Statement

In the School of Reverse Education, the kids already know how to multiply 10-digit numbers in their heads, and now they are learning to write decimal digits on paper. The professor asks them to do the following task: given a positive integer K, write down its multiples K, 2K, 3K, …, until all digits from 0 to 9 occur at least once on the paper. For example, if K = 13, they have to write down 8 integers: 13, 26, 39, 52, 65, 78, 91, 104. It can be proved that, for any positive integer K, the process will end at some point. There are N kids in the class and everyone gets a different starting number K_i (i = 1, 2, …, N). Can you tell how many numbers each kid has to write down?