(originally published in the magazine VARIANTIM No.80, April 2020)

Chess problems are, first and foremost, a form of art. As an observer of art, I am looking for something exciting, funny, enjoyable, thrilling. What is this thing? Like in other fields of art, in chess too, matters are subjective: each viewer has a different taste, all tastes are legitimate.

In this article I shall discuss things that are of personal interest to me in chess problems in general and help problems in particular.

Harmony is the very first thing which almost every chess problem enthusiast is looking for. It is designed to emphasize a central idea in several aspects. This topic deserves a different, deeper discussion; here I shall assume that it is more or less agreed upon, and will discuss other issues, in which I see important elements to create interesting problem; elements that some of us, chess composers, do not grant a serious weight. In fact, some excellent composers do not pay any importance to these elements, yet they are important to me.

I'd like to elaborate my views about four types of 'families' of such elements, which are essential, in my opinion, to derive satisfaction and enjoyment when we look at or solve a good problem. These families of elements contribute in raising the problems' artistic value.

We shall call the first family "visual elements". The second – "elements of non-triviality"; The third will appear under the headline of "paradoxical elements".

However, it is the fourth family of elements, as far as I am concerned, which raises a chess problem to new heights. To understand what exactly this fourth family is, we shall first define the previous three families.

(Editorial: in all diagrams below, click right/left parts of the needed diagram to play the solution forward/backward)
No.1 Viktoras Paliulionis
1st Prize Orbit 2012
white Se8 Kb1 black Qf3 Rf2 Kh7
h#6.5*set play(2+3)
No.2 Shlomo Seider
Schach-Echo 1976
white Kd8 Bb7 Pa6d6e2 Rf1 black Pg4b2c3d2e3c4e6 Bf5a3 Ke4 Rd5e5 Sg5b1 Qd4
No.3 V. Rudenko & V. Chepizhny
1st Prize Soyouz-Apollo, 1975
white Ke6 Sf5 Rd5d4 Pf2g4 black Ra6e1 Qb6 Pb5d6g6 Sh4h6 Kg5 Be3

{Set play:} 1... ... 2.Rf2-h2 Kb1-c1 3.Rh2-h6 Kc1-d2 4.Qf3-h1{!} Kd2-e3 5.Kh7-g6 Ke3-f4 6.Kg6-h5 Kf4-f5 7.Qh1-h4 Se8-g7 # {
            Solution:} 1...Kb1-c1 2.Qf3-a8 Kc1-d1 3.Rf2-f7 Kd1-e2 4.Rf7-b7 Ke2-f3 5.Qa8-a1{!} Kf3-g4 6.Qa1-h8 Kg4-h5 7.Rb7-g7 Se8-f6 #

1.Ba3*d6 Rf1-c1 2.Qd4-c5 Rc1*c3 3.Qc5-a3 Rc3*c4 # {,} 1.Qd4-a7 Bb7-c6 2.Ba3-c5 Bc6-a4 3.Bc5-d4 Ba4-c2 #

1.Be3-f4 + Sf5-e3 + 2.Bf4-e5 f2-f4 # {,} 1.Sh4-f3 Sf5-h4 + 2.Sf3-e5 Sh4-f3 # {,} 1.Sh6-f7 Sf5-h6 + 2.Sf7-e5 Sh6-f7 #


Geometrical elements usually provide an aesthetic impression, which on occasion is sufficient in itself to make a beautiful problem. For instance, No.1, in which the queen travels during the solution to all four corners. Line elements like Grimshaw, Turton, Indian theme and more, adds color and pleasant aesthetics. Such is the case in the Turton, demonstrated in Seider's charming problem (No.2). Another pretty visual element is Umnov, especially when it appears six times! (No.3).


As a rule, helpmates are not trivial to solve. Being a solver, I've discovered that I have a difficulty in solving helpmates. On the other hand, whenever I watch the solution, in most cases the full content of the solution becomes immediately evident.

