MathDB

Let

n \ge 3

be an integer, and consider a

n \times n

-board, divided into

n^2

unit squares. For all

m \ge 1

, arbitrarily many

1\times m

-rectangles (type I) and arbitrarily many

m\times 1

-rectangles (type II) are available. We cover the board with

N

such rectangles, without overlaps, and such that every rectangle lies entirely inside the board. We require that the number of type I rectangles used is equal to the number of type II rectangles used.(Note that a

1 \times 1

-rectangle has both types.) What is the minimal value of

N

for which this is possible?

Problem Statement