsger W. Dijkstra.
A cikin muhimmin aikinsa, Bayanan lura kan shirye-shirye mai tsari (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 “ingantawa mataki-mataki.”
Ƙarfin Janyewa Baya:
A cewar Dijkstra, wannan hanyar tana wakiltar babban mataki na farko wajen inganta tsarin “gwaji da kuskure” zuwa jerin hujjoji marasa kuskure da wani co
tatsuniya da asali:
A cewar labarin, lokacin da mai ƙirƙirar catur, Sissa bin Dahir, ya gabatar da wasan ga Sarkin Indiya, sarkin ya tambaye shi wane lada yake so. Sissa ya yi buƙata mai sauƙi: “Ina so a ba ni hatsi ɗaya na alkama a murabba'in farko na allon catur, biyu a na biyu, huɗu a na uku, kuma a kowane murabba'i na gaba, sau biyu na adadin na baya.” Da farko Sarki ya yi watsi da wannan buƙata, yana tunanin cewa ƙwayoyi kaɗan ne kawai na alkama; duk da haka, lokacin da aka fara lissafi, sai aka gane cewa babu ma'ajiyar kuɗi ko dukkanin alkamar duniya za su wadatar don cika wannan buƙata.
Rikodin Tarihi: Ibn Khallikan (1256)
An rubuta shi a karon farko a shekarar 1256 ta hannun mashahurin marubucin tarihin rayuwa da masanin tarihi Ibn Khallikan. Ibn Khallikan ya haɗa wannan lamari cikin aikinsa ba kawai a matsayin labari ba, har ma a matsayin hujja ta yadda lissafi ke faɗaɗa iyakokin tunani.
Gaskiyar Lissafi:
Wannan buƙatar da aka yi don murabba'ai 64 a kan allo na catur ita ce mafi tsarkin misali na ci gaban lissafi (haɓakar exponential). Adadin da ke kowane murabba'i ana ƙididdige shi ta amfani da ƙa'idar lissafi 2n-1 . Daidaitaccen ƙididdiga da ke bayar da jimillar adadin alkama shine kamar haka:
63
∑
i=0
2i = 264 − ɗaya
Babban adadin da ya biyo bayan wannan lissafi shi ne:
18,446,744,073,709,551,615
Me yasa yake da muhimmanci sosai?
Darasi na dabaru: Wannan matsala darasi ce ta dā ta hikima wadda ke koyar da shugabanni da masu tsara dabaru yadda ƙananan canje-canje (“ninka”) za su iya zama ƙarfafan da ba za a iya sarrafawa ba a tsawon lokaci.
