Question

Aflati numarul de trei cifre abc scris in baza 10 stiind ca a, b, c sunt cifre nenule distincte doua cate doua si a,bc +b,ca+c,ab=6,66. REPEDEE VA ROOOG!! DAU COROANA SI 50 DE PUNCTE!! ​

Answer 1

Răspuns:

Explicație pas cu pas:

$a,bc +b,ca+c,ab=6,66,~~\dfrac{abc}{100}+\dfrac{bca}{100} +\dfrac{cab}{100}=\dfrac{666}{100} ,~~\dfrac{abc+bca+cab}{100}= \dfrac{666}{100} ,~~deci~ abc+bca+cab=666,~100a+10b+c+100b+10c+a+100c+10a+b=666$

Deci 111a+111b+111c=666, ⇒111·(a+b+c)=666, ⇒a+b+c=6

abc∈{123, 132, 213, 231, 312, 321}