MathDB

On each cell of a

2005\times2005

chessboard, there is a marker. In each move, we are allowed to remove a marker that is a neighbor to an even number of markers (but at least one). Two markers are considered neighboring if their cells share a vertex.
(a) Find the least number

n

of markers that we can end up with on the chessboard. (b) If we end up with this minimum number

n

of markers, prove that no two of them will be neighboring.

Problem Statement