Sometimes, though, there are additional layers, that transform the solution to a non-trivial one. This family divides into two types: multiple choice and foresight.

• Multiple choice

This occurs when there are, ostensibly, various options to achieve the desired requirement, and one needs to understand why it is just a specific solution that is working

The simplest case is called dual avoidance, characterized by having to choose between two look-alike options. We can see that in Navon's piece (No.4). The interesting question in this problem, is why black move-order cannot be changed. It turns out that in both solutions, changing the move-order creates a pin of a white piece. By the way, harmony in the layers of tries is important, emphasizing the composer's idea. It is quite common that the main parts of the idea are demonstrated in the tries and not in the solution.

No.4 Emanuel Navon
3rd Prize, TT-199 SuperProblem, 2018
white Pe6a2 Qg4 Kh5 Sg5 black Qh8 Sg8c1 Ph7e7b5a3b2c2 Bf6d3 Kc3 Re1e3
h#2b) bPc2 = wPc2(5+14)
No.5 Menachem Witztum
4th-5th Prize TT-185 SuperProblem, 2017
white Pc2c3b5 Rf3g5 Kh5 black Pc7d7f4g3h2a4b2a3 Qa2 Ba1b3 Rb1c1 Kh1
h#2b) Kh1 -> d8(6+14)
No.6 Ofer Comay
1st Prize Israeli Ring Ty, 2014
white Bd8 Rg7 Pd5d4g4b3 Kf1 black Bf6b1 Rd7c2 Se1a3 Qb2d1 Kc1 Pd2d3

a) 1.Bd3-f5 {(Re5?)} Sg5-f3 2.Re3-e5 Qg4-d4 #{,} b) wPc2 1.Re3-f3 {(Be2?)} Qg4-a4 2.Bd3-e2 Sg5-e4 #

a) 1.Rc1*c2 Rg5*g3 2.Rb1-f1 Rf3*f1 #{,} b) bKh1-->d8 1.Bb3*c2 Rf3-e3 2.Qa2-g8 Rg5*g8 #

1.Rd7-c7 Rg7*c7{!} 2.Qb2*b3 Bd8-e7 3.Qb3*d5 Be7*a3 #{,}1.Bf6-g5 Bd8*g5{!} 2.Qd1*g4 Rg7-e7 3.Qg4*d4 Re7*e1 #

In Witztum's problem (No.5) the solution is evident, and the main point is revealed in two surprising tries. In the first phase, the try 1.♗xc2 ♖gxg3 2.♗d1 ♖f1# doesn't work because ♖f3 is pinned. In the second phase there is another try 1.♖d1 ♖e3 2.♖d5 ♖g8# which fails, this time because ♖g5 is pinned. These tries are the main content of the problem; if one is concentrating on the solution alone, one might miss the central points. These tries are not dual-avoidance, characterized by choosing between two similar possibilities, as described before. Here the tries present new ways to solve the problem, which is differentiated from the actual solution. I believe that such tries belong to a fascinating field, rich of possibilities, which has not been deeply researched yet.

An especially interesting case of dual-avoidance is called hideaway. It occurs when one side must get rid of a certain piece, but only one move is correct, as other moves by that piece ruin the solution.

In No.6 all black moves are designed for hideaway; almost all the problem's content revolves around the question, why a certain black move was chosen instead of others. Black would happily remove ♖d7 off the board, if he could. As it is, he should find a place where to put it. 1.♖xg7/♖f7/♖e7 prevent white's first move. 1.♖xd8 prevents white's second move; 1.♖xd5 prevents black's third move; 1.♖d6 prevents the mating move, while 1.♖b7/a7 guards against the mate. In the second solution, examining the reasons for the specific choice of moves for 1.♗f6, will reveal a complete harmony in avoiding duals. Notice that in this problem, the tries 1.♖xd5 and 1.♗xd4, a foresight is integrated, a concept we're going to discuss in a short while. An additional element here is a white Grimshaw on e7 which appears in the dual avoidance, which determines white's move-order.

