![]() ![]() This doesn't mean you should never move your knights to the edge - sometimes you need to move a knight via an edge square to get it where you need it to go - but you should aways think twice about leaving them there. Knights on the edge of the board have fewer squares to move to, take longer to reach the other side of the board, and can even be trapped. There is an old saying in chess - Knights on the rim are dim. There is nothing black can do to stop the white king from strolling over and capturing the knight. When a knight is on the edge of the board, a bishop three squares away like this can cover every sqaure the knight can move to. ![]() The crosses show where black's knight can move, and the spots show where white's knight can move.īlack has allowed his knight to become cut off behind enemy lines, and the white bishop is able to prevent it from escaping single handedly. Compare the white and black knights on the board below. The squares two squares diagonally from the knight take four moves to reach, despite being fairly close.īecuase the knight has limited range, it likes to be positioned in the centre of the board.It always takes at least 3 moves to move to an opposite coloured square if the knight can't move there in one go.A knight always moves to a different colour square than the one it stands on.There are a few things you should take note of that make working out knight moves easier: Try setting up a board and finding the different routes a knight could take to reach nearby squares. It's always important to bear in mind which squares your knight can reach quickly, and which ones would take a longer manoeuvre, in case you need to redeploy in a hurry. Strong players can tell at a glance how many moves it would take their knight to reach a particular square. finally the move $(2,1)$ exactly $k-2$ times, adding up to the vector $((2k-4),(k-2))$.On each square is the number of moves it would take the white knight to reach it.It takes four knight's moves to cross to the opposite corner of a $3$ by $3$ board and this can be done as shown in the diagram below We know that m is a whole number so it has to be at least $2k 1$ but, in addition to this, we know that m is an even number because the starting and finishing squares are the same colour, so m is at least $2k 2$. We should make a comment about notation here because you may meet vectors written in columns in school work, for example $\left( \begin$. In this article we shall call a move from one square on the diagonal of a chess board to the next a 'diagonal step'. Notice that we are labelling whole squares here and we can think of a lattice of whole numberĬo-ordinates with points at the centres of the squares. and, in general, the square in the $x$ column across and the $y$ row up as $(x,y)$. Label the squares: the bottom left-hand corner square as $(1,1)$, other squares across the bottom row as $(2,1)$, $(3,1)$ etc. We first find the smallest number of moves needed to go from one corner to the opposite corner of a $99$ by $99$ square board and then solve the problem for boards of any size. ![]() Take an even number of moves to get from a square of one colour to a square ofthe same colour. So, as all the squares on the diagonal are the same colour, the number of moves to go to a square along the diagonal from the starting point must be even because it must Ideas of vectors help us to solve problems about knight's moves on an extended chessboard (say a $99$ by $99$ square board).Ī single knight's move takes it two squares parallel to one side of the board and one square parallel to the other side.Any such move always takes the knight to a square of the opposite colour (you might like to check this). You do not need to know anything about chess to understand this article and it should help you to learn about vectors. ![]()
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