In Netflix’s Season 2 of The Devil’s Plan, we see contestants pit raw intellect, logic, and instinct against each other in puzzles that look simple — but spiral into labyrinths of consequence. The Knight’s Tour would fit right in.
This post explores the Knight’s Tour — a deceptively elegant chess puzzle — through the lens of game design, human reasoning, and AI tooling. It also shares a simple AI-generated interactive app to explore the puzzle hands-on.
🎮 The Knight’s Tour: A Game of Pure Movement
The Knight’s Tour asks a single question:
Can a knight move to every square on a chessboard exactly once?
It’s not a match. It’s not a capture. It’s a dance. The knight zig-zags in an L-shape — two squares in one direction, one square perpendicular — threading a needle through the entire board.
The tour has existed since at least the 9th century. Mathematicians, poets, and puzzle-solvers have obsessed over it. And it’s exactly the kind of elegant brain trap you’d expect to find in The Devil’s Plan, where complexity grows not from the rules but from your own decisions.
🛠️ Try It Yourself — A Simple Knight’s Tour App
We built a simple UI for you to try solving the Knight’s Tour yourself. You can select a board size and click to move the knight. It tracks visited squares and validates your moves.
This entire app was written using AI in under 5 minutes:
🧠 Solving the Tour: The Human Way vs. The Machine Way
There are multiple algorithms for solving the Knight’s Tour:
1. Brute-Force Backtracking
- Recursive
- Complete but inefficient
- Works like trial-and-error with memory
2. Warnsdorff’s Rule (Best for Humans)
- Always move the knight to the square with the fewest onward moves
- Doesn’t guarantee a solution but works almost every time, especially on 5×5+
- Simple mental heuristic, no tech required
3. Backtracking + Warnsdorff (Hybrid)
- Use Warnsdorff to guide a backtracking search
- Fast + complete
- This is what a smart AI would do
4. Graph Theory (Hamiltonian Path)
The Knight’s Tour problem can be modeled as a Hamiltonian Path problem — a path through a graph that visits every node exactly once.
Each square on the chessboard becomes a node, and every legal knight move between squares becomes an edge. The challenge is now transformed into a pure graph traversal problem:
Can you find a path that visits every node in this knight-move graph exactly once?
This abstraction is powerful because it allows us to apply general graph theory tools. For instance:
- You can use DFS with backtracking to search for Hamiltonian paths.
- You can apply path pruning, branch and bound, or heuristic optimizations.
- It generalizes well to other movement-based puzzles beyond chess.
However, solving Hamiltonian Path problems is NP-complete. This means:
- There’s no known algorithm that solves all cases efficiently.
- The computational cost grows exponentially with the size of the board.
Despite its power, this method is mostly useful for academic exploration, automated solving, or AI research — not manual play.
That said, modeling the Knight’s Tour as a graph gives you a different lens: it turns a medieval chess curiosity into a computer science classic.
🧭 Why Warnsdorff’s Rule is the Best Human Strategy
Humans don’t excel at brute-force recursion. We get lost. We forget what we tried.
But humans are great at heuristics:
- We can estimate.
- We can visualize.
- We can follow simple rules.
Warnsdorff’s Rule leans into that. By always moving to the square with the fewest onward moves, you:
- Prevent self-traps
- Prioritize flexibility
- Preserve options later
On a 5×5 board, starting in the center gives you 8 legal moves. Starting in the corner gives you 2. That alone can make or break your game.
🧩 Game Design Meets Human Cognition
The brilliance of a Knight’s Tour is that it’s purely cognitive:
- No outside knowledge
- No math formulas
- No language
Just you, a board, and a sequence of moves.
That’s why it would shine in a show like The Devil’s Plan. It tests how you:
- Think ahead
- Stay calm under pressure
- Adapt when things go wrong
You could teach it in 10 seconds. You could lose to it for a lifetime.