# Coloring the Chess Board v2

This is a follow up question to Coloring the Chess Board

We have 8x8 Chess board like grid (8x8 2D matrix) and we are trying to color every single square/cell. But the rules are interesting;

• You may start from any square you want and color that square for the beginning.
• You can continue coloring another square in the grid which is $$4$$ or $$5$$ squares away from the square you started and colored from and so on (vertically or horizontally).
• You cannot color the same square you colored before or come back again on that.

This time, you are not allowed to start from any square you want; you need to start from a corner square (in other words, in chess language a1,a8,h1,h8).

so

What is the maximum amount of squares you can color with the given rule above now?

We can get

64

Like this:

Fill everything except file e and ranks 4-5.
a1 a6 a2 a7 a3 a8
f8 f3 f7 f2 f6 f1
b1 b6 b2 b7 b3 b8
g8 g3 g7 g2 g6 g1
c1 c6 c2 c7 c3 c8
h8 h3 h7 h2 h6 h1
d1 d6 d2 d7 d3 d8

Fill rank 4
d4 h4 c4 g4 b4 f4 a4 e4

Fill the e-file
e8 e3 e7 e2 e6 e1 e5

Fill the rest of rank 5
a5 f5 b5 g5 c5 h5 d5

• so we dont have to start in the middle :)
– Oray
Commented Dec 5, 2018 at 10:21