Question

Determinati numarul abc barat pentru care abc barat=ab+bc+ca

Answer 1

Răspuns:

abc=100a+10b+c

100a+10b+c=ab+bc+ca

100a+10b+c=10a+b+10b+c+10c+a

100a-10a-a=10b+b-10b+10c+c-c=>89a=10c+b

10c+b ≤ 99 unde c=9,b=9 =>a=1

89=10c+b=>descompunem pe 89=10·8+9=>c=8,b=9

a=1,b=8,c=9=> numarul 189