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.
White to move:
[FEN "8/q1P1k3/8/8/8/8/6PP/7K w - - 0 1"]
Since my example is rather contrived and artificial, I'll also say that the so-called Lasker trap in the Albin Countergambit gives a more realistic setting, and one where a knight promotion is the best option as early as move 7:
1.d4 d5 2.c4 e5 3.dxe5 d4 4.e3 $2 Bb4+ 5.Bd2 dxe3! 6.Bxb4 $4 ...
In the specific position that you mention, the answer is a resounding no. The king and the knight will defend each other, and white will not be able to force mate.
However, the knight is a clumsy piece. If the knight is not positioned perfectly, then the rook will frequently be able to drive the knight to a bad square and deprive it of moves. Eventually, ...
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, ...
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 ...
Rooks are more suitable for open games where there are open lines. Knight are better for more closed games. Knights have the benefit of jumping over other pieces and rooks have the ability to move quickly whereas knights move very slowly.
Also, remember that you can't checkmate with just a Knight and King, so Rooks are probably more powerful in the endgame ...
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 ...
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 ...
During round 9 of the Istanbul 2012 Chess Olympiads, at the Nakamura-Kramnik table of the USA vs Russia match, we've witnessed another one of those promotions to knight at move 62 by white.
The relevant position (white to play):
[fen "8/2P1k3/8/8/5p2/5KbB/3pp3/3N4 w - - 1 62"]
1. c8=N+ (1. Kxe2? f3+ 2. Kxf3 Bxc7)
We can see here that if
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 ...
After answering this question, I was reminded of another important situation where underpromotion is necessary:
[FEN "8/8/8/8/8/2K5/1p5R/2k5 b - - 0 1"]
1... b1=N+! (1... b1=Q 2. Rh1++)
In this position, 1...b1=N+ is the only move to draw. Any other move will allow a quick mate, but after knighting the pawn, black sets up a drawing fortress.
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 ...
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 ...
There is always a situation where one piece can be better than another.
Rooks are superior to knights because they control more squares, and have more mobility. Also since they control whole ranks and files, they are able to bound the enemy pieces while knights and bishops are much more limited in that regard.
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
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 ...
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
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" ...
Like its cousin endgame KRBvKR, your ending of KRNvKR is usually drawn. It's not always drawn, of course, but generally speaking KRNvKR is much less dangerous and easier to defend than is KRBvKR. In Secrets of Pawnless Endings, John Nunn writes,
If the defending king is not in a corner there are a few situations when the rook and knight can win tactically ...
In one of my books I found this "uncredited" problem, it is probably not the problem you are referring to but I thought you may find it interesting, hope you like it.
2018 Update, thanks to user @Evargalo for adding some light about the author, we can know it was composed by Gijs van Breukelen.
8/3P3k/n2K3p/2p3n1/1b4N1/2p1p1P1/8/3B4 w - - 0 1
1. Nf6+ Kg7 ...
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"]
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.
and white has won a pawn, and has a big lead in development.
Let's assume that white is the side with the two knights, and black has the single pawn. The endgame study composer A. A. Troitzky gave an analysis (in a lengthy supplement to his 1937 Collection of Chess Studies) that established what is now known as the "Troitzky line":
So long as a white knight has the black pawn securely blockaded on one of these ...
Let's start with the 7x7 question:
Is there a forced win on a 7x7 board, with a bishop of the 'wrong' colour?
This seems to be the easier of the two questions to answer. First, convince yourself that this is the only mating pattern (the black king could also be on the dark square immediately to its left):
The key point is that it is not possible for ...
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 ...
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:
2. Ka1 Rc1#
Assuming White to move:
1. Ka1 Kc3
2. Kb1 Kb3
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,