Huarong Dao: The 81-Move Escape

Quick answer: Huarong Dao is a Chinese sliding block puzzle, sold in the West as Klotski, where a large square block must be worked to an opening past smaller ones. The classic layout needs a minimum of 81 moves, a result published by Thomas B. Lemann in Scientific American in March 1964.

Best for: people who like a puzzle where every move is legal, obvious, and probably wrong.

Ten blocks in a tray with two empty squares. You can see every piece and every possible move from the first second. It takes most people hours, and the shortest route is longer than almost anyone guesses.

What Is Huarong Dao?

A sliding block puzzle on a four by five grid. One large two-by-two block, several rectangles, several single squares, and two empty cells to manoeuvre in. The goal is to get the large block to an opening at the bottom.

Nothing can be lifted. Every rearrangement has to be routed through the two free cells, which is the constraint that makes it hard, and it belongs to the combination family described in the guide to mechanical puzzles alongside the other sliding block puzzles.

It is one of China's four classic puzzles, with the Luban lock, the nine linked rings and the tangram. Between them those four cover interlocking, sequence, sliding and dissection.

What Does the Name Mean?

It refers to a story, and the story is why the pieces are arranged the way they are.

Huarong Dao is the Huarong Pass, from the Three Kingdoms period. In the narrative the warlord Cao Cao is fleeing after defeat and must escape through the pass, blocked by enemy generals. The large block is Cao Cao. The rectangles are the generals. The small squares are soldiers. Getting the big block out of the bottom is the escape.

The modern name is more recent than the puzzle's feel suggests: it was given by Professor Jiang Changying in his 1949 book Science Entertainment. In the West the same puzzle is usually sold as Klotski, a name derived from Polish.

Why Is 81 Moves Significant?

Because for a long time nobody knew it, and the published answers were worse.

Before computers were turned on the problem, printed solutions ran to around a hundred steps. That was the state of the art: a sequence that worked, with no way to know whether it was wasteful.

Thomas B. Lemann established the 81-move minimum, published in Scientific American in March 1964. It is a small number with a lot of work behind it, and it is the same shape of achievement as peg solitaire's 18-move solution: a thing people had been doing for decades, finally measured.

Eighty-one moves for ten blocks is also the clearest illustration of why sliding block puzzles are formally hard. Almost nothing else gets that much solution out of that few pieces.

Why Is It So Hard With Only Ten Pieces?

Because there are only two free cells, and everything has to pass through them.

With two gaps in a twenty-cell grid, the puzzle is overwhelmingly full. Most moves are not available, and of those that are, most simply undo the last one. Progress requires long sequences that visibly achieve nothing, shuffling small squares around the board to reposition a gap four moves from now.

That is also why it defeats people psychologically rather than intellectually. The large block spends most of the solution going away from the exit, and the instinct to keep it moving toward the opening is the single biggest reason people fail.

How Do You Solve Huarong Dao?

Plan for the gaps, not the blocks. Nothing moves unless a free cell is adjacent to it, so the real question on every turn is where the two empty cells need to be next.

Work the small squares hardest. They are the most mobile pieces and they are how you reposition the gaps. Expect to spend most of your moves on pieces that are not the goal.

Move the large block away from the exit without flinching. It is required. If you refuse this you will not solve it.

Learn the position just before the end. As with most sliding puzzles, reasoning backwards from the final move constrains the previous several and is far more productive than exploring forwards.

How Is It Different From the 15 Puzzle?

Both slide, both are flat, and they are otherwise almost opposites.

In the 15 puzzle every tile is the same size and shape. The difficulty is combinatorial: the tiles are interchangeable as objects, and what matters is the permutation you are trying to reach. Half of all arrangements are provably unreachable, which is the famous result about it.

Huarong Dao has pieces of different shapes and sizes, and that changes the nature of the problem completely. A two-by-two block cannot pass through a one-wide channel at all, so the constraint is geometric rather than permutational. Nothing is unreachable for parity reasons; things are unreachable because they physically will not fit.

That is why the two puzzles feel so different to solve. The 15 puzzle rewards knowing a method. Huarong Dao rewards seeing several moves ahead, and no general method helps you.

Where Can You Get One?

Easily, and not from us. It is public domain, centuries old in concept, and sold in wood and plastic as Klotski, Huarong Dao, and a dozen other names.

Sliding puzzles are the one major family we make nothing in, which is covered honestly in sliding block puzzles. If the appeal is sequencing rather than sliding, the nearest things we make are Snake Cube, with a full walkthrough, and Tower of Hanoi.

The wider range is in mechanical puzzles.

Frequently Asked Questions

What is Huarong Dao?

A Chinese sliding block puzzle on a four by five grid where a large two-by-two block must be worked to an opening at the bottom past smaller rectangles and squares, using only two free cells. It is sold in the West as Klotski.

How many moves does Huarong Dao take?

The classic layout has a minimum of 81 moves. That result was established by Thomas B. Lemann and published in Scientific American in March 1964; earlier printed solutions ran to around a hundred steps.

Is Klotski the same as Huarong Dao?

Yes. Klotski is the name the puzzle acquired in the West and derives from Polish. Huarong Dao is the Chinese name, given by Professor Jiang Changying in his 1949 book Science Entertainment.

What does Huarong Dao mean?

The Huarong Pass, from the Three Kingdoms period. The large block represents the fleeing warlord Cao Cao, the rectangles are enemy generals and the small squares are soldiers. Getting the large block out is his escape.

What is the trick to solving Huarong Dao?

Plan where the two empty cells need to be rather than where the blocks should go, use the small squares to reposition those gaps, and accept that the large block must travel away from the exit for much of the solution. Refusing that last point is why most people fail.