Ann and Bob are going to play a game. Ann chooses a two digit numbers from 01-99. Bob then mirrows the number and adds the checksum to this number and announces the result to Ann. The players then alternately continue with this process, while reducing any result mod 100 (hence only two digit numbers will appear). Is it possible that Bob ends up with number 00? If yes, what are the possible numbers for Ann to start with?
Example of a possible sequence: : Ann: 59 -> Bob 95+14=109=09 mod 100 -> Ann 90+9=99