5/6/2017 – We have published a number of problems in the past months, initially without the solutions. After some days or weeks we added the solutions on the original page, but of course many readers might have missed this. And some may have missed the problems themselves. So today we bring you a special report with the problems of Pal Benko and Miguel Illescas, with their solutions. The prize winner of the Nihal Sarin puzzle will follow shortly.

On the first of April Pal Benko, the world-famous GM and problem composer, one to the greatest in the field, sent us a number of humorous problems. He called his piece "April Swindles", and if you missed it you can try solving them here. The solutions are given below the problems themselves. The first two represent the numbers 8 and 8, and stand for the age of the composer.

*Problem 1: For both positions the question is: how many mates are there for White in one move. The first problem is for kids, the second one is for adults – it needs some thought. In both cases: what was the last move, before the diagram?*

*Problem 2a: On how many squares can you put the black king so that White can mate in one move. And Problem 2b: Where can you put the black king so it is White to play and mate in two? We found these two problems unexpectedly difficult.*

*Problem 3: On how many squares can you place the white queen, so that, with Black to play, he can mate in one move, in two different ways?*

*Problem 4a: White to play, helpmate in three (i.e. both sides cooperate to get Black mated in three moves). P**roblem 4b: Second solution, White to play, helpmate in three. Here you have to consider the previous move by Black.*

*Problem 5a: Black to play, White checkmates all ten black kings, simultaneously, in two moves. Problem 5b: White to play, checkmates all ten black kings, simultaneously, in three moves.*

The solutions to problem 5 cannot be easily displayed on our JavaScript PGN player, which worries about "legality" or something like that. The solutions are:

1.K8d7 Bb5+ 2. Kdd6 Ne6#

1.b8N! Kdc8 2. Ba6+ K8d8 3. Ne6#!

All ten black kings are checkmated (problem 5b)

In an article entitled "On human and computer intelligence in chess" we presented the reaction of Miguel Illescas, a top Spanish GM and trained computer scientist, to a chess position published by famous mathematics professor Sir Roger Penrose. Miguel included a challenge:

Our readers were invited to analyse the above position, here on our news page, or with their favourite chess engine, to solve it with machine assistance. A number did, and in fact provided interesting feedback on the fortress theme. Here is the solution as provided by Miguel Illescas:

[Event "Fortress study"] [Site "?"] [Date "2017.03.20"] [Round "?"] [White "Illescas, Miguel"] [Black "White to play and draw"] [Result "1/2-1/2"] [Annotator "Illescas,Miguel"] [SetUp "1"] [FEN "1r6/1n1R1b2/8/1p1p3k/pPpPp1p1/2P1P3/P2K1PP1/8 w - - 0 1"] [PlyCount "27"] [EventDate "2017.??.??"] 1. Rxb7 $3 (1. Rxf7 g3 $1 2. fxg3 Nd6 3. Rf6 Rd8 4. Ke2 Kg5 {with advantage for Black.}) 1... Rf8 $1 (1... Rxb7 2. g3 $1 Kg5 3. Ke2 Rb6 4. Kf1 Rh6 5. Kg2 { Draw.}) 2. g3 $1 Kg6 $1 3. Rb6+ $1 (3. Ke2 Rh8 4. Rxb5 Rh1 5. Ra5 Be8 $1 { with advantage for Black.}) 3... Kg7 4. Rh6 $3 Kxh6 5. Ke2 $1 Kg5 6. Kf1 $1 Rh8 7. Kg2 a3 8. Kg1 $1 Ra8 9. Kg2 Ra4 10. Kf1 $1 Be6 11. Ke1 Ra8 12. Kf1 $1 Bf7 13. Kg2 Ra4 14. Kf1 {Draw.} 1/2-1/2

[Event "Fortress study"] [Site "?"] [Date "2006.05.07"] [Round "?"] [White "Illescas, Miguel"] [Black "White to play and draw?"] [Result "*"] [Annotator "Illescas,Miguel"] [SetUp "1"] [FEN "1r6/1nR2bp1/7k/1p1p4/pPpPp1p1/P1P1P3/3K1PP1/8 w - - 0 1"] [PlyCount "4"] [SourceDate "2006.05.01"] {This was my original study in 2006. I first thought that} 1. Rxb7 $1 {makes a draw} (1. Rxf7 g3 $1) {but Black can play} 1... Rf8 $3 ({After} 1... Rxb7 2. g3 $1 Rb6 3. Ke2 Kg5 4. Kf1 Rh6 5. Kg2 $11 {[%csl Rf7,Rg5][%cal Rh6h1]}) {White still tries} 2. g3 $1 {but after} (2. Ke2 g3 $1) 2... Kg6 $1 {the black rook will reach h1 one day and White is definitely worst.} *

