The Mate in 64 Problem: A Very Long Forced Mate Explained
The position
The problem is easy to describe and hard to solve. White has only a king and a queen. Black has sixteen pieces. In the Forsyth notation used by chess software the starting position reads 6n1/2p5/r6p/3Q1b1p/2K5/p1b1p1p1/kp3p2/q4r1n, with White to move.
Read from the notation, White’s king stands on c4 and the queen on d5. Black’s king is on a2, hemmed in by a queen on a1, a pawn on b2 and a bishop on c3 that White’s king can take. The remaining black men are rooks on a6 and f1, knights on g8 and h1, a bishop on f5 and pawns on c7, h6, h5, a3, e3, g3 and f2. Black outnumbers White sixteen pieces to two.
The task is the stipulation in the title: White to play and force checkmate in 64 moves, however Black defends.
Where it comes from
The position circulates in problem and endgame databases. A discussion of the position in February 2023, titled “Huntsman and mate in 64”, quoted several references for it. One was a reprint in the Hartford Weekly Times dated 19 June 1879. Others were the YACPDB problem database, entry 302978, and the Schwalbe problem database, entry P1182458. A second contributor added that it also appears in the HHdbVI collection and in the Chest database as a #64 problem. The sources do not name a composer, and nothing in them identifies the original stipulation, so the age of the position is documented by the newspaper reprint and the databases, not by an attributed composition.
The Schwalbe database, according to the same discussion, marks the problem as cooked. That is the problem composers’ word for a flaw: a position with a second solution or with dual moves, so that White has more than one way to proceed at some point. The duals the poster named arise around White’s third move, with the queen checks Qf7+ and Qd5+ both available.
An earlier discussion from June 2016, about the ChestUCI database, shows how the problem entered the engine community. Dann Corbit listed two positions marked #64 from that database and asked for mechanical solutions to them and to other unsolved entries.
What engines find
Engines find the mate. In 2023 a participant reported that the engine Huntsman found a mate in 64 starting 1.Kxc3+ at depth 104 in 14 seconds. The line as posted begins 1.Kxc3+ Kb1 2.Qxf5+ Ka2 and ends 64.Qh1#. Another participant ran a single thread on a 3.5 GHz machine with 8 GB of hash and reached a score of mate in 64 at depth 113 after roughly 621 seconds. With 30 threads and 32 GB of hash the same result came at depth 92 after about 3.2 seconds. A third user’s attempts did not reach the mate, and the first poster noted that this engine solves the problem only occasionally.
A question raised was whether a mate shorter than 64 moves has been ruled out. The reply was that it had not yet been proven, so 64 is the length found, not a length established as minimal in the discussion.
Compared with the longest mates
A mate in 64 sounds extreme, yet composed problems go much further. Walther Jörgensen, a Danish composer, published a mate in 200 in Die Schwalbe in 1976, and André Chéron found a small change in the same year that made it a mate in 203. John Nunn annotated the solution for ChessBase and called it the longest dual-free direct mate problem without pawn promotions. Its start position has 22 pieces: seven white units and fifteen black ones.
“Dual-free” has a precise meaning. A dual is a point where White’s continuation is not the only one, and long problems often contain king marches with a triangulation that can be played in two ways. Jörgensen’s problem has no such alternatives, so every one of the 203 White moves is forced, assuming best defence, and each must be played in the order given. A separate ChessBase article presents the same position as the longest “whistle-clean” direct mate, again with a goal of mate in 203 moves, and withholds the composer’s name so that readers can work on the problem first.
The mate in 64 differs in kind. Its database entry is marked as cooked, and engines reached it by search, so it is a long forced mate that White can win, not a model of uniqueness like the Jörgensen problem. For other long-mate material the chess history hub is the starting point, and the computer chess section explains how engines and tablebases are used.
Questions
Who composed the mate in 64?
The sources opened do not name a composer. They point to a newspaper reprint of 19 June 1879 and to problem databases.
Is the mate in 64 sound?
One database entry is described in the discussion as cooked, because of duals around White’s third move, so the position has more than one way to continue at that point.
What is the longest direct mate problem?
Jörgensen’s problem, published in 1976 and extended to 203 moves, is described by John Nunn as the longest dual-free direct mate problem without pawn promotions.