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 Erdös wins! by broll)

Excellent, Broll!  Very nice problem, Ady.

Posted by Steve Herman on 2017-05-28 09:58:54