Question 14
Suppose, the seed of any positive integer n is defined as follows:
seed(n) = n, if n < 10
seed(n) = seed(s(n)), otherwise, where s(n) indicates the sum of digits of n.
For example, seed(7) = 7,
seed(248) = seed(2 + 4 + 8) = seed(14) = seed (1 + 4) = seed (5) = 5 etc.
How many positive integers n, such that n < 500, will have seed (n) = 9?
Solution
For seed (n) = 9, all the numbers below 500 must have a digit sum of 9.
These numbers are all divisible by 9.
So total number of numbers below 500 and divisible by 9 is 55.
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