In this study I’ll talk about how the knight moves on an open board. You’ll learn how to quickly figure out how to get to any target square in the minimum number of moves.

The red squares can be reach in one move.

You may have been told that knights move in an L shape, but this is WRONG! OK, not totally wrong, but I find it more useful to think of knights moving in an “attack ring” (I just made that up). The knight can move to any of the red squares. Memorize this pattern, and it will be much easier to see all of the possible knight moves at once, instead picturing an L up to 8 times…

Notice that knights always attack from one color square to the opposite color. This is important to remember. It will keep coming up.

The pink squares can be reached in two moves.

Next, let’s see which squares are two moves away. To find them, we simply start at each of the red squares, and jump in the same attack ring pattern from there. The pink squares can be reached in two moves. So far so good.

Notice again that all of the squares that are 2 moves away are the same color. This makes sense, since knights aways jump to a different color.

* Odd number of moves => Opposite color square

* Even number of move => Same color square

The purple squares can be reached in three moves.

Let’s continue this further and see which squares we can get to in three moves. The purple squares can be reached in three moves. Convince yourself this is true by starting at any purple square and picture a knight attack ring around it. You’ll find that there are some pink squares on the ring (which can be reached in two moves), and you can follow the path back through the red square to where we began. Since the knight is on a light square, the purple squares are all dark squares.

You may also notice something is missing… C6, G6, C2, and G2 aren’t colored in! Why? Because it turns out knights have what I call a “blind spot” exactly there. The hole is the same color as our knight, but it can’t be reached in 2 moves. We can verify this, by working backwards. If you start at the hole on C6, picture the knight attack ring, and you’ll find that every square on it is purple (three moves away)

To reach the pink square, first jump to either red square.

Now that’s all well in good, but how can we use this in a game? We’ve learned that any time a piece is close to your knight on the same color square, you can attack it (not capture it) next move.

How? There’s a few patterns you can memorize to make it easier to see how to get to a target square in the quickest possible way. Here’s one. Let’s say you want to get to D5. You can hop through one of the red squares, and you’re there in 2 moves.

Similarly, reach the pink square by jumping through either red square.

Here’s another pattern. You can get E6 in 2 moves through either red square.

The “danger diamond” around a knight.

Because knight moves are symmetric, you can apply these patterns in any direction. With only this memorized, you can picture a “danger diamond” (made up name) around the knight. Any piece that is foolish enough to wander into the pink squares can be attacked (not captured) next move. If we memorize a few more patterns, we can extend the reach of our knight.

Pinwheel pattern.

This one looks like a pinwheel to me, which might help you remember it.

“Cone of sound waves” pattern to travel far.

If your knight has to travel far, it should come as no surprise that you need to first jump as far in that direction as possible. I picture this as a cone of sound waves shooting out of the starting point.

Another “cone of sound waves”.

Similar cone in the diagonal direction.

Now, no same-colored square anywhere near our knight is safe! (except for the blind spot)

Get to the purple square by jumping to either pink square. Get to either pink square through the red square.

Let’s move on to those tricky squares that take 3 moves to get to. How do we get there? There are many ways, but let’s look at one first. It can help to work backwards. Now that we’ve memorized patterns of squares that are 2 moves away, we can picture the attack ring around our target square, and see if any of them look like they can be reached in 2 moves from our starting square.

All of the ways to get to the purple square. First a red square, then pink, then purple.

Here’s all the possible ways to get to E5 in 3 moves. As you can see, you can start with ALMOST any square. Why do you think C3 and G3 are missing from the attack ring? Because, if we go there E5 will be in the knight’s blind spot! Remember from picture #3? If we go to C3 or G3, it’s actually now more difficult to get to E5!! It would take us 5 moves instead of 3. So aside from those squares, any move gets us closer to our goal.

Next from our new square, we look at where the target is in relation and use the patterns we memorized earlier for getting to a square in 2 moves to help us get there. Easy peasy.

The green squares are four moves away.

That’s all well and good if you have a strong knight in a central square, but what if you have a terrible knight in a corner? Well, same principles apply, except sometimes the squares you need are actually off the board, so it takes longer. For example, G2 above would normally be reachable in 2 moves based on where it is in relation to our knight, but here it actually takes 4 moves (remember, same color, always even). The green squares are reachable in four moves.

As you can see, on an open board, in the worst case, the knight takes 6 moves to get to any square. This happens only if it’s the opposite corner, and every other square can be reached in 5 or fewer. That’s quite a long time though, since a passed pawn only takes 5 moves to promote from starting position.

The green squares are four moves away

And, from an almost-corner square, it takes 6 moves to get to the opposite corner, same-color square.

I hope you all learned something from this as I did. Feel free to challenge me to a correspondence game on chess.com 😃. My user name is tonytonev.