MathDB

Let

Z

shape be a shape such that it covers

(i,j)

(i,j+1)

(i+1,j+1)

(i+2,j+1)

and

(i+2,j+2)

where

(i,j)

stands for cell in

i

-th row and

j

-th column on an arbitrary table. At least how many

Z

shapes is necessary to cover one

8 \times 8

table if every cell of a

Z

shape is either cell of a table or it is outside the table (two

Z

shapes can overlap and

Z

shapes can rotate)?

Problem Statement