How to Play — “Heng Dao Li Ma” Layout
The board: A 4×5 grid (4 columns, 5 rows). The bottom edge has a single exit gap at the center.
The pieces (10 total):
- Cao Cao — one 2×2 block (the piece you must free).
- Guan Yu — one 1×2 block lying horizontally.
- Four generals (Zhang Fei, Zhao Yun, Ma Chao, Huang Zhong) — four 1×2 blocks standing vertically.
- Four soldiers — four 1×1 blocks.
The pieces fill 18 of the 20 squares, so exactly two squares are always empty.
How pieces move: A piece may slide one square at a time, horizontally or vertically, into an empty square. A 2×2 or 1×2 piece needs its full footprint to be clear — it cannot squeeze through a one-square gap, cannot rotate, cannot be lifted, and cannot jump over another piece. In practice you are constantly shuffling pieces around the two empty squares to create room.
Winning: Slide Cao Cao down and out through the bottom-center exit. The moment Cao Cao occupies the two center squares of the bottom row, the puzzle is solved.
Scoring moves: A “move” is one piece sliding one square, or sliding several squares in a straight line in one continuous push. For this layout, the optimal solution is 81 moves.
The starting layout: Cao Cao sits at the top center (columns 2–3, rows 1–2). Guan Yu lies horizontally directly beneath him (columns 2–3, row 3) — the “horizontal blade” blocking his path down. The four vertical generals stand in the side columns and lower rows — the “standing horses.” The four soldiers fill the remaining gaps, leaving the two empty squares.
Strategy tips:
- Keep soldiers paired. Scattered soldiers waste the little space you have; two soldiers side by side can be shuffled as a unit.
- Aim for the endgame shape: “Cao Cao escorted by two soldiers, Guan Yu escorted by two soldiers.” This lets Cao Cao descend cleanly. If Cao Cao or Guan Yu gets surrounded by three or four soldiers, the position usually deadlocks.
- Move the small pieces first. Generals and Cao Cao can only move when a soldier has cleared the way ahead of them.
- Work in phases: first break Guan Yu away from directly under Cao Cao; then shuttle the generals to the sides to open the central column; finally walk Cao Cao down step by step.
The full 81-move sequence is too long to memorize — understanding these structural patterns is what actually gets you through.
History and Origins
The mechanics are Western, not Chinese. The puzzle’s direct ancestor is the Pennant Puzzle, patented by Lewis W. Hardy in the United States in 1909. The exact configuration played today — one 2×2 block, five 1×2 blocks (one horizontal, four vertical), and four 1×1 blocks on a 4×5 board — was patented in England by John Harold Fleming in 1932. Fleming’s patent even included a solution for the classic starting position.
How it reached China. The puzzle arrived in China in the 1930s. The earliest documented sighting: in 1938, Lin Dekuan of Northwestern Polytechnical University saw children in a Shaanxi village playing a paper version. In 1943, a New Fourth Route Army cultural instructor named Liang Qing learned the game from villagers in northern Jiangsu, promoted it among soldiers, and collected different starting layouts — giving each a poetic name. The layout with Guan Yu lying horizontally beneath Cao Cao was named “Heng Dao Li Ma” (横刀立马, “horizontal blade, standing horse”).
The Three Kingdoms skin. The game was re-themed around the famous episode from Romance of the Three Kingdoms: after Cao Cao’s defeat at Red Cliffs (208 CE), he fled along the muddy Huarong Dao path and was intercepted by Guan Yu, who let him go out of gratitude. The pieces were renamed accordingly — the 2×2 block became Cao Cao (the one you must “free”), the horizontal block became Guan Yu (the obstacle), the vertical blocks became four generals, and the small squares became soldiers. Historically, Cao Cao did retreat via Huarong Dao, but the Guan Yu encounter is literary invention.
The “ancient origin” claim is unsupported. Some sources trace the game to the ancient Luoshu magic square or “Nine Palaces” rearrangement puzzles, but there is no documentary or archaeological evidence. Chinese puzzle historian Jiang Changying wrote in 1949 that earlier records of a Huarong Dao toy simply do not exist, estimating its history at only a few decades. Scholar Wu Heling likewise concluded it was most likely a localized adaptation of the Western Red Donkey puzzle.
The 81-move solution. “Heng Dao Li Ma” was long considered brutally difficult. Earlier solutions ran to around 100 moves. The first published 81-move solution appeared in Martin Gardner’s “Mathematical Games” column in Scientific American, February 1964. Later computer searches confirmed 81 as the absolute minimum.
