KVPY SA Exam 2014 Question Paper

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