# Babson task

A Babson task (or simply Babson) is a directmate chess problem with the following properties:
* White has only one key, or first move, that forces checkmate in the stipulated number of moves.
* Black's defences include the promotion of a certain pawn to a queen, rook, bishop, or knight. (Black may have other defences as well.)
* If Black promotes, then the only way for White towards a forced checkmate in the stipulated number of moves is to promote a pawn to the same piece to which Black promoted.
Joseph Ney Babson [it] (1852–1929), the task's eponym, first conceived of the task in 1884, but never solved it. To devise a satisfying Babson task is regarded as one of the greatest challenges in chess composing. For almost a century, it was unknown whether such a task could exist.
The Babson task is a special form of Allumwandlung, a chess problem in which the solution contains promotions to each of the four possible pieces. Such problems were already known when Babson formulated his task.

## Forerunners of the Babson task

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This 1912 problem by Wolfgang Pauly is, as it were, a three-quarter Babson task: three of Black's promotions are matched by White.
The key is 1.b3, after which there are the following lines:
* 1...a1=Q 2.f8=Q Qb2 3.Qa8 Qxc1 (Qxb3 4.Qf3#) 4.Qf3#
* 1...a1=R 2.f8=R (2.f8=Q? a2 3.Qa8 stalemate (3.Qf6 stalemate)) a2 3.Rf6 Kxh4 4.Rh6#
* 1...a1=N 2.f8=N (2.f8=Q? Nxb3 3.Qa8 Nd4 and no mate) a2 3.Ng6 Nxb3 4.Nf4#
This is not a full Babson, however, because 1...a1=B 2.f8=B does not work; White must instead play 2.f8=Q, with similar play to above.

## Selfmate Babsons

The earliest Babson tasks are all in the form of a selfmate, in which White, moving first, must force Black to deliver checkmate against Black's will within a specified number of moves. In 1914, Babson himself published such a problem, in which three different white pawns shared the promotions.
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Henry Wald Bettmann composed the first problem in which one black pawn and one white pawn were involved in all promotions, winning 1st prize in the Babson Task Tourney 1925–26.
The key in Bettmann's problem is 1.a8=B, after which play is as follows:
* 1...fxg1=Q 2.f8=Q (2.f8=R? Qxf1 3.b5+ Kxc5; both 2.f8=B? and 2.f8=N? fail to Qg8!) Qxf1 3.b5+ (3.Qfxf1? Rxa6 is not checkmate, as White can play 4.Qxa6) Qxb5#; or Qxc5 3.b5+ (3.bxc5? Rxa6 is not checkmate, as White can play 4.Kb4; 3.Qxc5 checkmates black, entirely wrong for a selfmate) or 2...Q-any 3.anyxQ Rxa6#
* 1...fxg1=R 2.f8=R (2.f8=Q? Rxf1 3.Qfxf1 (3.b5 checkmates Black) Rxa6 is not checkmate, as White can play 4.Qxa6) R-any 3.anyxR Rxa6#
* 1...fxg1=B 2.f8=B (2.f8=Q? Bxc5 3.bxc5 (3.b5 checkmates Black; 3.Qxc5 checkmates Black) Rxa6 is not checkmate, as White can play 4.Kb4) B-any 3.anyxB Rxa6#
* 1...fxg1=N 2.f8=N (2.f8=Q? Nxh3! 3.Rxh3 Kd7) N-any 3.anyxN Rxa6#
Various other composers later composed similar problems.

