Given an integer, n, find the smallest integer m such that is divisible by n (i.e.n, is a factor of m ) and satisfies the following properties:
- m must not contain zeroes in its decimal representation.
- The sum of m's digits must be greater than or equal to the product of m's digits. Given n, find the number of digits in m's decimal representation.
Note: n is not divisible by 10.
How should I derive the Recurrence Relation for this problem?
My approach: Suppose the n = 32, I am multiplying n by 1,2,3... and checking for the number at the units place if the number at the unit's place is greater than the largest digit of n and the number at the tens digit is greater than smallest digit of n then I ignore the m generated and move to the next multiplication.
I am not able to come up with the recurrence relation for doing this operation. Please Help! Thanks!