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Knight Moves

9/27/2015

A knight positioned in the corner of the board can make two moves while a knight positioned on a central square can visit eight possible squares. (Side question: Given a number between 2 and 8, is it possible for a knight to have that number of possible moves? For example a knight on b1 can make 3 possible moves.) In the previous post we examined problems in which a pawn could make the maximum possible number of moves. In this post we will examine problems in which a knight can make its maximum eight moves. Such problems are often known as task problems. When a black knight makes its eight possible moves and the theme is called a knight wheel. When a white knight makes its eight possible moves it is called a knight tour. As usual you will scroll down for the solution to my problems and click on the diagrams for the solutions to the other problems.

7 + 8

Here is my knight tour. The key is strong in the sense that it makes multiple threats but each of the threats are enforced. It is clear that the wSc4 will make the tour. See if you can spot the black defenses that force 2.Sf5 and 2.Se2. Scroll down for the solution.

Stubbs, Charles Francis
Checkmate 1903

7 + 2

Here is an economical knight wheel. It also contains a classic bS vs wB duel - six different moves of the bS lead to six different moves of the wB.

Mansfield, Comins
Morning Post 1933

9 + 3

Mansfield's classic knight wheel. If you read my last post you will recognized that this is a changed waiter. There is a mate set for every move of the bS but one of the mates must be changed. Brain Harley referred to this problem as a knight wheel with 9 spokes.

Mansfield, Comins
Chess Life 1969

12 + 8

Manfield makes it look so easy! This time when he was over 70 years old. A beautiful flight giving key is the reason I could not resist adding this one to the blog. Two self-pins and two interference mates highlight the play.

Heathcote, Godfrey
Hampstead and Highgate Express 1905

10 + 11

No post on the knight wheels would be complete with out Heathcote's masterpiece. In the knight wheel task the threat will often be to capture the knight making the wheel. When the knight moves it defeats the threat. Here that is not the case. Here the key is 1.Rc7 threatening 2.Sc3. The move of bSd4 defeats the threat because it will open a flight square after the wS closes the wBb2's line. What follows is beautiful: 2 self blocks, 5 line interferences, and a self pin.

Boyer, Jean-Pierre
Europe Echecs 1983

9 + 3

We end our knight wheels with a beautiful little try problem. A wQ vs bS duel. The wQ can mate if it can just get access to a square in the bK's field. The wS can mate on b6 if a guard is placed on e5. Let's give it a shot. A clever device handles the cook-tries, that try to capture the knight: 1.g3/g4/Qe1/Qh4 is met by 1...d3! which closes the line of guard to e4. So the wQ starts her march:

1.Qg1? (2.Qd4) Sf2!
   1.Qf1? (2.Qc4) Sd6!
1.Qd1? (2.Qxd4) Sd2!
   1.Qc1? (2.Qc4/Qc6) Sc3!
   1.Qh2? (2.Sb6) Sg3!
   1.Qh3? (2.Qe6) Sc5!
   1.Qh5? (2.Sb6) Sg5!
   1.Qh6? (2.Qe6/Qc6) Sf6!

The only square left is 1.Qh8! with the double threat of 2.Qa8/Sb6. Wow.

Loyd, Samuel
Paris Ty. 1878

7 + 10

Loyd executes a knight tour with a nice Novotny key 1.Rf3!

Bottacchi, Antonio
Good Companions, 8th American Chess Congress 1921

8 + 4

Here is classic Meredith. The wS and bQ go to battle and what results is a complete knight tour.

Latzel, Gerhard Paul
Die Schwalbe 1956

4 + 3

Now a try problem. The wS should make the key but what square should it land on? Seven of the tries are refuted in different ways.

Lipton, Michael
American Chess Bulletin 1957

9 + 7

Another try problem. Which knight should make tour? The try provides a complete wS tour but is defeated by a unique defense.

Morse, Jeremy
problem (Zagreb) 1965

14 +8

A now a monumental task problem. The double knight wheel (16 forced mates between two wS's) has been done by by Petrovic 1963. The matrix to the right does not quite accomplish because it only attains 15 distinct mates (2.Sg7 is missing). But it has a much better key and play.

