MathDB

Players

A

and

B

play a "paintful" game on the real line. Player

A

has a pot of paint with four units of black ink. A quantity

p

of this ink suffices to blacken a (closed) real interval of length

p

. In every round, player

A

picks some positive integer

m

and provides

1/2^m

units of ink from the pot. Player

B

then picks an integer

k

and blackens the interval from

k/2^m

(k+1)/2^m

(some parts of this interval may have been blackened before). The goal of player

A

is to reach a situation where the pot is empty and the interval

[0,1]

is not completely blackened. Decide whether there exists a strategy for player

A

to win in a finite number of moves.

Problem Statement