Question 107
On a large square grid, Marco considers a rectangle 2020 cells long and 2 cells high. He joins every lower-row cell center to every upper-row cell center, using $2020^2$ segments. Segments that intersect, even only at an endpoint, must have different colors.
(a) Prove that 4038 colors are insufficient.
(b) Prove that 4039 colors suffice.
(a) Prove that 4038 colors are insufficient.
(b) Prove that 4039 colors suffice.