Petrović, Nenad
Chess 1946

16 + 6

Here is an example that combines a knight wheel and a knight tour! The key makes multiple threats but every threat is enforced and a complete knight tour results. Moreover, a complete knight wheel results from the moves of bSd5.

For the first problem the key 1.Re4 makes 7 threats (2.Sb3/Sc2/Sc6/Se6/Sf5/Sf3/Se2). The key gives a flight and the king's move 1...Kc5 forces 2.Sf5. The move 1...c2 forces 2.Se2. Moreover, 1...Sxb5 defeats all of the threats but finishes the knight tour. Answer to the side question: A knight can have 2,3,4,6, or 8 moves.

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Changed Waiters

9/18/2015

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A position in which every black move has a set white continuation is known as a complete block. To solve such a problem one just needs to find a white move that preserves all of these set white moves - a waiting move. Sometimes there is not waiting move to be found and one has to change one or more of the mates. If there is no threat after the key then such a problem is called a changed waiter or mutate. The Warton brothers specialized in changed waiters and their work is represented below. Since I love mutates (who doesn't) I have selected several problems. As usual we begin with one of my own.

Moen, Kabe
Original 2016

6 + 5

Here is a simple mutate that was made by modifying one of my other problems. The set play is as follows:
1...Qd4,Qd3,Qd2 2.RxQ
1...Qxd1 2.Rxd1
1...f5 2.Bxe5
No waiting move is available so one of the mates must be changed. The nice key 1.Rh1! unguards e5 to access the sixth rank. 1...f5 2.Rh6. There is not a lot of play but the position is elegant and open without any white pawns.

Shinkman, William
1900??

4 + 2

We begin with a very simple miniature from the Wizard of Grand Rapids that will give you a taste of what mutates are about. Black has one move, 1...Sg6, to which white can respond with 2.Qxg6#. However, there is no waiting move available because any move by white will either free the king or unguard g6. Instead a new, pure, mate (each square in the kings field is covered only once) is arranged that uses the knight to self block on g6.

Mansfield, Comins
The Observer 1919

6 + 4

Here is an elegant example from Comins Mansfield. The key only changes one mate but the change is a nice one. The R+P battery changes gets swapped for a royal battery. Click on the diagrams solutions.

D'oily Bernard, Henry
Grantham Journal 1928

9 + 9

Here is a beautiful changed waiter. It seems that there should be a waiting move that preserves all of the set mates yet there is not. The bQ controls the squares d3 and e6. If she moves then she will lose her control over these squares (focal play). If the bP on a7 or bS move then they will interfere with her lines. In either case the wS will be able to mate on the critical squares. The key abandons this plan by giving up the guard on e4 and changing the foci to f1 and f6. All while sacrificing the wR in the process.

Warton, Joseph and Warton, Thomas
Western Daily Mercury 1918

9 + 10

A classic Warton brothers problem. The key changes two of the mates. The bishop hides behind the queen to take over pinning duties for the queen which now can be pinned herself.

Warton, Joseph and Warton, Thomas
The Observer 1942

9 + 10

Another Warton brothers classic. Again, only one change but a beautiful one. The set double pin mate gets changed into a Gamage unpin.

Bwee, Touw Hian
Die Schwalbe 1967

8 + 8

One of my favorite changed waiters in terms of surprising change. The R+P battery gets swapped for a Bristol clearance.

Bwee, Touw Hian
Sinfonie Scacchistiche 1967

8 + 10

Here is a tour de force. The key changes all four set mates, sacrifices the wSe3, and adds a mate.

Warton, Joseph and Warton, Thomas
The Observer 1946

5 + 7

We end with one of my favorite three movers of all time. Notice that the wB on e1 is ready to mate with BxR as soon as the bB on h2 relinquishes its guard on the g3. The bB on h7 gives black an extra move. However, any moves by bBh7 lead to an immediate capture by the wB, wK, or wS on c5. This is the grab theme and in this case a complete block. No waiting move that preserves these captures is to be found. What remains is to give the bB the square f5 while closing the other line for the bR for: 2.Ba5 ~ 3.Bd8#.

