Inkinga encane chess

Ngaphezu kwenkinga ye- knight eyaziwayo nenkinga yabesifazane, kuneminye imibuzo eminingi ethokozisayo emhlabeni we-chess. Ngithinte izinto ezimbili ezincane ezibalulekile ezifakiwe ekubhaleni ngaphambili kwebhulogi . Uma ubhekana nezinkinga ze-chess ngokwezibalo, uthola ngokushesha ukuthi izibalo zinikeza izimpendulo ezilula futhi ezikhanyisayo zemibuzo eminingi.


Njengesibonelo, manje ngizobhekana nale nkinga elandelayo: Bheka ibhodi elingenalutho, elijwayelekile le-chess elinamasimu angama-64 bese ngibeka indlovukazi emhlophe kunoma yisiphi isikhundla \((x,y)\) . Ngabe intokazi inezinyathelo ezingaki?

Sisebenzisa izakhiwo zokulinganisa zebhodi, siguqula onke amaphoyinti \( (x,y) \in \{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\} \) emaphephandabeni wayo endaweni ephansi ngakwesobunxele \( (x',y') \in \{1,2,3,4\} \times \{1,2,3,4\} \) bese ukhetha ubuncane \(z\) kwezixhumanisi ezimbili. Ekugcineni, sithola \(7\) ovundlile, \(7\) mpo kanye \( 7 + 2\cdot(z-1)\) ukuhamba kwe-diagonal, yingakho:

\[ f:\{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\}, \\ f(x,y) = 2 \cdot \min(-|x-4,5|+4,5; -|y-4,5|+4,5)+19 \]

Isifundi esithambekele singayandisa kalula le nkinga kumabhodi we-chess osayizi \(n^2\) .

Emuva