In the 19th century, the threemover was considered to be the ideal length of problem by
solvers. Over time the threemover developed two main streams, one concentrating on
checkmating positions, the other stressing the interplay of the pieces. For convenience
these are termed modelmate problems and strategic problems. Today the latter
is the dominant type.
ModelMate Problems
Some threemovers are built around a combination of artistic mates, in the style known as
Bohemian, after the school of composers who developed the principles of such
problems in the late 19th century. To explain Bohemian problems, we must first consider
checkmates. Problemists, unlike players, are interested in the quality of checkmating
positions, and classify mates according to certain features. A pure mate is one in
which the squares around the mated king are guarded or blocked in one way only and the
square on which the king stands is attacked once. An economical mate is one in which
all of the white pieces on the board with the possible exception of king or pawns
participate. A mate that is both pure and economical is called a model mate.
In a Bohemian problem there is no main variation or variations; the composer combines a
number of variations of equal value ending in diverse model mates. The white force is
highly mobile, with pieces swapping the duties of delivering the mating check and guarding
flight squares. Quiet continuations, that is nonchecking continuations, are highly valued.
Accuracy of play in nonthematic variations is considered of minor importance.
(1) C. A. L. Bull
Casopis Ceskych Sachistu, 1923
Mate in 3

The lightlyset 1 is a typical example of a Bohemian problem. The
giveandtake key 1.Qa3 threatens 2.Sxe6, with 3.Qb3 to follow (if 2...Sc5
3.Rb4). Instead of actively attempting to defeat the threat, Black can
cooperate in making the mate a model by capturing the e7 knight: 1...Sg6
2.Sxe6 Sxe7 3.Qb3. Such a mate is called a slaughter model. A pair of
thematic variations involve the knight and rook exchanging guarding and
checking functions: 1...Kd4 2.Sxe6+ Ke5 3.Re1, and 1...Sc7 2.Rb4+ Kc5 3.Se4.
Finally 1...b5 leads to a mate which is almost a repeat of the threat model
1...b5 2.Rc1+ Kd4 3.Qc3.

There are two exceptions to the above definition of a model mate. A double check is
considered acceptable if each check taken by itself could be countered, although the
insistence on the unique guard of each flight still holds. If one of the mating pieces
pins a piece which could otherwise frustrate the check the resulting mate is called a
pinmodel, whether or not the pinned piece occupies a square in the king's field.
(2) F. Matousek
1st Prize, Jas, 1935
Mate in 3

2 illustrates a variety of pinmodels. In each variation a different piece
delivers the mating check, and two black pieces are pinned, the pawn on both
rank and file. The key 1.Bc5 threatens 2.Qh1+ Kxd2 3.Qc1, and gives the
thematic variations 1...Sxc5 2.Qh1+ Kf2 3.Sd1, 1...Kxd2 2.Qh6+ Re3 3.Bb4 and
1...Rh8 2.Qe4 either Re8 3.Rd1. The last mate is called a sideboard model,
a type considered a little inferior as there are less squares around the king
to be guarded.

When two or more mates have similar arrangements of blocking and guarding pieces around
the mated king the mate is referred to as an echo. Bohemian composers were
particularly interested in echoed mates.
(3) J. Pospisil
Zlata Praha, 1885
Mate in 3

The flightgiving key of 3, 1.Qd1, threatens 2.Qf3+ Kd4 3.Qxd3. After
1...Kf5 2.Qf3+ leads to the model 2...Ke6 3.Sc5, a mate which is echoed after
1...Bg4 or 1...Bxg2 2.Qg4+ Kd5 3.Sb4. After 1...Kd4 or 1...Bf5 2.Qa4+ Kd5
3.Sxc7 is a model which differs slightly in that the guard and block on either
side of the king have been swapped. This mate is echoed by 1...Kd5 2.Qb3+ Kc6
3.Sb8. Unusually for a Bohemian problem the play is completely accurate.

Strategic Problems
Strategic problems, where the emphasis is on the interplay between black and white pieces
following the key move, have been the most popular form of threemover for most of the last
century, and improvements in constructional techniques have seen increasing complexity.
Very often a type of strategy is repeated in multiple variations.
(4) I. A. Schiffmann
1st Prize, Dutch East Indies Chess Association, 1929
Mate in 3

The key of 4 is 1.g6, threatening 2.gxf7 followed by 3.Rxd8. Black can defend
by moving the rook along the rank to give the queen access to h4. After 1...Rd2
White continues 2.Ka5 and 3.Sa6 mate, because the rook has prevented the
possible defence 2...Qe1, pinning the knight. This idea is called
anticipatory interference, and is repeated in three further variations:
1...Re2 prevents a queen check from f1, for 2.Kxb5 any 3.Sa6. 1...Rf2 cuts out
Qg1 for 2.b7 and 3.Ba7, and finally 1...Rg2 is followed by 2.Bb7 and 3.Sc6, as
2...d4 no longer defends. After 1...d4 2.b7 operates again.

