MathDB

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 Statement