MathDB

On a

49\times 69

rectangle formed by a grid of lattice squares, all

50\cdot 70

lattice points are colored blue. Two persons play the following game: In each step, a player colors two blue points red, and draws a segment between these two points. (Different segments can intersect in their interior.) Segments are drawn this way until all formerly blue points are colored red. At this moment, the first player directs all segments drawn - i. e., he takes every segment AB, and replaces it either by the vector

\overrightarrow{AB}

, or by the vector

\overrightarrow{BA}

. If the first player succeeds to direct all the segments drawn in such a way that the sum of the resulting vectors is

\overrightarrow{0}

, then he wins; else, the second player wins. Which player has a winning strategy?

Problem Statement