Ukongeza kwingxaki ye- knight eyaziwayo kunye nengxaki yokumkanikazi, mininzi eminye imibuzo enomdla kwilizwe lechess. Ndichukumise kwizinto ezimbini ezithandekayo kubhlog langaphambili. Ukuba ujongana nemathematika neengxaki zechess, uya kufumanisa ngokukhawuleza ukuba imathematics inika iimpendulo ezilula nezikhanyayo kwimibuzo emininzi.
Njengomzekelo, ngoku ndiza kunyanga le ngxaki ilandelayo: Jonga ibhodi engenanto, yesiqhelo yechess enamabala angama-64 kwaye ubeke ukumkanikazi omhlophe nakwesiphi na isikhundla \((x,y)\) . Zingaphi izinto ezinokwenzeka ngoku ukumkanikazi?
Sebenzisa iipropathi zebhodi ehambelanayo, siguqula yonke indawo \( (x,y) \in \{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\} \) quadrant esezantsi ekhohlo \( (x',y') \in \{1,2,3,4\} \times \{1,2,3,4\} \) kwaye ukhethe ubuncinci \(z\) kwezi zilungelelaniso zimbini. Okokugqibela sifumana \(7\) oxwesileyo, \(7\) nkqo kunye \( 7 + 2\cdot(z-1)\) amathuba okudibanisa, yiyo loo nto iziphumo:
\[ f:\{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\}, \\ f(x,y) = 2 \cdot \min(-|x-4,5|+4,5; -|y-4,5|+4,5)+19 \]
Umfundi othambekileyo angayandisa ngokulula ingxaki kwiibhodi zechess zesayizi \(n^2\) .