Question

Aflati cifrele a, b, c (in baza 10) stiind ca ab+bc+ca=abc.

Answer 1

10a+b+10b+c+10c+a=100a+10b+c
11(a+b+c)=100a+10b+c
11c-c=100a-11a+10b-11b
10c=89a-b
b=89a-10c
 a,b c cifre dela 1 la 9
pt a=1
c=8, b=9 pt c<8, b>9 nu mai e cifra

pt a=2 b min=198-90>9 nu ai cautam
deci singura solutie este
a=1; b=9; c=8
verificare
19+98+81=100+98=198  Adevarat