• Foresight

In a practical game we enjoy witnessing a case, where a player performs a move, the reason to which is clarified only consequently after several moves. In help problems there are quite a few such themes, where the reason for a specific move is revealed only at later stages of the solution: blocking a flight square or closing a line in advance; abstaining from blocking a line in advance, ambush and more.

Haymann & Shamir's problem (No.7) demonstrates closing a line in advance: in his first move black chooses to close a line, which is already closed. He is doing that because the closed line is going to be opened. White closes an already closed line as well in his second move. Mark's work (No.8) shows an ambush, with white king hideaway: the white piece enters a line which is doubly closed and becomes effective only after the two blocking pieces open the line.

No.7 Jean Haymann & Shaul Shamir
7th-8th Place WCCT 2016-17
white Bc8 Sb6d6 Kc4 black Ka3 Pc2e3f3c5c6e7 Sd4d5 Rh4g5 Qf7 Bh8
h#3b) Sd6 -> c1(4+13)
No.8 Mark Erenburg
1st Prize Tel Aviv 2019
white Kc7 Bb6 Re7 Pe3b3 black Ra8f6 Sc8 Bd2b5 Ke2 Pf2h2h3e6d6c2
No.9 Ofer Comay
1st Prize Israeli Ring Ty 1990
black Pe6d2 Bc8c7 Sd1 Rf1f4 Qh2 Kg6 white Pe3e4 Re5 Kb4
h#4b) wRe5 = wBe5(4+9)

a) 1.Sd5-f6 +{!} Kc4-c3 2.Qf7-a2 Bc8-g4{!} 3.Sd4-b3 Sd6-c4 #{,} b) wSd6-->c1 1.Sd4-f5 +{!} Kc4*c5 2.Rh4-a4 Bc8-e6{!} 3.Sd5-b4 Sb6-c4 #

1.Ke2-d3 Kc7-d8 2.Kd3-c3 Re7-b7{!} 3.Bb5-d3 Bb6-d4 #{,} 1.Ke2-f3 Kc7-b7 2.Kf3-g3 Bb6-d8{!} 3.Rf6-f3 Re7-g7 #

a) 1.Kg6-f6 Re5-a5{!} 2.Rf4*e4 + Kb4-c5 3.Kf6-e5 Ra5-b5 4.Rf1-f6 Kc5-c6 #{,} b) wBe5 1.Sd1*e3 Be5-a1{!} 2.Bc7-d6 + Kb4-c3 3.Kg6-f6 Ba1-b2 4.Kf6-e5 Kc3-d3 #


Whenever, throughout the solution, something happens contrary to our expectations, a paradoxical element is generated, e.g. when black captures a white piece in a helpmate. Why is this a paradox? Because naturally, a capture of a white piece weakens the white army, something which is, allegedly, opposed to the common mission – delivering mate to black king.

Here one too may divide the paradoxes to several types: time paradox, material paradox, space paradox, building and destroying. Other types exist, for example, giving check to white king. In my view, paradoxical elements are the jewel in the crown of art in general and in helpmates in particular.

• Time paradox

Generally speaking, time is a critical obstacle in solving a problem. The majority of helpmates in two will be easily solvable, and in a number of ways, if we only had three moves in our disposal. Therefore, a move which spends a tempo is paradoxical: the relevant side not only require no extra time, but he must make a move while being careful that it doesn't harm his plans.

Examples for time paradox: Zugzwang, tempo-move, switchback, Rundlauf, or Zig-zag (a piece can move to a certain square immediately, but it chooses to move to another square first and later to its final destination).

In No.9 we have the tries 1.♖b5!? and, in the twin, 1.♗b2!? – which fail on account of the Zugzwang created following black's third move.

