x < 100, such that
n = 100·q + x. 3.a) To determine which sublist each account number is allocated to, you need to find
the remainder when the account number is divided by 100. For the account number n,
saying that n mod 100 = x is equivalent to saying that there are integers q
and x, with 0x < 100, such that
n = 100·q + x.
i) 2473871 would be allocated to the sublist 71.
ii) 3569842 would be allocated to the sublist 42.
iii) 9085000 would be allocated to the sublist 0.
iv) 8574642 would be allocated to the sublist 42.
b) The function H is not one-to-one. Any two account numbers which have the same final two digits will be allocated to the same sublist. See for example parts ii) and iv) in part a).