MathDB

Alphonse and Beryl play a game starting with a blank blackboard. Alphonse goes first and the two players alternate turns. On Alphonse's first turn, he writes the integer

10^{2011}

on the blackboard. On each subsequent turn, each player can do exactly one of the following two things:
(i) replace any number

x

that is currently on the blackboard with two integers a and b greater than

1

such that

x = ab,

or
(ii) erase one or two copies of a number

y

that appears at least twice on the blackboard.
Thus, there may be many numbers on the board at any time. The first player who cannot do either of these things loses. Determine which player has a winning strategy and explain the strategy.

Problem Statement