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Pawn Moves

9/13/2015

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A pawn in its game array position (not on the edge of the board) can make 4 possible moves: forward one square, forward two squares and, if the opportunity presents itself, it can capture on the adjacent diagonal squares. In a problem, when a black pawn makes its four possible moves the theme is called a Pickaninny. When a white pawn makes its four possible moves in the course of a problem the theme is called an Albino. We have seen examples of both themes already in the half-pin and AUW posts. As usual we begin with an unpublished problem of my own and then get into some of my favorite examples.

8 + 5

Here is my Pickaninny. The bPd7 is set up to make its four possible moves. Notice that there are mates set for all of blacks moves except 1...d6. See if you can find the key that deals with this move and scroll down for the solution.

Ouellet , Charles.
The Problemist 1987

5 + 3

Here is a simple near miniature that perfectly executes the Albino theme. The key is 1.Rbb5(-).

Bwee, Touw Hian.
Die Schwalbe 1977

11 + 6

One of the most effective ways to demonstration the themes in a two mover is to use try play. In the following problem there are mates set for all of black moves except 1...PxP. There are four ways to move wPc2 to prevent this from happening. However, each of the four Albino tries prevents one of the set mates.

Reeves , Arther Christopher.
Probleemblad 1965

9 + 10

We end with a beautiful combination of the Albino and Pickaninny themes. In this example the wPc2 offers four albino tries that are each uniquely refuted by the four pickaninny moves of bPe7.

Solution to the first problem: notice that the wQ controls the squares d5 and d6. If these squares are blocked with the bPd7 then the wQ can use this to her advantage. In particular, notice the dual after 1...d5 2.Qf4/Qh2. The key 1.Kg6(-) clears the way for the wQ to handle 1...d6 with 2.Qg5 and gets rid of the dual.

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Allumwandlung

9/6/2015

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Allumwandlung (AUW for short) is German for "complete promotion", that is, during the problem a pawn is promoted to a knight, bishop, rook, and queen. In a two mover one way to accomplish AUW is through a twinning or quadrupling as it would be.

b)-c5,c6,e7 c)-b8,f7 d)-b8,c6,e7

6 + 2

Here is my attempt at AUW. I was inspired by the below matrix to make a quadruplet that accomplishes AUW but does not have crude keys. However the alterations are too much to be considered as an actual quadruplet. Scroll down for solution.

Speckmann, Werner.
Shakhmaty v SSSR 1965

b)-c6 c) further-b7 d) further-a5

6 + 1

A classic from the German miniaturist. This is a progressive twin which means that c) is derived from b)'s diagram and d) is derived from c), Each progression reduces one piece. Very elegant but the keys are crude - checking or flight taking. Click on the diagram for the solution.

Shinkman, William Anthony
Detroit Free Press 1883

10 + 5

Here is the first three mover posted to the blog. This is one of my personal favorite Shinkman problems. The key is very crude but the play that follows is amazing. Click on the diagram for solution.

Niemeijer, Meindert
Tijdschrift vd NSB 1928

9 + 8

Here is a problem that combines AUW with another theme: the pickaninny theme. The capture key is crude but the accomplishment is well justified: all four moves of the bPf7 yield a different promotion. Click on the diagram for solution.

Abdurahmanović, Fadil
Turnier jugoslawische Bundesrepubliken 1957

6 + 1

Now a try problem. The bK has three flights, none of them with mates provided. The wP on c7 is begging to be promoted. Each possible promotion leads to a different try: 1.c8=Q stalemate! 1.c8=R 2.Ke6! 1.c8=B 2.Kc6! 1.c8=S 1.Kc4!. Each under promotion is refuted by a unique flight of the king. What remains is to provide the bK a fourth flight on e4 giving the star flight theme.

Shanahan, Ian
The Problemist Supplement 2001

5 + 5

Finally we end with a two mover that accomplishes black AUW and combines with another theme: combinative separation. The key makes 3 different threats and all possible combinations \(7=2^3-1\) of these threats are given by black's possible moves (4 different from the bPg2's possible promotions). Very mathematical! Click on the diagram for solution.

Solution: The promotions go in turn: (a) 1.f8=S (b) 1.f8=B (c) 1.e8=R (d) 1.f8=Q. As mentioned above none of the keys take any flight squares from the king, in fact, they give flight squares in (a) and (b) by setting up indirect batteries and sacrificing the wS.

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