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Lesson 4 of 8

Knight distance: how many jumps between two squares

With the knight, "right next to" does not mean "close". Learn the traps, the rhythms and the parity check.

Take the interactive lessonThe 1-minute video, quick questions, then the real drill. The article below is the full reference.

Practise it now, free

Knight Maze

The problem to solve

In a game you constantly ask: "how many moves to bring my knight from g1 to that nice d5 square?" Blindfolded, judging that distance fast and right saves you from launching a maneuver that costs one move too many. Typical questions: "from a1, in how many jumps does the knight reach h8?" (six, and only two pairs on the whole board cost six: a1-h8 and a8-h1), "who gets to e5 first: my knight from b1 or his from g8?" (neither: both are three jumps away, so it is a dead heat and the move order decides).

Knight distance is deeply counter-intuitive: the square right next door can be farther than a distant one. That is what makes it treacherous, and worth mastering.

Definition and bounds

The knight distance between two squares is the minimal number of jumps from one to the other on an empty board.

  • All distances run from 0 to 6.
  • Where the knight stands sets its own ceiling: from a central square (c3 to f6) nothing on the board is more than 4 jumps away, from an edge square at most 5, from a corner 6.
  • The maximum, 6, happens only between opposite corners (a1 to h8, a8 to h1). Everything else on the board is 5 jumps or fewer.

The core: the neighborhood traps

This is where intuition fails, and what must be engraved:

  • The square right next door (orthogonal): a1 to b1, or a1 to a2 = 3 jumps.
  • The immediate diagonal square: 2 jumps in the middle of the board (d4 to e5), but 4 jumps from a corner (a1 to b2). The corner is the worst case for such a close square.
  • A square one knight-move away (a1 to c2, a1 to b3) = 1 jump only.

The message to engrave

With the knight, "adjacent" does not mean "near". The neighbor square costs 3 jumps, the diagonal one 2 (4 when the corner is the one right next to it), while a square at L-range costs just 1.

The rhythms to memorize

To estimate without computing everything, two sequences radiating from the knight:

  • From a central knight, in a straight line (along a file or a rank), the distances go 3 - 2 - 3 - 2 as you move away square by square.
  • From a central knight along a diagonal, they go 2 - 4 - 2 - 4. Near the edges and corners the rhythms break: count those.

These two rhythms cover the majority of quick estimates.

The color check (parity)

The knight changes color on every jump (knight lesson). Therefore:

Parity check

An ODD number of jumps lands on the OPPOSITE color of the start square. An EVEN number lands on the SAME color. If your estimate breaks this, it is wrong: recount.

The one trap parity cannot catch

Two squares along a diagonal (d4 to f6) is always 4 jumps, never 2. Both squares are the same color, so the parity check passes a wrong answer of 2 without blinking. It is the only common count where the free check does not save you.

Example

You estimate "4 jumps" toward a square of the opposite color? Impossible: 4 is even, so same color. Parity does not tell you by how much you are wrong, only that the true distance is odd: recount, it is 3 or 5, never 4.

How to estimate in your head

  1. Color first: same color start and target means an even distance; different colors mean odd. That removes half the candidate answers.
  2. Order of magnitude: next door in a straight line is 3; immediate diagonal is 2, or 4 from a corner; far is 3 to 5 (a1 to g8 is 5, and so is a1 to h1); the opposite corner is 6.
  3. Refine: lay 1 or 2 mental jumps toward the target (the 2x3 rectangle from the knight lesson) and count.

Try it: the distance map

Place the knight anywhere: every square shows its exact distance, with a heat map. Hover a square to see a shortest path and the parity check, then test yourself in the quiz.

Why it matters

  • Knight maneuvers: knowing in how many moves the knight reaches its ideal outpost, to decide if the detour is worth it.
  • Races: in endgames, judging who (knight, king, pawn) arrives first on a key square.
  • Blindfold calculation: pruning variations by knowing in advance that a square is "too far" for the knight.

Recommended training progression

  1. The neighborhood traps: memorize 3 (orthogonal), 2 (diagonal, 4 from a corner), 1 (knight move).
  2. The gap table: 2-and-1 is 1 jump, 1-and-0 is 3, 1-and-1 is 2 (4 from a corner), 2-and-2 is 4, 3-and-2 is 3, 3-and-3 is 2.
  3. Distance quiz: "from X to Y, how many jumps?"
  4. Verify with color parity systematically.
  5. Real journeys: not just the distance, but the path.

In-app drill

/train/knight-maze trains the actual paths behind these distances.

Common mistakes

  • Believing the neighbor square is 1 jump away. It is 3 (orthogonal) or 2 (diagonal, 4 from a corner). The most widespread error.
  • Skipping the parity check. It is free and catches every count that lands on the wrong color.
  • Overestimating long distances. The max is 6, and only corner to corner; nearly everything is 5 or less.
  • Computing a path without a clear target: fix the destination square, then work backward 1-2 jumps.