What the Solver Found in the Old Manuals

Where the positions come from

The three books are on dpxq.com, the two classical ones typed from 1980s and 1990s annotated reprints of Ming and Qing woodblocks. We mined every public-domain manual on its two 古谱 shelves, 2,938 records, and published the ones that replay as studies here, after telling the site’s owner, with a link back to each record. The diagrams and the moves are centuries old; every modern editor’s note stays on dpxq, because that part is not ours to republish.

A record arrives as two strings. 適情雅趣 第011局 群鼠争穴 is a board of two digits per piece, reading from Black’s back rank, and a move list in the same coordinates. Both are one long line in the file; they are broken up here, four pieces to a group:

[DhtmlXQ_binit]
72999999 59999957 22771799 99999941
12994299 30996099 68028229 48999999

[DhtmlXQ_movelist]
22204220 72320232 77706042 17373222
57362232 36443222 4432

[DhtmlXQ_comment0]
红弃双车，双炮胜

That becomes a position and a line by replaying it through the same rules kernel the site plays with. The replay is the first check, and it tests our copy of each record: a solution recorded short still replays cleanly, but a mis-typed piece usually produces an illegal move somewhere, and those records are dropped whole. Then Pikafish sweeps each position for a verdict that contradicts the book’s, which is where the engine can say “this is not a Red win” and stop.

The sweep cannot say whether the solution is the only one. That takes exhaustive search: every legal Red move at every turn, every Black reply, to the end of the claimed length. On these boards, with twenty pieces and a nine-to-thirteen-ply solution, it finishes in seconds to a few minutes per problem. The whole audit below is a few hours of laptop time.

What counts as a fault

Four things can be wrong with a solution that still mates. A second key: another first move forces the mate in the same number of moves, so the diagram has two answers. A dual: further in, after some defence, Red has two winning continuations. A faster mate: the book prints a mate in seven and a mate in five exists, which breaks the stipulation outright. A longer mate: the book is right about who wins and wrong about how long, because Black has a better defence than the one printed.

The dual is where the two traditions differ. Western chess composition has treated it as a fault since the nineteenth century. 朱鹤洲’s ten-character standard for judging 排局 asks for 新深妙多走少美无趣名, novelty, depth, brilliance, many variations, every attacking piece moving, few pieces, a pretty diagram, no idle piece, amusement and an apt title. Uniqueness is not on the list.

Forty-five of 172 are clean

Most of the findings are duals, and they are clear-cut. 適情雅趣 第011局 群鼠争穴 is a mate in seven: both chariots are given up, and the cannons and the horse do the rest. At Red’s sixth move the book plays 傌六进五, and 傌六进七 mates from the same position in the same number of moves.

The second keys are the ones a composer would care about. 第015局 妙振兵铃 opens with a chariot check and mates in six; pushing the soldier on d9 up beside the general mates in six as well, by a different arrangement of the same pieces. Seven of those in 適情雅趣 alone.

適情雅趣 第108局 争舟走渡 prints a mate in seven, thirteen plies. At Red’s first move the soldier can take the advisor beside the general instead, 兵四平五, and that mates in six. Nine of the 172 can be mated faster than printed.

When the record itself is broken

渊深海阔 第217局 疾诛文丑 claims a mate in five with every move a check, and the printed line does mate. It mates because Black’s fourth move walks into it. Black has a second legal move there, 车5退8, swinging the chariot that has stood on e2 since the diagram back to e10; after it Red has no check at all, so a continuous-check mate is over on the spot, and no quiet move mates either.

No editor prints a Red win in a position where Red is lost, so the diagram as typed is probably not the composition. Which piece is wrong is a question a machine can help with: try every single-piece edit to the diagram, and ask which of them makes the book’s own line a forced mate in five. Of 154 edits, four do. Three of them concern the black chariot on e2, and the fourth puts a black soldier on e3, in that chariot’s file.

remove the black chariot on e2
the black piece on e2 is a horse, not a chariot
the black piece on e2 is a soldier, not a chariot
black soldier on d2 belongs on e3

We sent the board and the line to the person who maintains dpxq’s records, in Chinese, with our guess that the chariot was a soldier in the book. His answer was 古谱就有错呀: the old manuals have errors in them. He did not check a printed copy, so whether the chariot is the book’s mistake or the transcriber’s is still open. If you have a printed edition of 渊深海阔, the square is e2.

The other two, 第202局 and 第265局, are worse off. No single-piece edit restores either of them, so whatever went wrong took more than one piece with it, or the move list is mis-typed as well. All three are still in the 渊深海阔 study as dpxq records them, and the audit study carries the finding.

Those three are the ones inside the 172. Across the whole corpus, 34 records are flagged as corrupt: the diagram as typed does not support the claim printed beside it. Ten of them claim mate by continuous checks, and nine are refuted inside the book’s own line, in four manuals; in each, the search ran six moves past the recorded length and found no continuous-check mate. They have a study of their own, linked below, ordered by how decisive the refutation is: in 第217局 Red is left without a single check, and in the last Red still has ten checks that go nowhere.

An exact search that reports no forced mate looks identical whether the composition is broken or the record is, and one engine evaluation at the root separates them in seconds. Five positions we had flagged as cooked turned out fine that way: Red does force the mate, later than the printed line.

The four great positions: nothing broken

七星聚会, 蚯蚓降龙, 野马操田 and 千里独行 are the street positions, argued over since 百局象棋谱 in 1801. They claim a draw, and a draw cannot be proved without the repetition law. What can be tested is whether the claim breaks, with one side forcing a mate. Across twenty-nine records of those four and their relatives, the search found no mate that contradicts the book. On eight it proved that neither side mates within its depth; on the rest it ran out of budget for one side or both before it could say.

The audit was wrong three times first

The counts above come from the fourth version of the audit. The first was a pass over the quiet compositions, and it searched the position after the key as though Red were to play twice. It reported 176 of 190 sound. The number meant nothing, because every search had started on the wrong side.

The second judged every composition as a chess mate-in-n. A quiet 排局 claims only 红先胜, Red plays and wins, and against that claim a second key and a faster mate are not faults. About half the faults that pass counted went away. Both mistakes were in the quiet-move audit, shelved for the reason in the next section; the 172 above are continuous-check problems, where the length is part of what the book claims.

The third was running the exact search without the engine screen described above. Eight records were first read as broken compositions: five are the Red wins past the search’s reach in the table, and three are the broken records above.

A fourth was in the helpmates, the problems where both sides cooperate to reach mate. The composer that built them tested for checkmate, and xiangqi also scores 困毙, a side left with no legal move, as a loss. A line ending in 困毙 is a second solution, so 22 of the 186 helpmates we had published as sound had lines the composer could not see, 64 in the worst of them. A re-check that counts 困毙 is written and has not shipped yet.

Four bugs, and each was a rule we knew and had not put into the tool: whose move it is, what a 排局 claims, that a mistyped record looks like a broken composition, and that 困毙 loses.

What we did not check

The quiet compositions, which are most of the corpus. A 宽紧杀 runs past twenty plies on a board with twenty pieces, and the exhaustive search that settles a nine-ply problem does not finish there. A proof-number search gets further and still runs out on the long ones. Everything above is about continuous-check problems only.

None of this is a claim about the compositions as compositions. A dual in 適情雅趣 is a dual by a standard 適情雅趣 was not written to, and the geometry that made these positions worth copying for four hundred years does not depend on whether the line is unique.