Question 152
Given a foundation that is in a form of a $6\times 6$ square, 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 $3\times 1$. Every layer consists of $12$ bricks and each brick fully covers exactly two gaps of length $1$. Such covering is called *strong*, if every gap is covered by a brick at least in one of the layers. Determine the minimum amount of layers required for a strong covering.
(Bogdan Rublyov)
(Bogdan Rublyov)