## Directmate Babsons

Composing a Babson task in directmate form (where White moves first and must checkmate Black against any defence within a stipulated number of moves) was thought so difficult that very little effort was put into it until the 1960s, when Pierre Drumare began his work on the problem, which occupied him for the next twenty years or so. He managed to compose a Babson task in which the knight is replaced with the nightrider (a fairy chess piece which moves by making any number of knight moves in the same direction on unblocked squares) but found it hard to devise one using normal pieces: because of the knight's limited range, it is difficult to justify a knight promotion by White in response to a knight promotion by Black on the other side of the board.
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When Drumare eventually succeeded using conventional pieces in 1980, the result was regarded as highly unsatisfactory, even by Drumare himself. It is a mate in five (first published Memorial Seneca, 1980). The key is 1.Rf2, after which captures by Black on b1 are answered by captures by White on g8.
Efficiency in chess problems is considered a great boon, but Drumare's attempt is very inefficient: no fewer than 30 pieces are on the board. It also has six promoted pieces in the initial position (even a single promoted piece is considered something of a "cheat" in chess problems), which is in any case illegal: one of the white f-pawns must have made a capture, and the white and black b- and c-pawns must have made two captures between them, making three in total, yet only two units are missing from the board. Despite all these flaws, it is the first complete Babson task.
In 1982, two years after composing this problem, Drumare gave up, saying that the Babson task would never be satisfactorily solved.
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The following year, Leonid Yarosh, a football coach from Kazan who was virtually unknown as a problem composer until that point, came up with a much better Babson task than Drumare's: the position is legal, it is much simpler than Drumare's problem, and there are no promoted pieces on board. First published in March 1983 in the famous Russian chess magazine Shakhmaty v SSSR, this is generally thought of as the first satisfactory solution of the Babson task. Drumare himself had high praise for the problem.
The key is 1.Rxh4, and the main lines are:
* 1...cxb1=Q 2.axb8=Q Qxb2 (2...Qe4 3.Qxf4 Qxf4 4.Rxf4#) 3.Qb3 Qc3 4.Qxc3#
* 1...cxb1=R 2.axb8=R (2.axb8=Q? Rxb2 3.Qb3 stalemate) Rxb2 3.Rb3 Kxc4 4.Rxf4#
* 1...cxb1=B 2.axb8=B (2.axb8=Q? Be4 3.Qxf4 stalemate) Be4 3.Bxf4 Bxh1 4.Be3#
* 1...cxb1=N 2.axb8=N (2.axb8=Q? Nxd2 and no mate) Nxd2 3.Nc6+ Kc3 4.Rc1#
However, Yarosh's problem has a small flaw: the key is a capture, something which is generally frowned upon in problems. Also, when first presented, the black piece at h4 was a pawn, but a computer discovered an additional solution by 1.axb8=N hxg3+ 2.Kh3 Bxb8 3.Qxc2 and mate next move. Yarosh then substituted a knight on that square; now 1.axb8=N fails to 1...Nf3+ 2.Bxf3 Bxb8 3.Qxc2 Bxg3+ and White is too late. Nevertheless, when Dutch author Tim Krabbé saw this version in the Soviet publication 64, he records that the realisation that somebody had at last solved the Babson task had the effect upon him as if he had "... opened a newspaper and seen the headline 'Purpose Of Life Discovered'."
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Yarosh continued to work on the problem, and in August 1983, he created an improved version with a non-capturing key, which appeared in Shakhmaty v SSSR. Many chess problemists, including Tim Krabbé, consider the problem one of the greatest ever composed. Again, it is a mate in four.
The key here is non-capturing and also thematic (that is, it is logically related to the rest of the solution): 1.a7!. The variations are largely the same as in the original:
* 1...axb1=Q 2.axb8=Q Qxb2 3.Qxb3 Qc3 4.Qbxc3# (alternatively, 2...Qe4 3.Qxf4 Qxf4 4.Rxf4#)
* 1...axb1=R 2.axb8=R (2.axb8=Q? Rxb2 3.Qxb3 is stalemate) Rxb2 3.Rxb3 Kxc4 4.Qa4# (alternatively, 2...Re1 3.Rxf4+ Re4 4.Rxf4#)
* 1...axb1=B 2.axb8=B (2.axb8=Q? Be4 3.Qxf4 stalemate) Be4 3.Bxf4 B(any) 4.Be3#
* 1...axb1=N 2.axb8=N (2.axb8=Q? Nxd2 and no mate) Nxd2 3.Qc1 Ne4 4.Nc6# (alternatively, 2...Nc3 3.Rxf4+ Ne4 4.Rxf4#)
There is another defence for black that is non-thematic and also leads to mate in four: 1...Qxd8+ 2.Kg7 axb1=Q 3.Rxf4+ Qe4 4. Rxd4# However, this is not considered a flaw according to the rules of the Babson task.
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Yarosh composed a completely different Babson task later in 1983 and another in 1986. Several other Babsons were later composed by other authors, including one by Drumare in 1985. The solution of this Babson is 1.fxg8=Q dxe2 2.Nxe3 e1=Q/R/B/N 3.gxf8=Q/R/B/N and now mate in two in all variations.

