Nā Puzzles o ka Pule

KA PILI

He mea pono e hoʻomaopopo, ʻaʻole ia he mea nui pehea mākou e hoʻopili ai i nā helu ma ke kolamu hoʻokahi, ke kolamu ʻumi, a me ke kolamu haneli, no laila he mea hoʻokahi ia e noʻonoʻo ai.

E hoʻomaopopo he 45 ka huina o nā huahelu āpau mai ka 1 a i ka 9. Mai kahi ʻāpana o ke kumumanaʻo helu (e noʻonoʻo "e hoʻolei ana i nā 9"), no ka mea, ʻo ka huina o nā huahelu he hoʻonui o 9, ʻo ka huina hopena o nā helu ʻekolu huahelu ʻekolu he hoʻonui o 9. No laila, ʻo ka helu kokoke loa a mākou e manaʻolana ai ʻo 999, me 1008, a me 990 e hele kokoke mai ana ma hope o kēlā.

I mea e kokoke ai i ka 1000, makemake mākou i ke kolamu haneli e hoʻohui i ka 8 a i ʻole 9. No laila, noʻonoʻo mākou i kēlā mau hihia ʻelua.

Hihia 1: ʻO ka huina o ke kolamu haneli he 8 (ʻo ia hoʻi he 1 + 2 + 5 a i ʻole 1 + 3 + 4). I kēia hihia, makemake mākou i ka huina o nā helu ʻelua huahelu ʻekolu i loko o ke kolamu ʻumi a me nā ʻekahi e kokoke i ka 200. I kēlā hihia, makemake mākou i ka huina o nā huahelu ʻumi he 18, 19, a i ʻole 20 - ʻo ka huina like o nā huahelu ʻekahi he 45 - (8 + 18) = 19, 45 - (8 + 19) = 18, a me 45 - (8 + 20) = 17. ʻO ka huina holoʻokoʻa e pili ana i kēia mau hiʻohiʻona ʻekolu, ʻo ia hoʻi 999, 1008, a me 1017.

ʻAʻole hiki iā mākou ke hana i kahi ʻoi aku ka maikaʻi ma mua o 999. Makemake mākou e hoʻohui nā helu haneli i ka 8, nā helu ʻumi i ka 18, a me nā helu hoʻokahi i ka 19. Eia kekahi mau pane hoʻohālike: 152 + 368 + 479 = 999 a me 194 + 237 + 568 = 999.

Hihia 2: ʻO ka huina o ke kolamu haneli he 9. I kēia hihia, makemake mākou i ka huina o nā helu ʻelua huahelu ʻekolu i loko o ke kolamu ʻumi a me nā ʻekahi e kokoke i ka 100 e like me ka hiki. Eia nō naʻe, no ka mea ua hui pū nā helu haneli a hiki i ka 9, ʻo nā helu ʻekolu liʻiliʻi loa no ke kolamu ʻumi e hiki ke hui pū ʻia he 21 - 9 = 12 (loaʻa ka 21 mai ka huina o nā helu mai 1 a 6). No laila, he mea ʻole kēia.