57
Yes, it can
This particular knight's tour is closed, meaning that it starts and finishes in the same square. Therefore, the knight can start at any square on the board and finish on the same square, since it just starts at a different point along the cycle.
31
It's impossible. Knights require an even number of moves to reach a square of the same color as where they started, or correspondingly an odd number of moves to reach the opposite color. Both sides need to make an even number of moves to reach the starting position.
28
They're connected knights.
As the other answers said, this isn't typically that smart a thing for knights. OTOH, rooks are very often made stronger by connecting them (it allows them to thwart any queen intrusion). Thus you'll more often hear about it being “a good idea to connect rooks now”. But I think I've also heard the term used with knights. Just, ...
25
Depending on whether occupied squares need to be covered as well, the number is:
[Title " 12 knights, Without Covering Occupied Squares"]
[FEN "8/5N2/1NN1NN2/2N5/5N2/2NN1NN1/2N5/8 w - - 0 1"]
[Title " 14 knights, With Covering Occupied Squares"]
[FEN "8/2N1NN2/2N1N3/2N3N1/2N1N3/1NN1NNN1/8/8 w - - 0 1"]
Problems like this are called domination problems and ...
24
Actually, the bishop and knight mate is not as slippery as it appears. I have checked this on a tablebase program I wrote. On a 10x10 board, the side with the bishop and knight (say white) can force mate in at most 47 moves. White can even force mate on a 16x16 board, in at most 93 moves. I believe mate can be forced on an arbitrarily large even size ...
24
It is a fairly short and simple explanation:
They can combine to attack any square, not just squares on one color. As part of that they can also shift the attack better from one square to another.
22
The weaker side needs to keep Knight close to his King in order to achieve draw.
There are some special cases where the stronger side wins even in those situations, like when Knight is cornered or pinned in such a way that puts weaker side in zugzwang.
If the Knight is far away from the King then the result of the game depends whether or not the defending ...
answered Mar 10 '14 at 21:18
AlwaysLearningNewStuff
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20
it's a bishop for knight in my favor
So what? You will have moved the knight 3 times to your opponent's bishop 1 move and you will have improved your opponent's position by opening the f file for him. So, not in your favour after all.
the bishop makes my position slightly vulnerable because of the pin on the queen
No, it doesn't. If it ever becomes a ...
19
14 non-attacking bishops
We may consider the white-square bishops and the black-square bishops separately.
At most 7 bishops can be placed on white squares, namely, at most one bishop on each of the 7 white diagonals parallel to the h1-a8 diagonal. In fact, we can put bishops on the 7 white squares b1, d1, f1, h1, c8, e8, g8.
The solution for black-square ...
16
It is true, that sometimes occupying weak squares with your pieces will just lead to exchanges and no advantage whatsoever. But there is a well known dictum in chess, that "the threat is stronger than the execution".
This means that just threatening to occupy a weak square can severely restrict your opponent's possibilities. Just imagine you brought a ...
16
An exhaustive computer search shows that as expected K+N cannot in general
force stalemate against a lone K.
In fact, the defending King can avoid stalemate as long as it's not on
one of the six-square triangular neighborhoods of the corners
shown in the following diagram
[Title "Danger Zone"]
[fen "kkK2Kkk/kK4Kk/K6K/8/8/K6K/kK4Kk/kkK2Kkk w - - 0 0"]
even ...
16
Well, simply put, they chose to follow the USCF "Article 14: The Drawn Game rule 14E: Insufficient material to win on time, 14E3: King and two knights."
While it is not a forced mate, there is a mating position that is possible, thus they could have easily followed the FIDE rule, and allowed the side with the knights to continue playing.
It was probably a ...
16
One of the ways I teach kids how knights move is to put the queen and the knight on the same square. The knight can go to the nearest squares that the queen can't go to.
It is this unique complimentary nature of the two pieces which means that they form such a potent combination. With queen plus any other piece this is missing and there is a duplication of ...
15
I've seen the term "redundant knights". In general, redundant pieces are pieces can get in each other's way. Here's a quote I could find about the general principle, but not specifically about knights:
Interestingly, two of Lasker’s other points were:
• The principle of
redundancy: Two pieces that move the same way on the same squares can
easily ...
14
Your description of the computer's suggestions doesn't quite match the position, but if you mean the computer suggests Nxe5, that is correct, as Bxd1 leads to a variation of Legal's Mate.
Nxe5 Bxd1
Bxf7+ Ke7
Nd5#
If, instead,
Nxe5 dxe5
Qxg4
and white has won a pawn, and has a big lead in development.
14
John Watson's "Secrets of Modern Chess Strategy" contains a section titled "Folklore or Reality? Queens and Knights" John lists some folks that say Queen and Knight are better
Capablanca
Shirov
Silman
And refers to Steve Meyer's book "Bishop vs Knights" which also says the Queen + Knight is better.
I am currently playing through "Karpov move by move" ...