(5) Vincent L. Eaton
1st Prize, American Chess Bulletin, 1950
Mate in 3

Eaton's 5 is built around the various ways in which White can unpin his own
pieces. The key is 1.Bd3, which prevents Black from cutting the line connecting
bishop and rook, and places Black in zugzwang. After 1...Sf2 White continues
2.Re6+, unpinning the knight, so that after 2...Sxd3+ 3.Sd2 mates. Similarly
complex play features in the variation 1...Sc4 2.Sd2+ Sxd2+ 3.Re6. A trio of
variations allow the king to unpin the knight and rook by vacating a2. 1...c5
allows 2.Kxa3 because the potential bishop check at d6 has been eliminated,
while 1...Sb5 allows 2.Ka1 because there is no longer a check at c2. 1...Sb1 is
simply met by 2.Kxb1. Any move of the e8 bishop allows 2.Rxf7+, since the
bishop cannot recapture to reestablish the pin of the knight. 1...c6 prevents
the e8 bishop from attacking the key piece, and is followed by 2.Bc3,
threatening various rook discoveries. In this line 2…Sf2 unpins again for
3.Re1. The mopup variations are 1...gB anywhere 2.Qe3, and 1...Bf4 2.Rxg2+
Ke1 3.Rxg1. The variety of play in this problem is quite astonishing.

(6) H. Maruta, Oey Gien Tiong & Touw Hian Bwee
1st Prize, BCF Tourney No. 133, 19721973
Mate in 3

Many problems successfully mix formal and strategic elements. The remarkably unified
6 features an ABBCCDDA cycle of continuations and mates. The
arrangement on the fifth rank is called a halfpin, since if either
bishop or pawn moves off the line the remaining piece will be pinned. All of
the thematic variations exploit the halfpin. The key, 1.Qh1, threatens 2.Qh3+
Sg4 3.Qxg4. 1...Rxg3 unguards f4, allowing White to drag the pawn from the
halfpin line, 2.Rf4+ A exf4 3.e4 B. 1...Rg7 unguards the
potential mating square d4, for 2.e4+ B Bxe4 3.Sd4 C. 1...Sc4
unguards the line b1e4, allowing 2.Sd4+ C exd4 3.Qxf3 D (If
2...Ke4 3.Qb1). Finally 1...Sg4 shields the white king from a bishop check,
leading to 2...Qxf3+ D Bxf3 3.Rf4 A. Such a superbly constructed
problem makes light of the challenges facing the composer, who must not only
find a matrix that allows the cyclic play, but must also arrange a threat that
will be defeated by all the thematic black moves. In this case three heads were
better than one!

(7) Matti Myllyniemi
1st Prize, Suomen Shakki, 1952
Mate in 3

When solving it is always worth looking for prominent set play, as the problem may
be built around changed play. In 7 there are two set variations.
After 1...f5 White must release the stalemate with 2.Rf3 gxf3 3.gxf3, while
after 1...fxe5 2.Re2 exploits the fact that the black pawn must move on to f4
for 2...exf4 3.exf4. No pure waiting move is possible, and the key is 1.Bh6,
giving the variations 1...f5 2.Re2 f4 3.exf4 and 1...fxe5 2.Rf3 gxf3 3.gxf3.
The set continuations have been reversed after the key, an idea known as
reciprocal change. The problem is a mutate, a type rarely seen in
the threemover compared to the twomover.

In recent years many of the modern pattern themes which have been developed in the
twomover have been transferred to the threemover. A number of such themes feature effects
which appear paradoxical. Keller's problem illustrates one of the most popular paradox
themes, the Dombrovskis theme, where black defences which defeat try threats are met
by those very moves after the key.
(8) Michael Keller
1st Prize, Schweizerische Schachzeitung, 1985
Mate in 3

White's try 1.Bb6? threatening 2.Qxd4 mate is refuted by 1...Sf3!. Similarly 1.Bc7?
threatening 2.Rxd6 mate is refuted by 1...Se4!. The key is 1.gxf4, threatening
2.Qxh1+ followed by capturing the knight. Black can defend by playing 1...Sf3
or 1...Se4, the two moves which defeated the try threats. After 1...Sf3 White
plays 2.Qxd4+!, the move which 1...Sf3 originally defeated! This gives the
continuations 2...Kxd4 3.Rxd6 and 2…Sxd4 3.Se3, which is now possible because
the key removed the pawn guard on e3. 1...Se4 is followed by 2.Rxd6+ (again the
move which it originally defeated) 2...Kxd6 3.Qxd4 and 2...Sxd6 3.Re5, now
possible because the key put a guard on e5.

The success or otherwise of such problems lies in the ingenuity of the mechanism which
allows the paradoxical effects.
