Nā Huinaha Kilokilo – 4
I loko o kahi Huina Kilokilo, ua hui pū nā lālani, nā kolamu, a me nā diagonals i ka helu like. ʻAʻole kēia huina mua he Huina Kilokilo. ʻO ka lua he Huina Kilokilo me ka huina mau o 12.
KA PILI
E hoʻopiha i kēia mau huinaha kilokilo ʻelua me ka hoʻohana ʻana i kēia mau helu ʻelua: 1) {6, 7, 8, 9, 10, 11, 12, 13, 14} a me {3, 6, 9, 12, 15, 18, 21, 24, 27}.
HE ʻAHOLAHA
E nānā i nā Kiʻikuhi Magic a pau āu i ʻike ai ʻaʻohe o lākou mau komo pālua. E hana i kahi papa o kāu mau hopena a e nānā i nā ʻano. Inā hāʻawi ʻia ʻoe i kekahi kaʻina helu ʻē aʻe i hoʻokaʻawale like ʻia, e like me {4, 9, 14, 19, 24, 29, 34, 39, 44}, hiki anei iā ʻoe ke hoʻopiha koke i ka Kiʻikuhi Magic?
Notes
KA HOʻOPIʻI A ME KA ʻIMI ʻANA
E hoʻomaka me ka hoʻonā ʻana i ka mana maʻamau 1 - 9 o kēia puzzle.
No ka hana ʻana i kahi Huinaha Kilokilo me 6 a 14, e hoʻohui wale i 5 i kēlā mau komo āpau. No ka hana ʻana i kahi Huinaha Kilokilo no {3, 6, 9, 12, 15, 18, 21, 24, 27}, e hoʻopili wale i nā komo āpau o ka hopena mua.
E nānā kākou i ke kumu e hana ai kēlā. Manaʻo mākou he a + b + c = S kā mākou, kahi ʻo S ka huina i hoʻohana ʻia no nā lālani, nā kolamu, a me nā diagonals āpau. Ma ka puzzle 1 - 9 mua, ʻo S he 15.
Inā hoʻohui kākou i 5 i nā helu āpau, (a + 5) + (b + 5) + (c + 5) = (a + b + c) + 15 = S + 15. ʻO ka huina o nā helu i loko o ka puzzle hou he 15 ka nui aʻe ma mua o ka mea mua, no laila ua like nō ka helu o nā helu a pau (hou).
Inā hoʻonui kākou i ka 3, a laila (3a) + (3b) + (3c) = 3(a + b + c) = 3S. ʻO ka huina o nā mea i loko o ka puzzle hou he ʻekolu manawa ia o ka huina mua.
Inā mākou e hana i kekahi hui pū ʻana o ka hoʻonui ʻana a me ka hoʻohui ʻana, hana mau ia. Manaʻo mākou e hoʻonui mākou me m a laila hoʻohui iā n. Loaʻa iā mākou (ma + n) + (mb + n) + (mc + n) = (ma + mb + mc) + (n + n + n) = m (a + b + c) + 3n = mS + 3n. No laila, ʻaʻohe mea he aha ʻo m a me n, ʻo nā mea hou e hoʻohui pū ana i ka mea like!
ʻOiaʻiʻo, ʻaʻole mākaukau kāu mau haumāna no kēia algebra, akā ma ka hele ʻana i kēia mau laʻana e ʻike lākou i nā ʻano o ke ʻano o kēia hana