(a, b) jumpers
Under an (a, b) jumper (also (a, b) figure ), where a and b are natural numbers , one understands a game piece that moves on a given two-dimensional game board with a square grid from one field to another, the a fields in one index direction and b fields in the other is removed. The target field can be empty or occupied by an opposing piece, which is then captured. It does not matter whether or not the skipped intermediate fields are occupied. The term is especially important in fairy tale chess and in chess mathematics . In English, such a character is called a leaper .
The movement possibilities of an (a, b) diver are rotationally and mirror-symmetrically, as is generally the case for chess pieces with the exception of pawns . For example, a (0,1) or (1,0) jumper can move one square forward, one to the left, one to the back or one to the right.
An (a, b) jumper always has eight squares on a free, sufficiently large chessboard if a and b are different and not equal to zero. If a and b are the same, the figure dominates four fields, as does an (a, 0) figure.
(a, b) jumpers are examined in chess mathematics. The most common question is whether a given rectangular board can be used as an analogue to the knight's walk, whereby the piece reaches each square exactly once.
Examples of (a, b) jumpers
Modern chess
The only (a, b) jumper in modern chess is the knight - he is the (1,2) figure. The king is a union of (1,0) and (1,1) figures. Tower and runner are so-called riders .
Historical chess
In the original Persian-Arabic chess there were two more (a, b) figures:
For an (a, b) jumper, pieces on anything other than the target field are insignificant, and thus the Alfil can skip pieces that are (1,1) away from him - in contrast to the modern runner, who as (1,1 ) -Rider cannot skip a piece along its diagonal.
Fairytale chess
In fairytale chess , other (a, b) figures are used, such as:
- Vizier : (0,1) jumpers
- Dabbaba : (0.2) jumpers
- Dromedary : (0.3) jumpers
- Camel : (1,3) jumpers
- Zebra : (2,3) jumpers
- Giraffe : (1,4) jumpers
- Hase (English Lancer ): (2,4) -springer
- Antelope : (3,4) jumpers
- Ibis : (1.5) jumpers
- Corsair : (2.5) jumpers
- Flamingo : (1.6) jumpers
Vizier, dabbaba, camel, zebra and giraffe also appear in historical chess variants.
A number of associations of (a, b) jumpers have also been given their own names, e.g. B. the gnu, which is a union of jumper and camel.
Root n jumpers
In chess math, combined (a, b) jumpers whose jumps are the same length are particularly popular. They are called root-n-jumpers , where n is the square of their move length. The simplest such figure is the root 25 jumper (or simply 5 jumper), a combination of (3,4) jumper and (0,5) jumper. Other examples are
- Root 50 jumpers: (5.5) and (1.7) jumpers
- Root 65 jumpers: (4.7) and (1.8) jumpers
Other games
- In Stratego , most of the tokens are (1,0) figures.
- In Xiangqi, the bodyguard pulls like a heel, so he's a (1,1) jumper. The general is a (1.0) jumper or vizier. On the other hand, the horse (analogous to the jumper) and elephant (analogous to the Alfil) are not jumpers in this sense, because they cannot jump over pieces standing in the way.
literature
- Evgeni J. Gik: Chess and Mathematics , Frankfurt a. M. 1987. ISBN 3-87144-987-3
Web links
- Fairytale chess dictionary of the swallow
- GP Jelliss: Knight's Tour Notes . (English)
- GP Jelliss: Theory of moves . (English)