MathDB

Olya and Tolya are playing a game on

[0,1]

segment. In the beginning it is white. In the first round Tolya chooses a number

0 \leq l \leq 1

, and then Olya chooses a subsegment of

[0,1]

of length

l

and recolors every its point to the opposite color(white to black, black to white). In the next round players change roles, etc. The game lasts

2024

rounds. Let

L

be the sum of length of white segments after the end of the game. If

L > \frac{1}{2}

Olya wins, otherwise Tolya wins. Which player has a strategy to guarantee his win? A. Naradzetski

Problem Statement