Given a $3\times 3$ grid, we call the remainder of the grid an “angle” when a $2\times 2$ grid is cut out from the grid. Now we place some angles on a $10\times 10$ grid such that the borders of those angles must lie on the grid lines or its borders, moreover there is no overlap among the angles. Determine the maximal value of $k$, such that no matter how we place $k$ angles on the grid, we can always place another angle on the grid.
Problem
Source: China south east mathematical olympiad 2013 problem7
Tags: combinatorics unsolved, combinatorics
