Is every board solvable?

Not every start square on every board size works, but standard boards have many solutions. Try a corner start if you are stuck.

Does the fewest-exits rule always work?

It works on most boards and is a very strong guide, but not a guarantee. Use backtracking when it fails.

In a Knight's Tour the knight must visit every square exactly once, moving in an L shape. It looks hard, but one simple rule solves most boards.

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1. Know the knight's move
A knight moves two squares one way and one square at right angles. It always changes square colour, so the path alternates between light and dark squares.
2. Use the fewest-exits rule
From where you stand, count how many unvisited squares each possible move would lead to. Choose the move with the fewest. This is known as Warnsdorff's rule and solves most boards.
3. Visit corners and edges early
Squares near the edge and corners have the fewest exits, so they are the ones that get stranded. Take them while you still can.
4. Watch for isolated squares
If an unvisited square has only one or two neighbours left, plan your path through it before it disappears.
5. Backtrack calmly
If you get stuck, undo a few moves and take the second-best choice at the last decision. Most dead ends come from one early mistake.

Is every board solvable?: Not every start square on every board size works, but standard boards have many solutions. Try a corner start if you are stuck.
Does the fewest-exits rule always work?: It works on most boards and is a very strong guide, but not a guarantee. Use backtracking when it fails.