Some cells of a $10\times10$ board are marked so that each cell has an even number of neighboring (i.e. sharing a side) marked cells. Find the maximum possible number of marked cells.
Source: Mongolia MO 2001 Grade 10 P6
Tags: combinatorics
Some cells of a $10\times10$ board are marked so that each cell has an even number of neighboring (i.e. sharing a side) marked cells. Find the maximum possible number of marked cells.