# Pilikia chess liʻiliʻi1114

Ma waho aʻe o ka pilikia naita naita kaulana a me ka pilikia mōʻī wahine, nui nā nīnau pīhoihoi ʻē aʻe i ka honua o ka mōkākā. Ua hoʻopā wau i kekahi mau ʻike liʻiliʻi i loko o kahi hoʻokomo blog ma mua. Inā pili ʻoe i ka makemakika me nā pilikia chess, ʻike koke ʻoe i ka makemakika i nā pane maʻalahi a hoʻomālamalama hoʻi no nā nīnau he nui.

Ma ke ʻano he laʻana, e mālama wau i kēia pilikia: nānā ʻoe i kahi papa chess manuahi ʻole me 64 mau māla a hoʻonoho i kahi mōʻī wahine keʻokeʻo i kēlā me kēia kūlana $$(x,y)$$ . Ehia mau neʻe hiki i ke mōʻī wahine i kēia manawa?

Ke hoʻohana nei i nā kumu hoʻohālikelike o ka papa, hoʻololi mākou i kēlā me kēia kiko $$(x,y) \in \{1,2,3,4,5,6,7,8\} \times \{1,2,3,4,5,6,7,8\}$$ i kona ʻaoʻao ma ka quadrant hema hema $$(x',y') \in \{1,2,3,4\} \times \{1,2,3,4\}$$ a koho i ka palena iki $$z$$ nā kuhi ʻelua. I ka pae hope loa e loaʻa iā $$7$$ papamoe, $$7$$ ʻākau a me $$7 + 2\cdot(z-1)$$ nā diagonal hiki, no laila kēia hopena:

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

Hiki i ka mea heluhelu makemake hoʻonui maʻalahi i ka pilikia i nā papa chess o ka nui $$n^2$$ .

Hope