Oleg and (the ghost of) Erdös play the following game. Oleg chooses a non- negative integer a1 with at most 1000 digits.
In Round i the following happens:
Oleg tells the number ai to Erdös, who then chooses a non negative integer bi, and then Oleg defines ai+1 = |ai-bi| or ai+1 = ai + bi.
Erdös wins if a20 is a power of 10, otherwise Oleg wins.
Who is the winner, Oleg or Erdös?
(In reply to my solution
Hint: - no way, Oleg is the loser.
Please, give it a retry, prior to seeing the official solution, I'll wait.