13
If given the choice should I opt for an endgame with a single Bishop or a single Knight?
In order to properly answer this question I must point out differences between bishop and knight:
Bishop is a faster piece and has a longer range of fire, but can cover only half of the board.
Knight on the other hand, is a slow and clumsy piece but covers squares of ...
answered Apr 20 '14 at 0:49
AlwaysLearningNewStuff
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13
For knights, the maximum is 32. Since knights can only attack the color opposite of the square they’re on, placing one on 32 squares of the same color is therefore optimal.
[FEN "N1N1N1N1/1N1N1N1N/N1N1N1N1/1N1N1N1N/N1N1N1N1/1N1N1N1N/N1N1N1N1/1N1N1N1N w - - 0 1"]
As for bishops, 14 is the highest possible.
[FEN "B7/B6B/B6B/B6B/B6B/B6B/B6B/B7 w ...
12
I noticed a simplification of @RosieF's solution:
Label the squares with two-number labels as follows:
4,2 0,3 1,4 2,0 3,1
1,0 2,1 3,2 4,3 0,4
3,3 4,4 0,0 1,1 2,2
0,1 1,2 2,3 3,4 4,0
2,4 3,0 4,1 0,2 1,3
Then two knights may occupy two squares x,y
and X,Y iff those squares' first numbers x and X are different and
their second numbers y and Y are ...
12
The concept of a knight which is so powerfully placed (generally on e6/e3) that the game wins itself dates, according to Winter, from:
An observation by Zukertort after 26 Ne6 in the simultaneous game
Steinitz v Maas, London, 5 November 1873:
‘The appearance of the knight at K6 [e6 for white, e3 for black] is generally, for the opponent,
the ...
11
There are even positions where one promotes R or B to save a draw by getting stalemated (rather than win by avoiding stalemate). One example is the Traxler-Dedrle setup:
[FEN "4rN1K/5qP1/8/8/8/8/k7/8 w - - 0 1"]
1. g8=B!! (1. g8=Q Rxf8 2. Qxf8 Qxf8) Rxf8
WTM loses with 1 g8Q? Rxf8 2 Qxf8 Qxf8+ but draws with 1 g8B!! when Rxf8 is stalemate (NB the g8B ...
11
Yes, since K+R is an easy beginner checkmate. In fact, the Knight will get in the way. The only value of the Knight will be to get White into Zugzwang quicker (easier?), which helps Black push the king to an edge.
To answer the specific question, from above, assuming Black to move:
1... Kc3
2. Ka1 Rc1#
Assuming White to move:
1. Ka1 Kc3
2. Kb1 Kb3
3. ...
11
You must be thinking of this classic Korolkov study (I-II Prize "64" 1937, according to Chernev's Chessboard Magic!; P1288537 in PDB). It's not a problem, nor in 7 moves, but seems to match the rest closely:
[Title "White to play and win (Korolkov 1937)"]
[Fen "4N3/2PP2P1/6b2/2bN2R1/6pk/p7/K1pn4/8 w - - 0 0"]
1.Rh5+ Kxh5 2.Nf4+...
11
Without any pawns Queen vs Knight endgame is a theoretical win for the Queen.
Actually, most chess sites that have checkmates practice offer this very problem as one of them, along side many other classical ones such as Queen vs Rook, Two Bishops, etc.
Take a look at this mate problem in lichess
The same problem in chess.com
Here is an example of how you ...
11
First, the good: You are probably winning this throughout the game, and thus, improving your position gradually was the perfect plan. It also was one of the best examples of Shereshevsky's "Do Not Hurry" principle that I have ever seen. Black could do nothing, so gradually improving, and eventually converting, was perfect since you had all the time in the ...
11
It's probably first worth revisiting why the "standard" moves are normally preferred.
A white knight on c3 defends white's central square e4 and attacks black's central square d5. That is that knight attacks/defends/supports 2 out of the 4 central squares. In the opening those 4 squares are the most important squares on the board (unless you fall ...
11
14.Nxd4 takes a pawn on d4, and it attacks the bishop on h5. So if black takes back with 14...cxd4, then white has 15.Bxh5, leaving white a pawn up (knights and bishops have roughly the same value). And if black wants to avoid this with 14...Bxe2, white can take back with the knight on d4 (15.Nxe2) so that it is safe too; again, white wins a pawn. And if ...
10
In analyzing and studying this endgame, I believe I have found a very simple way to explain the defensive technique (for this example, we will consider the defender to be Black). Once I learned this technique, I played some blitz Rook vs Knight endgames vs top chess programs and drew all of them.
Knight's Box
I found it useful to visualize the technique ...
10
As far as I know, there's no standard terminology for this. It is usually not the best configuration for two knights; they are stronger when positioned side by side, so that they cover a lot of squares in the same area.
If I had to describe the situation, I'd go for something like 'mutually protecting knights'.
There's a related concept which is called the '...
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