Question 72
Davide plays the following game. He starts with an integer between 1 and 99, and at each move replaces his current number $n$ by the number formed by the last two digits of $51n+50$ (or just the last digit if the tens digit is 0). What is the maximum number of different numbers he can obtain during the first 100 moves of a single game?
(A) 2
(B) 4
(C) 51
(D) 99
(E) 100
(A) 2
(B) 4
(C) 51
(D) 99
(E) 100