Lokacin da injinan ƙarfe ke samar da tarinbututun ƙarfe, suna haɗa su cikin siffofi masu siffar murabba'i don sauƙin jigilar kaya da ƙirgawa. Kowace fakiti tana da bututu shida a kowane gefe. Bututu nawa ne ke cikin kowace fakiti?
Amsa: 3n(n-1)+1, inda n shine adadin bututu a gefe ɗaya na hexagon na waje na yau da kullun. 1) * 6 = bututu 6, da kuma bututu 1 a tsakiya.
Cire tsari:
Kowanne gefe yana ɗauke da bututun n. Mafi girman Layer ɗin ya ƙunshi bututu (n-1) * guda 6, Layer na biyu (n-2) * guda 6, ..., Layer na (n-1) na (n-(n-1)) * 6 = bututu 6, kuma a ƙarshe bututu 1 a tsakiya. Jimilla shine [(n-1) + (n-2) + ... + 1]*6 + 1. Furucin da ke cikin maƙallan yana wakiltar jimlar jerin lissafi (jimillar kalmomin farko da na ƙarshe da aka raba da 2, sannan a ninka su da n-1 don samar da n*(n-1)/2).
Wannan a ƙarshe yana samar da 3n*(n-1)+1.
Tsarin: 3n(n-1)+1 Ana maye gurbin n=8 cikin tsarin: 3×8(8-1)+1 = 24×7+1 = 168+1 = sanduna 169
Lokacin Saƙo: Oktoba-20-2025
