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CAT-2008-Previous Years Paper
Suppose, the seed of any positive integer i is defined as follows: seed(n) = n, if n < 10 = 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)= (1 + 4) = seed = 5 etc. How many positive integers n, such that n < 500, will have seed(n) = 9?
Our answer would be the number of integers between 1 and 500, which are divisible by 9.
The smallest is 9 and the largest is 495.
In the first 499 natural numbers, we have 495 as the last multiple of 9, and this is 55th multiple of 9.