No.10 Ofer Comay
1st Prize Sabra 2003 (v)
white Rd8e1 Bc7c4 Qf1 Pg2f3 Ke8 black Pf4c5 Ba5f5 Sh5 Kf6
No.11 Ofer Comay
6th Com The Problemist 2010
white Rc7 Kg3 Qh8 Sc4d4 Pa4f2 black Ba6d8 Qe1 Pe2b2c5f5 Sc2e5 Kc3 Ra3
h#2b) Kg3 -> a5 (7+11)
No.12 Ofer Comay
2nd Prize Tzuica 2016
white Ph6e7 Qe8 Se6c5 Bc4 Rf5b8 Kc8 black Kh5 Bh3f6 Pg6g5b4a2 Rc1h7
hs#4b) Kh5 -> a1(9+9)

1.Ba5*c7{!} Re1-e5 2.Kf6*e5{!} Qf1-a1 #{,} 1.Ba5*e1{!} Bc4-e6 2.Kf6*e6{!} Qf1-a6 #

a) 1.Se5*c4{!} Rc7-d7 2.Kc3-d2 +{!} Sd4-b3 #{,} b) wKg3-->a5 1.c5*d4{!} Qh8-g8 2.Kc3-b3 +{!} Sc4-d2 #

a) 1.Rf5-f1{!!} Bh3*e6 + 2.Qe8-d7 Be6*c4 3.e7-e8=S Bc4*f1 4.Qd7-h3 + Bf1*h3 #{,} b) bKh5-->a1 1.Bc4-f1{!!} Rc1*c5 + 2.Qe8-c6 Rc5*f5 3.e7-e8=R Rf5*f1 4.Qc6-c1 + Rf1*c1 #

• Material paradox

To build a mating position for the black king, we will usually try to make use of the full force of the white army. When a white piece is captured, or a white pawn makes a minor promotion, the white force is weakened, thus creating a paradox. Examples for material paradox are: capture of white pieces in a helpmate; capture of white or black pieces in helpselfmates; Zilahi; Cyclic Zilahi; minor white promotion in helpmates; minor white or black promotion in helpselfmates; promoting a fairy piece.

In No.10 black captures a white piece in every move.

• Building and destroying

When one side spoils a structure, which seems set towards mate, a paradox is produced. Sometimes during the solution, a spoiler and a correction of the same element are executed. For instance, blocking a line and reopening it; pinning and unpinning; spoiling a ready-made mate; battery destruction; Phenix (capture of a piece followed by promoting to the same piece). In No.11 there are two batteries aimed towards the black king; black's first move dismantles one battery, while the second move of the black king moves away from the line of the second battery.


Finally, we arrive at the fourth, most appealing family.

Scrutinizing the previous three problems, we can detect that the artistic impression is produced, not only because of the paradox, but also on account of the integration, in one problem, of other attractive elements that were mentioned. In No.9, the impression of the Zugzwang try is enhanced, as it combines foresight; the Zugzwang is not immediate and is created only following white's second move. In No.10, capture of white pieces appears together with hideaway of a white piece. Problem No.11 combines batteries' destruction with Zilahi.

No.13 Ofer Comay
3rd HM, TT Crete 2010
white Qh8 Bg8 Rf8 Ph7g7d6 Ke5 black Kd2 Se1h3 Pf2g3a4b5d7g6 Bf3e3 Rc4
h#3b) Be3 -> g5(7+12)
No.14 Ofer Comay
Variantim 2019
white Kb1 Ba2f1d1d3h3g4h5f5g6e6f7g8e8d7c6a4a6c2h7 Pb3c4d5e4f3e2h2 BLb7c8b5g2 black Ka5 Pe3f4e5d6c5b4
h#19.5Bishop Lions(31+7)
No.15 Ofer Comay
3rd Prize The Problemist 2018
white Bc8 Rh8 Pf7e2h2c6g4g5 Ke5 black Qf8 Bg7 Pa3c2d2g2 Ra2g1 Sa1b1 Kc1
h#3.52 solutions(9+11)

a) 1.Bf3-g4 Rf8-f3{!!} 2.Kd2-e2 Bg8*c4 + 3.Ke2*f3 Qh8-a8 #{,} b) bBe3-->g5 1.Rc4-b4 Bg8-c4{!!} 2.Kd2-c3 Rf8*f3 + 3.Kc3*c4 Qh8-c8 #

