Question 78
On a $7\times7$ board, four cells marked $X$ form a castle if they are the vertices of a rectangle whose sides are parallel to those of the board, as shown:
a) Mark 21 cells of the $7\times7$ board with $X$ so that no castle is formed.
b) Prove that any choice of 22 marked cells contains a castle.
a) Mark 21 cells of the $7\times7$ board with $X$ so that no castle is formed.
b) Prove that any choice of 22 marked cells contains a castle.