Question 146
Given a foundation that is in a form of a rectangle $2m \times 2n$ that is divided into smaller $1 \times 1$ squares. There is a gap of length $1$ between any two adjacent squares. The foundation is covered by several layers of bricks of size $2 \times 1$. Every layer consists of $2mn$ bricks and each brick fully covers exactly one gap of length $1$. Such cover is called *strong*, if every gap is covered by a brick at least in one of the layers. What is the minimum amount of layers that make a strong cover?
(Bogdan Rublyov)
(Bogdan Rublyov)