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 a_i to Erdös, who then chooses a non negative integer b_i, and then Oleg defines a_i+1 = |a_i-b_i| or a_i+1 = a_i + b_i.
Erdös wins if a₂₀ is a power of 10, otherwise Oleg wins.

Who is the winner, Oleg or Erdös?

(In reply to my solution by Daniel)

Hint: -   no way,   Oleg is the loser.

Please, give it a retry, prior to seeing the official solution, I'll wait. 

Posted by Ady TZIDON on 2017-05-27 05:39:08