Question

a,b, c numere consecutive
a+2=b+1=c
abc+bca+cab=999
a,b,c, = ?

Answer 1

a + 2 = b + 1 = c ⇒ a = c - 2; b = c - 1

abc + bca + cab = 999

100 a + 10 b + c + 100 b + 10 c + a + 100 c + 10 a + b = 999

111 a + 111 b + 111 c = 999

111 × ( a + b + c ) = 999

a + b + c = 999 : 111

a + b + c = 9

( c - 2) + ( c - 1) + c = 9

3 × c = 9 + 1 + 2 = 12

c = 12 : 3

c = 4

a = c - 2 ⇒ a = 4 - 2 ⇒ a = 2

b = c - 1 ⇒ b = 4 - 1 ⇒ b = 3

234 + 342 + 423 = 999 ( corect)