MathDB

The figure shows a

2\times 2

grid that has been filled with the numbers

a, b, c

, and

d

. We say that this grid is ordered if it is true that

a > b > c > d

or that

a > d > c > b

.
\begin{tabular}{|l|l|} \hline a & b \\ \hline d & c \\ \hline \end{tabular} In how many ways can the numbers from

1

1000

be arranged in the cells of a

2 \times 500

grid (

2

rows and

500

columns) so that each

2 \times 2

sub-grid is ordered?

Problem Statement