Ibhalansi Yepani Nezisindo – 3
Ibhalansi yepani ikutshela ukuthi izinhlangothi zayo ezimbili zinesisindo esifanayo noma ukuthi uhlangothi olulodwa lusinda kunolunye.
INSELELE
Uneqoqo elikhulu kakhulu lezisindo ezingama-ounces angu-4 kanye nama-ounces angu-7 ongazisebenzisa ezinhlangothini zombili zebhalansi yepani. Ungakala into engama-ounces angu-3 ngokusebenzisa isisindo esingama-ounces angu-4 kanye nento ngakolunye uhlangothi kanye nesisindo esingama-ounces angu-7 kolunye. Yiziphi izisindo ongazikala kahle nokuthi yiziphi ongakwazi ukuzikala kahle?
ISIVIVINYO
Imiphumela yakho ishintsha kanjani uma unezisindo ezingama-ounces angu-5 no-9? Kuthiwani ngezinye izisindo ezingenaso isihlukanisi esivamile esingaphezu kuka-1? Ungazithola yini iziphethini kudatha yakho? Bekungenzekani uma ubunezinhlobo ezintathu zezisindo ongazisebenzisa - ake sithi ama-ounces angu-3, ama-ounces angu-4, nama-ounces angu-7?
amanothi
INSELELE
Ukuvumela izisindo ezinhlangothini zombili zebhalansi yepani kufana nokuvumela ukuphindaphinda okuhle nokubi kwezinombolo zombili. Isibonelo, ake sithi silinganisa into ngokubeka into ngesisindo esisodwa sama-ounces angu-7 ohlangothini olulodwa kanye nezisindo ezintathu zama-ounces angu-4 kolunye uhlangothi. Isibalo sithi + 1 x 7 = 3 x 4. Ukubeka i-multiple ka-7 ngakolunye uhlangothi kunikeza = 3 x 4 – 1 x 7 = 5. Sidale i-multiple engemihle ka-7 ngokuyibeka epanini elifanayo nento.
Ngakho-ke, sibheka zonke izinombolo ezingadalwa ngokungeza noma yikuphi ukuphindaphinda (okuqondile, okungu-zero, noma okungekuhle) kuka-4 kunoma yikuphi ukuphindaphinda kuka-7. Lokhu kubizwa ngokuthi i-Theorem kaBezout. I-Theorem ithi isethi yazo zonke izamba ezingaba khona zokuphindaphinda kwezinombolo ezimbili iyisethi yazo zonke izinombolo eziningi ze-common divisor yazo enkulu kakhulu. Ngoba i-common divisor enkulu kakhulu ka-4 no-7 ingu-1, kulokhu singakala yonke inombolo ye-ounce eyodwa, okuyizinombolo zonke.
Enye indlela yokubona ukuthi lokhu kuyiqiniso ukusebenzisa i-Chicken McNugget Theorem evela ku-“Pan Balance with Weights – 1.” Ake sithi izinombolo ezimbili zingu-n no-m. Kusukela kuleyo theorem, siyazi ukuthi sisebenzisa ama-multiples angewona ama-negative kuphela, singashaya isisindo ngasinye siqala ngo-(n – 1) x (m – 1). Ikakhulukazi, singabhala isisindo (nxm) – 1 njengesamba se-multiple ka-n kanye ne-multiple ka-n. Bese u-1 = [(nxm) – 1] – nxm usitshela ukuthi u-1 angabhalwa njengesamba se-multiples ka-n no-m.
ISIVIVINYO
Ngenxa yokuthi u-5 no-9 bane-divisor evamile kakhulu ka-1, singalinganisa wonke amanani ngalezi zinsimbi futhi.
Uma ubunezisindo ezintathu ezinenani okungenani elilodwa elinesihlukanisi esivamile esingu-1, ubungakwazi ukukala zonke izisindo ezingaba khona futhi ubuzoba nezinketho eziningi zokuthi ungakwenza kanjani.