*The solutions to the Nihal Sarin problems will follow soon!*

Discussion and Feedback
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@satman:

I wasn't talking about chess problems of the forced mate in 2 or 3 variety. Those should be okay. I was talking about the kind of problems and "studies" that typically get featured here on ChessBase. They seem to have a mountain of analysis to them and by the end, I'm exhausted and not that impressed. I guess I just don't find them as aesthetically pleasing as the composer. I'd rather spend that kind of time and energy playing an actual blitz game.

I wasn't talking about chess problems of the forced mate in 2 or 3 variety. Those should be okay. I was talking about the kind of problems and "studies" that typically get featured here on ChessBase. They seem to have a mountain of analysis to them and by the end, I'm exhausted and not that impressed. I guess I just don't find them as aesthetically pleasing as the composer. I'd rather spend that kind of time and energy playing an actual blitz game.

If you took the trouble to find out about chess problems you'd see that 90% of them are mates in just 2 or 3 moves with usually only 3 or 4 variations - hardly as intimidating as you claim.

As the spokesman for the 'average' player you'll be pleased to learn that with problems you don't have to worry about those things that the average player finds so troublesome.

No need to fret about opening theory, endgame theory, middlegame strategies, the fine points of positional play etc,etc - just show us the tactics!

As the spokesman for the 'average' player you'll be pleased to learn that with problems you don't have to worry about those things that the average player finds so troublesome.

No need to fret about opening theory, endgame theory, middlegame strategies, the fine points of positional play etc,etc - just show us the tactics!

@satman:

"But isn't it the complexity that attracts us to chess?"

Think of it this way. Would a human find a forced mate in 257 moves beautiful? Along with its 56 main variations? You know, the kind of thing computers can identify? Well, that's how most compositions by "master composers" (that abide by all their conventions) look to beginners and average players (i.e. 95% of the chess-playing community). These masters may find that sort of thing highly appealing among themselves and in their elitist publications but it certainly doesn't mean most players do.

Personally, I'm far more attracted to say, a sacrifice combination in a real game. Something master composers might say wasn't worth spit from a traditional composition standpoint. Yet, it's just the sort of thing that ChessBase writes whole articles about and makes headlines. So and so sacrificed a rook! So and so sacrificed a queen! And then Danny King in his wonderful English accent says in his commentary that there was "a beauuutifulll move here". That's what probably appeals to most players.

"But isn't it the complexity that attracts us to chess?"

Think of it this way. Would a human find a forced mate in 257 moves beautiful? Along with its 56 main variations? You know, the kind of thing computers can identify? Well, that's how most compositions by "master composers" (that abide by all their conventions) look to beginners and average players (i.e. 95% of the chess-playing community). These masters may find that sort of thing highly appealing among themselves and in their elitist publications but it certainly doesn't mean most players do.

Personally, I'm far more attracted to say, a sacrifice combination in a real game. Something master composers might say wasn't worth spit from a traditional composition standpoint. Yet, it's just the sort of thing that ChessBase writes whole articles about and makes headlines. So and so sacrificed a rook! So and so sacrificed a queen! And then Danny King in his wonderful English accent says in his commentary that there was "a beauuutifulll move here". That's what probably appeals to most players.

But isn't it the complexity that attracts us to chess?

Don't we admire those players who strive for complexity in their games - Tal, Shirov, Mamedyarov, Nakamura?

In problems we get complexity distilled and served up in small packages, which in most

cases certainly aren't 'waaaay too complicated' for players.

Yes, there's all those weird positions which could never occur in the game, but that shouldn't be reason to be put off.

They say that to succeed in chess one must be able to recognise the typical patterns that occur in the game, and learn the strategy/tactics that stem from them.

In problems there are also typical patterns which occur over and over, just different from those in the game, but again it's good to be familiar with them.

Of course this means spending some time and effort but the results make it worthwhile if you approach it with an open mind.

Don't we admire those players who strive for complexity in their games - Tal, Shirov, Mamedyarov, Nakamura?

In problems we get complexity distilled and served up in small packages, which in most

cases certainly aren't 'waaaay too complicated' for players.

Yes, there's all those weird positions which could never occur in the game, but that shouldn't be reason to be put off.

They say that to succeed in chess one must be able to recognise the typical patterns that occur in the game, and learn the strategy/tactics that stem from them.

