abc + ab + bc + ca + a + b + c = 29 ⇒ abc + ab + bc + ca + a + b + c + 1 = 30 ⇒ (a + 1) (b + 1) (c + 1) = 30 Product can be 2 × 3 × 5 ⇒ digits are 1, 2, 4 so possible number = 3! = 6 Product can be 1 × 5 × 6 ⇒ digits are 0, 4, 5 so possible number = 2 × 2! = 4 Product can be 1 × 3 × 10 ⇒ digits are 0, 2, 9 so possible number = 2 × 2! = 4 Total numbers = 14