## The cyclic Babson

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In a cyclic Babson, rather than Black’s promotions being matched by White, they are related in cyclic form: for example, Black promoting to a queen means White must promote to a bishop, Black promoting to a bishop means White must promote to a rook, Black promoting to a rook means White must promote to a knight, and Black promoting to a knight means White must promote to a queen.
The August 2003 issue of the German problem magazine Die Schwalbe contained the problem to the right, a mate in four by Peter Hoffmann. Hoffmann had previously published a number of conventional directmate Babsons, but this one is significant because it is the first cyclic Babson. However, as with Drumare's original Babson task, the problem uses promoted pieces and has a capturing key.
The key is 1.Nxe6, threatening 2.hxg8=Q and 3.Qf7#. The thematic defences are:
* 1...d1=Q 2.hxg8=B (2.hxg8=Q? Qd7+ 3.Bxd7 stalemate; 2.hxg8=N+? Kxe6 and no mate), threatening 3.c4+ Q-moves 4.BxQ#
** 2...Qd7+ 3.Bxd7 Kxg6 4.Rxh6#
** 2...Qxc1 3.Rxg5 (threat: 4.Rf5#) hxg5 4.Qh8#
* 1...d1=B 2.hxg8=R (2.hxg8=Q? stalemate; 2.hxg8=N+? Kxe6 and no mate) Kxe6 3.Rd8 3.Kf6 Rd6#
* 1...d1=R 2.hxg8=N (2.hxg8=Q? Rd4+ 3.c4 stalemate) Kxe6 3.Qxe2+ K-moves 4.Qe5#
* 1...d1=N 2.hxg8=Q (2.hxg8=N+? Kxe6 3.Qxe2+ Ne3! and no mate) Nxb2+ 3.Kb5(Bxb2) and 4.Qf7#
There are also a number of sidelines.
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In the September 2005 issue of Schach [de], the first cyclic Babson without promoted pieces in the initial position was published. Again, the composer was Peter Hoffmann.
The key is 1.Nxb6. The thematic defences are:
* 1...d1=Q 2.exf8=B (2.exf8=Q? Qd4+ 3.Bxd4 stalemate; 2.exf8=N+? Kd6 3.Be5+ Kc5 and no mate)
** 2...Qd4+ 3.exd4 Kxf6 4.d5#
* 1...d1=B 2.exf8=R (2.exf8=Q? stalemate; 2.exf8=N+? Kd6 3.Be5+ Kc5 and no mate)
** 2...Kd6 3.Qd2+ with mate after any move by black
* 1...d1=R 2.exf8=N+ (2.exf8=Q? Rd4+ 3.Bxd4 stalemate; 2.exf8=B? Rd7 3.c8=Q(B) stalemate)
** 2...Kd6 3.Be5+ Kc5 4.Qxc2#
* 1...d1=N 2.exf8=Q (2.exf8=N+? Kd6 3.Be5+ Kc5 and no mate)
** 2...Nxc3+ 3.Kxa5 Ne4 4.c8=Q#

## Babson Task in an endgame study

Achieving a Babson Task in an endgame study was for long time considered impossible, because of the enormous complexity requested to make every promotion the only winning move, avoiding duals and keeping the position legal. Some partial Babsons have been showed in form of a study, but at maximum 3/4 of the theme was achieved (usually missing the Rook variation).
In October 2024, the Israelian chess composer Gady Costeff published on EG a sound attempt of a complete Babson Task in an endgame study, which was the first in the history of chess composition. Unfortunately, the position was illegal for just one missing White capture (and had three white Knights in the initial position). The composer declared to have worked on that position for more than 13 years, trying to make it legal, but eventually giving up and publishing it anyway, out of competition.
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In January 2025, again on EG, the Italian chess composer Daniele Guglielmo Gatti showed a complete Babson Task in an endgame study. The composer declared to have worked for 45 days after having seen the Costeff's failed attempt, creating a much different position that keeped some core elements and ideas of Costeff's one, but managing to make it legal, sound, with improved economy and without promoted pieces. This made him effectively the first composer in history to correctly achieve the task in an endgame study, 141 years after the theme was proposed by his eponym.
The solution of the study follows:
— 1…f1=Q 2.hxg8=Q! Ne5+ 3.dxe5 Qf4+ 4.Ne4! avoids stalemate and wins,
— 1…f1=R 2.hxg8=R!/i Rxg1/ii 3.Nd6/iii exd6 4.Ne4+ Kh7 5.Nf6 mate,
— 1…f1=B 2.hxg8=B!/iv Kg7 (Qxe1; Nf3+! wins) 3.c6 Qxe1 4.c7 Qb1 5.Nxe6+ Kxg8 6.c8=Q+ Kh7 7.Ng5+ Kg7 8.Qf5 Qxa2+ 9.Kc5 e1=Q 10.Ne6+ Qxe6 11.Qxe6 wins,
— 1…f1=N 2.hxg8=N+!/v Kg7 3.Nxe6+ Kxg8 4.Rxe2 Nxe3+ 5.Rxe3 Qd2 6.Ree1 Qxa2+ 7.Kb4 Qb3+ 8.Ka5 wins.
i) Thematic try: 2.hxg8=Q? Ne5+! 3.dxe5 Rf4+! 4.Ne4 Qc3+ (or Qxb5+) 5. Kxc3 stalemate.
ii) Rxe1 3.Rxe1 with: Qxe1 4.Nf3+ wins, or g1=Q 4.Nxe6+ (Rxg1? Bd5! mate;) Kh7 5.Rg7+ Kh8 6.Rxg1 wins.
iii) Threatens 4.Nf7 mate. Prematurely 3.Ne4+? Kh7! wins as there is no mate on f6.
iv) Thematic try: 2.hxg8=N+? Kg7 3.c6 Qxe1 4.c7 Qb1 5.Nxe6+ Kh7 The point: no promotion with check 6.c8=Q Qxa2+ 7.Kb4 Qb3+ 8.Ka5 (Kc5? Qc2+ skewer) e1=Q+ 9.Kb6 Qxe3 another point 10.Nf6+ Kh6 11.g5+ Qxg5 12.Ng8+ Kh5 and draw.
v) Other promotions all fail to Nxe3 mate.