Nā ʻĀpana Huinahā
Loaʻa iā ʻoe ʻelua mau puʻupuʻu. No kahi huinahā 1 ma ka n, ehia mau ala e hiki ai iā ʻoe ke hoʻopiha iā ia me ka hui ʻana o nā huinahā 1 ma ka 1 a me nā huinahā 1 ma ka 2? No kahi huinahā 2 ma ka n, ehia mau ala e hiki ai iā ʻoe ke hoʻopiha iā ia me nā huinahā 1 ma ka 2?
KA PILI
No ke aha i hāʻawi like ai kēia mau puzzle ʻelua i nā pane like? He aha nā pane ke lōʻihi nā huinahā i hoʻopiha ʻia he 10? Pehea lā ke lōʻihi lākou he 20?
HE ʻAHOLAHA
Pehea e like ai kēia mau pilikia ʻelua kekahi i kekahi a me nā puʻupuʻu mua? Pehea e loli ai nā mea i loko o ka puʻupuʻu 1 ma ka n inā hoʻohana mākou i ka 1 ma ka 1 a me ka 1 ma 3 mau ʻāpana? Pehea e loli ai nā mea i loko o ka puʻupuʻu 1 ma ka n inā hoʻohana mākou i ka 1 ma ka 1, 1 ma ka 2, a me ka 1 ma 3 mau ʻāpana?
Notes
KA PILI
He mākaukau ikaika ka ʻike ʻana pehea e hoʻopili ai i nā hopena mua i kahi ʻāpana a i ʻole kahi puzzle hou āpau.
Ua like loa ke ʻano o kēia mau puʻupuʻu ʻelua. ʻO nā ʻāpana kū pololei ma ka huinahā 2 xn e pili ana i nā ʻāpana 1 ma ka 1 ma ka huinahā 1 xn, a ʻo nā ʻāpana moe ma ka huinahā 2 xn e pili ana i nā ʻāpana 1 ma ka 2 ma ka huinahā 1 xn. No laila, ʻaʻohe ʻokoʻa maoli ma waena o nā puʻupuʻu ʻelua.
Eia kekahi, ua like loa ka puzzle huinahā 1 xn me ka puzzle ʻanuʻu ma "Fibonacci - 2." ʻO ka hele ʻana i hoʻokahi ʻanuʻu i ka manawa ua like ia me ke kau ʻana i kahi huinahā 1 ma ka 1, a ʻo ka hele ʻana i ʻelua ʻanuʻu i ka manawa ua like ia me ke kau ʻana i kahi huinahā 1 ma ka 2. Ua like nā puzzle ʻelua, no laila ua like ka nānā ʻana a me nā hopena.
HE ʻAHOLAHA
Inā mākou e hoʻohana i nā huinahā 1 ma ka 1 a me 1 ma ka 3, nui nā loli. E nānā i nā waiwai mua a noʻonoʻo pehea lākou e helu ʻia ai. Loaʻa iā mākou ka 1, 1, 2, 3, 4, 6, a me 9 no nā waiwai mua. Ma keʻano laulā, ʻo ka waiwai aʻe ka huina o ka waiwai o kēia manawa a me hoʻokahi ʻanuʻu ʻelua ma mua o kēlā. He maʻalahi ka helu ʻana, akā ʻaʻole ia he moʻo Fibonnaci hou.
Inā mākou e hoʻohana i ka 1 ma ka 1, 1 ma ka 2, a me ka 1 ma ka 3, e loli nui nā mea. I kēia manawa, hāʻawi ʻia nā waiwai mua e 1, 2, 4, 7, 13, a me 24. ʻO ka waiwai aʻe ma ke kaʻina hana, ʻo ia ka huina o nā waiwai ʻekolu ma mua.
ʻO nā moʻo e like me kēia e wehewehe ana i kā lākou mau huaʻōlelo aʻe e kahi ʻano i hoʻonohonoho ʻia e pili ana i nā huaʻōlelo ma mua ua kapa ʻia ʻo nā moʻo recursive. ʻAʻole ʻo nā Helu Fibonacci wale nō ka moʻo recursive, akā ʻo lākou paha ka mea kaulana loa.