Knight Tour Strategy: Routes, Tie-Breaks and the Clock

Updated October 2026

Knight asks you to complete a knight's tour: jump around a small chessboard in L-shaped moves and land on every square exactly once. Solving one board is a classic puzzle. Solving board after board against a clock that gets shorter every time is a different challenge, and the players with the longest runs are not the ones who think hardest but the ones who barely need to think at all. This guide covers how the game sets up each board, how the timer works, a reliable rule for finding a tour, and ready-made routes you can memorise.

How a run is structured

Your score is the number of boards you complete. The first two boards are five squares by five; from the third board onward every board is six by six, and it stays that size for the rest of the run. The board itself never changes beyond that, so the sixth board of a run is exactly the same puzzle as the third.

To begin a board you tap a starting square. From then on you may only move like a chess knight: two squares in one direction and one square at right angles. Legal destinations are highlighted, every square you have visited shows the move number on which you reached it, and you cannot return to a numbered square. When you fill the last square the board is cleared and the next one appears after a short pause.

The run ends in one of two ways. If you reach a square from which no unvisited square is a knight's move away while empty squares remain, you are stuck and the game is over. If the board's time runs out, the game is also over. You can also end a run deliberately with the New button after clearing at least one board, which takes you to the score card so you can save the result.

The clock and why it eventually wins

Each board has its own countdown, shown next to the hint under the board. The first board gets 45 seconds, and every board you clear takes 1.2 seconds off the next one. There is no minimum. Board 10 gets 34.2 seconds, board 20 gets 22.2 seconds and board 30 gets 10.2 seconds. Board 38 would get only 0.6 seconds, far too little for 36 taps, so every run is guaranteed to end somewhere before then.

A few details matter for planning:

• The clock starts when the board appears, not when you pick your first square. Time spent choosing a start is time lost.
• The clock pauses between boards. During the short transition after a clear, no time is charged to either board.
• The clock uses real time. Switching to another app does not stop it.

Divide the budget by the 36 moves of a six by six board and you get the pace the game demands: about 1.2 seconds per move at the start of the six by six stage, 0.6 seconds per move around board 20 and under 0.3 seconds per move by board 30. Early on you can afford to think. Later you cannot.

Where you may start on the small board

On a five by five board a complete tour is only possible from some squares. Colour the board like a chessboard so that the corners are light: there are thirteen light squares and twelve dark ones, and because a knight always changes colour when it moves, a tour that visits all 25 squares must begin and end on the larger light group. The game respects this and only highlights the thirteen squares from which a tour exists, which include all four corners and the centre. On six by six boards every square is a valid start.

The fewest-exits rule, and how to break ties

The best-known method for finding a tour by hand is the fewest-exits rule, published by H. C. von Warnsdorff in the nineteenth century. From your current square, look at every legal destination and count how many unvisited squares each of them could reach next. Move to the destination with the smallest count. The idea is to visit awkward squares while you still can, instead of leaving them stranded.

The rule is good but not perfect, because there are often ties. We tested it in a simulation of the game's two board sizes, starting from every legal square and breaking ties at random, twenty thousand tours per size. On the six by six board it completed about 97 percent of tours, failing mostly from the four central starting squares. On the five by five board it completed only about 77 percent; starts in a corner or the centre always worked, while starts in the middle of an edge failed about half the time.

A simple tie-break fixed every case in the same simulation: when two or more destinations have the same count, choose the one farthest from the centre of the board. With that addition, all twenty thousand tours on each board size were completed. In practice that means "fewest exits first, and if in doubt, go toward the rim".

Routes worth memorising

Since every six by six board is identical, the fastest possible approach is to stop solving and start remembering. The grids below show one complete tour for each board size, both starting in the top-left corner, written the way the game numbers your squares. Move 1 is your starting tap, then follow the numbers in order. We generated them with the rule above and checked every step by computer.

Five by five, used on boards 1 and 2:

  1  20   9  14   3
 10  15   2  19  24
 21   8  25   4  13
 16  11   6  23  18
  7  22  17  12   5

Six by six, used on board 3 and every board after it:

  1  22   9  32   3  24
 10  29   2  23  16  31
 21   8  33  30  25   4
 28  11  26  17  34  15
  7  20  13  36   5  18
 12  27   6  19  14  35

You do not need to memorise all 36 numbers as a single list. Learn the route in chunks of six. Ten of the first fifteen moves land on the outer ring of the board, so the opening deals with the awkward edge squares while plenty of options remain, and the four corners are reached on moves 1, 12, 24 and 35. If you ever lose your place, fall back on the fewest-exits rule from wherever you are; it is the most reliable way to carry on.

Playing fast without getting stuck

• Start in a corner every time. It is a valid start on both sizes, plain fewest-exits never failed from a corner in our simulation, and it lets you reuse the memorised route.
• Tap your start immediately. The clock is already running. Decide your opening before the board appears.
• Watch for squares with a single way in. If an unvisited square can now only be reached from where you are standing, go there now. Leaving it means it can never be filled.
• Keep your eyes on the highlights. The game only highlights legal moves, so a mis-tap on an unhighlighted square simply does nothing. Use that as a safety net rather than a reason to hurry.
• Bank on the early boards. The first few boards give you over a second per move. Use them to rehearse the route smoothly, so that by board 20 your hand moves on autopilot.

Your best number of boards is stored on your device. With a memorised route and a corner start, the limiting factor becomes purely how quickly you can tap 36 squares accurately, which is exactly what the shrinking clock is designed to measure.