Question

If abc is a three digit number, prove that abc+ bca+ cab is a multiple of 111.

Answer 1

if abc is a three digit number

⇒ abc can be written as 100a + 10b + c

similarly bca can be written as 100b + 10c + a

similarly cab can be written as 100c + 10a + b

abc + bca + cab = 100a + 10b + c + 100b + 10c + a + 100c + 10a + b

⇒ abc + bca + cab = 111a + 111b + 111c

⇒ abc + bca + cab = 111(a + b + c)

⇒ abc + bca + cab is a multiple of 111