The Path To Reach Any Square On The Board From Memory: Colored Patterns For Knights

For me, visualizing patterns leads to faster and more accurate decision making, I find them helpful in committing things to memory. I put this together hoping a few others may find this useful.

The patterns in the figures below are based on the fact that the number of moves it takes to travel between two squares of the same color will always be even, likewise when the target square is a different color it will always be odd. 

Based on this very simple premise its very easy to determine the number of moves to any location. Patterns that follows the Knight around the board make this fast and easy to remember.

At the bottom of this post are diagrams that highlight the change in coverage with a 2nd Knight on the board, based on how far apart their spaced and if they’re on the same or different color.

OBVIOUSLY I’M NOT HIGHLIGHTING SQUARES THAT CAN BE REACHED IN A SINGLE MOVE

Color Coordinates:

# of Moves

Odd   (Travels To Square Of Different Color)

3 = Orange

5 = Red

Even (…. Square Of The Same Color)

2 = Green

4 = Blue

*6 = Unmarked (Traveling to/from a1/h8 or a8/h1 are the ONLY six move coordinates)

**Each Photo I Uploaded Contains Four Figures/Diagrams **

Top Left = Diagram #1

Top Right = Diagram #2

Bottom Left = Diagram #3

Bottom Right = Diagram #4

Diagrams 1-3 illustrate the changes in coverage after two potential moves 

Diagram 4 is an extreme example showing the only square that takes 6 moves & that ten squares now take 5 moves to reach. It also highlights an important exception with the corner and the diagonal connected I will explain below. This diagram might be something useful to know in the End Game for Pawn chasing. 

There are a slew of useful, repeating and often geometric patterns with the Knight that are quite easy to see. As most of them should be self evident from looking at them, I’m only going to discuss a couple.

Just remember that ALL the patterns in diagrams 1-3 are the same and apply to everywhere on the board. The farther you are from the center more of the 4 & 5 move patterns are visible. 

Observations

* First let’s look at diagram #3 with Nd4

- Notice “The Box” of four blue squares. This is very important and you can see it follows the knight around everywhere it goes. The Key Point is that it ALWAYS takes 4 moves to reach a diagonal square that is two spaces away. This also applies to the path of a target square; if you accidentally land on a square that is two diagonals from your target it will take an EXTRA 4 moves. I will illustrate this in an example lower down in the post.

* Diagonals (refer to diagrams #1 & #4

- Diagram #1 illustrates the repeating pattern with diagonals which is as follows: 2,4,2,4,4,4 

1 & 3 squares away = 2 Moves  

All the rest = 4 Moves

As this pattern is for all diagonals, the first 4 move square explains “the box” in diagram #3 and the next one (four diagonals away) is the blue square on h8. Its always the same pattern with more or less being exposed depending on the Knight’s location.

The Diagonal Exception

In diagram #4 there is an exception when the Knight is in the corner

- Moving to OR from a corner and the next diagonal is always 4 moves due to the lack of available squares. Therefore only the one of the diagonals can be reached in 2 moves

Diagrams #1 & #2  illustrate how “the box” with four blue corners affects travel to a target square. Although the Knight can reach any of it’s adjacent squares in 3 moves, one becomes unavailable after the first move. Each of the 4 adjacent squares have 2 moves the knight can land on that are two diagonal spaces away (2 files & 2 ranks). Shown in diagram #2, if the Knight goes to either of the blue squares (f3 & f7) it would take an additional 4 moves to reach the target d5. The other six options can still reach it in two more moves.

Diagram #3 demonstrates that every adjacent square to a Knight has two incoming squares that cannot be reached. Green and red show all eight squares that can move to the target orange square in 1 move, with red denoting the two the Knight can’t reach in 2 moves. The pattern is always the same, the off limit squares are always on the opposite rank or file as the knight which makes them two diagonals away.  

In Diagram #4, the target is the orange square with the green squares showing every move that can land on it. The knights cover every square that can land on blue in 1 move. However, all of them can make a different fist move, utilize the green squares and make it to the orange square on move 3.

Images Below Show Difference In Coverage With 2nd Knight

Changed to a less ambiguous title. Hoping that one or two people that may find it useful stumble across this before it disappears into the abyss of past posts

Busterlark, thank you for the feedback/comments, hope it ends up being useful. I assumed this post got lost in the mix of new topics. I had no idea that anyone had seen it until a couple minutes ago

It's helped me conceptualize a bit about how square coverage works and why knights are usually positioned where they are. So, your work has not gone unappreciated!

But if you wanted more specific feedback, I was also curious what square coverage looks like if the knights are on "usual squares," for example. Knights on c3 and f3 (so many openings employ this). Knights on d2 and f3 (again, a lot of openings). Knights on f3 and g3 (usual in a Ruy Lopez, mirrored in some Sicilians). It was easy enough for me to extrapolate what knight square coverage for those configurations looked like based off of these images already -- but, I mean, if you're looking for more ideas, that's something that I can see being very useful.