In problems there are also typical patterns which occur over and over, just different from those in the game, but again it's good to be familiar with them.

Of course this means spending some time and effort but the results make it worthwhile if you approach it with an open mind.

@turok: Traditional chess problems (by "master" composers) tend to be waaaay too complicated for most players to appreciate. This includes many (if not most) professional players as well. Very likely only a very small percentage of the chess-playing community actually finds them aesthetically-pleasing, interesting or even worth their time solving. So your feelings on the subject are perfectly understandable, if not the norm.

i just never saw the purpose of some of these but i know some really enjoy them.

With all respect to Mr Benko, I'm sure he would be the first to concede that he was not 'one to [sic] the greatest in the field' of problem composition.

It would be nice if Chessbase did occasionally show some examples by those who really are the greats of modern composition.

It would be nice if Chessbase did occasionally show some examples by those who really are the greats of modern composition.

@Frederic 5/7/2017 12:13 That was a nice rejoinder... you can feel the indignation in Frederic's comment. He quickly jumped to Paul Benko's defense :)

@Frederic You are indeed right. Sorry for my incorrect comment. The Rh8 can be captured by White Queen in my above solution.

So Five squares for the white Q is the correct solution, not 8.

So Five squares for the white Q is the correct solution, not 8.

"How come there are two mistakes on these puzzles by Pal Benko? -- He's probably getting old and doesn't use a computer to verify the problems."

Maybe this applies to our readers? "On the puzzle "Where is the White Queen?", the solution is eight squares and not just five. a3,a1,e4,e3,e2,e1,h4,h1 those are possible squares for white queen where black can still deliver mate by Kf7# and 0-0#". Really? wQa1, wQh4, wQh1: 1...Kf7+ 2.Qxh8.

Pal is one of the most astute human beings I know. My hope is that when (actually if) I reach his age I will be half as awake and half as creative as he is.

Maybe this applies to our readers? "On the puzzle "Where is the White Queen?", the solution is eight squares and not just five. a3,a1,e4,e3,e2,e1,h4,h1 those are possible squares for white queen where black can still deliver mate by Kf7# and 0-0#". Really? wQa1, wQh4, wQh1: 1...Kf7+ 2.Qxh8.

Pal is one of the most astute human beings I know. My hope is that when (actually if) I reach his age I will be half as awake and half as creative as he is.

The comment in problem 4b "In such problems en passant and castling are considered legal if you cannot prove that they are not," was inserted by me. It is indeed not accurate: only if retrograde analysis reveals that the last move had to be a double step of a pawn then a given en passant capture is legal. For instance:

Black's previous move can only have been ...g7-g5 (...Kg7-h6 is impossible since the f6 pawn could not have just moved to give check). Therefore en passant capture is legal and the solution is 1.h5xg6 e.p. Kh5 2.Rxh7#.

Black's previous move can only have been ...g7-g5 (...Kg7-h6 is impossible since the f6 pawn could not have just moved to give check). Therefore en passant capture is legal and the solution is 1.h5xg6 e.p. Kh5 2.Rxh7#.

In problem 2b, black king can also be on a3,a2 or a1 and white mates with 1.Rb5! followed by a8Q

@Mark S:

"How come there are two mistakes on these puzzles by Pal Benko?"

He's probably getting old and doesn't use a computer to verify the problems.

"How come there are two mistakes on these puzzles by Pal Benko?"

He's probably getting old and doesn't use a computer to verify the problems.

How come there are two mistakes on these puzzles by Pal Benko?

On the very first diagram above, "what was the last move" adult puzzle, the last move of black was 1...e1{B} underpromotion to a bishop and white can deliver 6 types of mates.

On the puzzle "Where is the White Queen?", the solution is eight squares and not just five. a3,a1,e4,e3,e2,e1,h4,h1 those are possible squares for white queen where black can still deliver mate by Kf7# and 0-0#

@JoshuaVGreen: You are correct. This is one of many composition "conventions" and I've come across it myself. Also, because castling cannot (always?) be proven even via retrograde analysis, they should be avoided in traditional problems, I believe.

In your solution to Benko's H#3 (2 solutions), the statement "In such problems en passant and castling are considered legal if you cannot prove that they are not" is simply WRONG. True, castling is assumed to be legal unless it can be proven otherwise, but en passant is considered ILLEGAL unless it can be proven otherwise. The reason for this distinction is simple -- one can NEVER prove that castling is legal (without a bunch of extra information), but it can be possible to prove that en passant is.

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