Question

abcd+abc+ab+a=8502,abcd=?

Answer 1

abcd+abc+ab+a=8502

numerele sunt scrise in baza 10; de ex 754=7•100+5•10+4

a,b,c,d<10;  (abcd=1000a+100b+10c+d)

=> (1000a+100b+10c+d)+(100a+10b+c)+(10a+b)+a=8502

1111a + 111b + 11c +d =8502

a=1; nu poate fi 8 pt ca 1111•8=8888

a nu poate fi 6 pt  ca b,c,d <10

=> 111b+11c+d=8502-7777

111b+11c+d=725

=> b=6

11c+d=725-666

11c+d=59

=>c=5 si d=59-55

d=4

a=7;  b=6;  c=5;  d=4

abcd=7654

verificare: 7654+765+76+7=8502