Question 7
A grid has 1000 columns and n rows, where n is odd and greater than 2020. A white bug starts in one corner; black chess bishops occupy the two nearest corners. The bug moves one cell horizontally or vertically, or by a knight’s move. It must reach the opposite corner, visiting every cell not occupied or attacked by a bishop exactly once and never visiting a forbidden cell. Prove that the number of such routes is independent of n.