Question

Sa se determine numerele de forma abc, cu a,b,c cifre distincte pentru care are loc egalitatea: abc-cba=495

Answer 1

abc=100a+10b+c
cba=100c+10b+a
abc-cba=(100a+10b+c)-(100c+10b+a)=495
100a+10b+c - 100c-10b - a=495
99a -99c=495
99(a-c)=495
a-c=495/99
a-c=5
a=9 ⇒  9-5=c⇒c=4
a=8 ⇒ 8-5=c⇒c=3
a=7⇒  7-5=c⇒c=2
a=6⇒  6-5=c⇒c=1
si b= 0,1,2,3,4,5,6,7,8,9

nr sunt:904, 914,924,944,954,964,974,984
            803,813,833,843,843,863,873,893
            703,723,732,742,752,762,782,792
            601,621,631,641,651,661,681,691