Ina whakaputahia e ngā mira maitai he puranga ongā paipa maitai, ka paiherea kia rite ki ngā āhua hexagonal kia māmā ake ai te kawe me te tatau. E ono ngā paipa o ia paipa i ia taha. E hia ngā paipa kei roto i ia paipa?
Whakautu: 3n(n-1)+1, ko n te maha o ngā paipa i te taha kotahi o te tapaono pūmau o waho rawa. 1) * 6 = 6 paipa, me te 1 paipa i waenganui.
Te whakaputanga tātai:
Kei ia taha ngā paipa e n. Kei roto i te paparanga o waho rawa ko (n-1) * 6 paipa, ko te paparanga tuarua (n-2) * 6 paipa, ..., ko te paparanga (n-1) (n-(n-1)) * 6 = 6 paipa, ā, i te mutunga ko te paipa kotahi kei waenganui. Ko te tapeke ko [(n-1) + (n-2) + ... + 1]*6 + 1. Ko te kīanga kei roto i ngā pūwero e tohu ana i te tapeke o tētahi raupapatanga tātai (ko te tapeke o ngā kupu tuatahi me ngā kupu whakamutunga ka wehea ki te 2, kātahi ka whakareatia ki te n-1 hei hua ko te n*(n-1)/2).
Ko te mutunga iho, ko te 3n*(n-1)+1 te hua.
Tātai: 3n(n-1)+1 Whakakapia a n=8 ki te tātai: 3×8(8-1)+1 = 24×7+1 = 168+1 = 169 ngā rākau
Wā tuku: Oketopa-20-2025