1...Kb1-a1{!} 2.Ka5-b6 Bc2-b1 3.Kb6-a7 Bd3-c2 4.Ka7-a8 BLb5-d3 5.Ka8-b8 Bc6-b5 6.Kb8-c7 Bd7-c6 7.Kc7-d8 Be6-d7 8.Kd8-e7 Bf5-e6 9.Ke7-f6 Bg4-f5 10.Kf6-g5 Bh3-g4 11.Kg5-h4 h2-h3 12.Kh4-g3 h3-h4 13.Kg3-h2 Bg4-h3 14.Kh2-h1{!} Bh5-g4 15.Kh1-g1 h4-h5 16.Kg1-f2 h5-h6 17.Kf2-e1 Bg6-h5 18.Ke1-d2 Bh7-g6 19.Kd2-c3 h6-h7 20.Kc3-d4 h7-h8=BL #

1...Ke5-e4 2.Qf8*h8{!!} f7-f8=R{!!} 3.Kc1-d1 Rf8-f1 + 4.Kd1*e2 Bc8-a6 #{,} 1...Ke5-d5 2.Qf8*c8{!!} f7-f8=B{!!} 3.Kc1-b2 Bf8*a3 + 4.Kb2-c3 Rh8-h3 #

Combining such elements in one problem is a pleasure and much to my taste, especially if several elements from different families are integrated into one move. Integrating several elegant elements into one specific move, resembles an artistic peak, when the entire problem is designed to highlight this peak.

In No.12, white's first move (1.♖f1!! or 1.♗f1!!) demonstrates hideaway and a sacrifice that only materializes in black's third move. This means that there is an integration of three families in one move: material paradox, hideaway and foresight. Black's Rundlauf, a sort of time paradox, constitutes also a pretty visual element, thus complementing the artistic impression by combining two additional families.

In No.13, the center of the problem appears in white's first move (1…♖f3!!, and in the twin, 1…♗c4!!). This move combines an Umnov (visual element), hideaway (multiple choice) and a sacrifice of a white piece (material paradox), a sacrifice which is accepted only in black's last move (foresight). Hence, an integration of four families in one move.

No.14, aimed only at brave souls, contains the fairy piece bishop-lion, moving like bishop but must jump over some piece at any move. The point appears in moves to all four corners, a visual element. In the moves where it occurs, another element is added; the move 1…♔a1! combines foresight with hideaway (1…♔b2? ♔c1?). The moves 4.♔a8! and 14.♔h1! combine foresight with time paradox (losing a tempo), while the move 20…e8=BL# shows a promotion to a fairy piece, which is considered as particularly weak.

In the last problem (No.15) there are two points of focus. Following 1…♔e4, the move 2.♕xh8!! combines hideaway with a capture of a white piece (Zilahi). White responds by 3.f8=♖!!, which combines a minor promotion (material paradox) for a reason which will be revealed at a later stage (foresight) and Phenix (destroying and building). In the second solution, after 1…♔d5 the very same elements reappear with 2.♕xc8!! f8=♗!!

I suppose that a majority of composers do not put particular emphasis on the ideas I have presented, because, as I stated at the beginning of this article, it is all leaning on my personal, subjective taste, undiscussed in composing circles. I believe that my background as a chess player, and my attraction as a chess player to sacrifices with deep foresights as the most beautiful chess game combinations, established my current taste. Even today I look for one move that contains paradoxical elements with deep foresight as the most desirable achievement in any chess problem, including helpmates.

Yet I hope that some readers will identify with these ideas, and that I have succeeded to spur fresh thoughts in others, by presenting this view, regarding evaluation of helpmates and taking pleasure from it.

Finally, I wish to thank Amatzia Avni for the translation into English.

Published on Superproblem.ru: May 5, 2020

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