Prove the lead wins the game
Source: 2009 Korean MO #5
March 29, 2009
analytic geometrycombinatorics proposedcombinatorics
Problem Statement
There are m \plus{} 1 horizontal lines and vertical lines on the plane so that m(m \plus{} 1) intersections are made.
A mark is placed at one of the points of the lowest horizontal line.
2 players play the game of the following rules on this lines and points.
1. Each player moves a mark from a point to a point along the lines in turns.
2. The segment is erased after a mark moved along it.
3. When a player cannot make a move, then he loses.
Prove that the lead always wins the game.
PS I haven't found a student who solved it. There can be no one.