5

Part of 1997 Israel Grosman Mathematical Olympiad

Problems(1)

max no of partitions of an n x n square

Source: Israel Grosman Memorial Mathematical Olympiad 1997 p5

Consider partitions of an

n \times n

square (composed of

n^2

unit squares) into rectangles with one integer side and the other side equal to

1

. What is the largest possible number of such partitions among which no two have an identical rectangle at the same place?

combinatoricscombinatorial geometry