To solve the chess puzzle where you need to catch all the pawns with the jump of the horse (knight), following the rules you've specified, here's how you can approach it:

Game Setup:

• Pawns: Fixed on the board, their positions change with a pattern.
• Knight: Moves according to standard chess rules, capturing one pawn at a time.
• Objective: Capture all pawns once and only once, in a specific order.

Difficulty Levels:

• Easy: 6 pawns
• Medium: 10 pawns
• Hard: 20 pawns
• Master: 50 pawns

Commands:

• back: Go back one move.
• reset: Restart the scheme.
• hints: Restart the scheme and provide suggestions.

Strategy:

1. Understand the Pattern: Observe how the pawns' positions change. This is crucial to planning your moves.
2. Plan Your Route: Since you must capture each pawn exactly once, plan a route that allows you to do so efficiently.
3. Use Hints: If you're struggling, use the hint system to guide you on which pawns to take first (green) and last (blue).

Example for Easy Difficulty (6 Pawns):

Initial Setup:

Let's assume the pawns are placed on the following squares (using standard chess notation):

1. a2 (green)
2. b4
3. c6
4. d4
5. e2
6. f4 (blue)

Suggested Route:

1. Start at b1 (Knight's starting position).
2. Move to a3 and capture pawn on a2 (green).
3. Move to c2 and capture pawn on b4.
4. Move to e3 and capture pawn on c6.
5. Move to g2 and capture pawn on d4.
6. Move to e1 and capture pawn on e2.
7. Move to f3 and capture pawn on f4 (blue).

Hints:

• First Pawn (Green): a2
• Last Pawn (Blue): f4

Commands Usage:

• If you make a mistake, use back to undo your last move.
• If you want to start over, use reset.
• For guidance, use hints to get suggestions on the order of pawns to capture.

Tips for Higher Difficulties:

• Medium (10 Pawns): Plan your route carefully, considering the changing positions of the pawns.
• Hard (20 Pawns): Use the hints more frequently to stay on track.
• Master (50 Pawns): This will require a deep understanding of the pattern and possibly multiple attempts to perfect your route.

By following these strategies and using the commands effectively, you should be able to solve the puzzle at any difficulty level. Good luck!