Nā Puzzles o ka Pule

KA PILI

E kākau wau i ka huaʻōlelo ma A/B x C/D i mea e maʻalahi ai ke kamaʻilio ʻana.

Māhele 1: A/B x C/D = 2/3. E hoʻonui i nā ʻaoʻao ʻelua me 3 x B x D, no laila lilo kēia i 3 x A x C = 2 x B x D. E nānā i kēia me ka hoʻohana ʻana i nā kumu mua 2 a me 3 - pono kēia mau mea e kaulike ma nā ʻaoʻao ʻelua o ka hoohalike. Mai 3, 6, 9, loaʻa iā mākou ʻehā mau kumu o 3 e hana pū me. Mai 2, 4, 6, 8 loaʻa iā mākou ʻehiku mau kumu o 2 e hana pū me. Aia ʻelua mau hihia no ka lawelawe ʻana i nā 3.

• Hihia 1: ʻAʻole ʻo A a ʻo C paha he 3 a i ʻole 6, a ʻo B he 3 a i ʻole 6.
  • B=3: 3 x A x C = 2 x 3 hoʻemi ʻia ka x D i A x C = 2 x D. ʻO nā hopena no kēia he 1 x 4 = 2 x 2, 1 x 8 = 2 x 4.
  • B=6: 3 x A x C = 2 x 6 x D hoʻemi ʻia i A x C = 4 x D. ʻO ka hopena no kēia he 1 x 8 = 4 x 2.
• Hihia 2: ʻO A he 3 a i ʻole 6, a ʻo B he 9.
  • A=3: 3 x 3 x C = 2 x 9 x Hoʻemi ʻia ʻo D i C = 2 x D - ʻo nā koho no (C, D) ʻo ia (2, 1), (4, 2), a me (8, 4).
  • A=6: 3 x 6 x C = 2 x 9 x Hoʻemi ʻia ʻo D i C = D, he mea hiki ʻole ia.

No laila, ua hāʻawi ʻia nā hopena i ka pilikia:

• (1 x 4) / (3 x 2)
• (1 x 8) / (3 x 4)
• (1 x 8) / (6 x 2)
• (3 x 2) / (9 x 1)
• (3 x 4) / (9 x 2)
• (3 x 8) / (9 x 4)

Māhele 2: A/B x C/D ~ 5/11. E hoʻonui i nā ʻaoʻao ʻelua me 11 x B x D e hoʻolilo i kēia i 11 x A x C ~ 5 x B x D. Makemake mākou e ʻimi i nā huahelu he 11 e kokoke ana i nā huahelu he 5 a hiki ke hana ʻia me ka hoʻohana ʻana i ka 1 a i ka 9.

Eia ka papa inoa e noʻonoʻo ai. He mau huina kēia i kaʻawale i ka 1 a hiki ke hana ʻia me ka hoʻohana ʻana i ka 1 a i ka 9: 11 x 4 ~ 8 x 5; 11 x 9 ~ 20 x 5; a me 11 x 16 ~ 35 x 5. ʻOi aku ka nui o nā helu, ʻoi aku ka maikaʻi, no laila e nānā kākou i kēia mea hope loa.

(2 x 8) / (5 x 7) = 16 / 35 ua kokoke loa i ka 5/11 - ʻokoʻa lākou ma 1 / (35 x 11) = 1 / 385.

Malia paha e ʻoi aku ka maikaʻi o nā huina i ʻelua a ʻekolu paha ke kaʻawale? ʻAʻohe moho e like me ka hoʻomaikaʻi ʻana.