MathDB

5

Part of 2017 Regional Olympiad of Mexico Northeast

Problems(1)

no of ways to arrange numbers 1-1000 on 2x500 grid , each 2x2 is ordered

Source: Mathematics Regional Olympiad of Mexico Northeast 2017 P5

9/21/2022
The figure shows a 2×22\times 2 grid that has been filled with the numbers a,b,ca, b, c, and dd. We say that this grid is ordered if it is true that a>b>c>da > b > c > d or that a>d>c>ba > d > c > b.
\begin{tabular}{|l|l|} \hline a & b \\ \hline d & c \\ \hline \end{tabular} In how many ways can the numbers from 11 to 10001000 be arranged in the cells of a 2×5002 \times 500 grid (22 rows and 500500 columns) so that each 2×22 \times 2 sub-grid is ordered?
combinatorics