by **Arnaldo Rodrigues D’Almeida**

Inventor of
the ** REX** chess

e-mail: (email removed contact us for address) .com.br Webmaster www.geocities.com/xadrezrex

The notation’s goal is to register the moves of a game. The analysis of the games, move by move, will allowthe player to learn the tactics and opponent's strategies. Besides, you can notice your mistakes and successes, what will contribute to improve your performance.

The
notation consists in describing the origin positions and destiny of the piece
that was moved. The representation of those positions is made by Cartesian
coordinates. **Cartesian notation** is based
on two orthogonal axes coordinates. The Cartesian coordinates are formed by the
numeration or ordering of letters of the ranks and files.

There
are hexagonal chess boards that don't have files like in a traditional chess
(for example: ** REX** and

*REX*

Others hexagonal chess
boards don't have ranks like in a traditional chess (for example: **Glinski**,
and **Hexabeast** – see forward), however, ranks will be considered the
group of hexagons disposed in the horizontal and aligned in straight line that
crosses hexagons from corners. Theses hexagons have the same color.

I
suggest that all hexagonal chess variants use the **Cartesian notation**, as ** REX**
chess. This notation system has some advantages:

1-
**Practical
notation** - You can
write the moves of the matches without removing the piece from the board (for
example: **Glinski** chess);

2-
**Standard
notation** - It is
possible to use this notation for all chess variants that use hexagonal or
square cells;

3-
**Easy
notation** - Except
for a large board, it is possible to represent the move with only 4 symbols (letters
and/or numbers),
2 represent the initial position and 2 represent the final position;

4-
**Movement
previews** - It
allows correlating, by equations, the movements of the pieces, what is
fundamental in computer’s programs (see forward);

5-
**Similarity
with chess** – The
traditional chess and square chess variants (small and large boards) use the
same notation.

Some
hexagonal chess variants use the notation based on two axes non orthogonal
coordinates, as in **Hexabeast** Chess (see figure below).

**Hexabeast
Chess**

The
figure below shows **Hexabeast** Chess with Cartesian notation as suggested
by the author.

**T**here
are two basic moves which can describe the movement of all pieces:

**Orthogonal move:** a move wherein a piece moves in straight line that crosses hexagons from
orthogonal sides. Orthogonal moves always go through hexagons of *different*
colors (Rook).

**Diagonal
move:**a
move wherein a piece moves in straight line that crosses hexagons from corners.
Diagonal moves always go through hexagons of the *same* color (Bishop).

**Note:**
The **Knight**
move is a composed move. It moves one cell as Bishop
and another as a Rook, or vice-versa, but the
second move shall be to the same direction as the first one. For example: **Knight**
can be moved 1 hexagon along diagonal and 1 forward hexagon along orthogonal.

**W**hen the
notation is based on two axes’ coordinates, it is possible to preview all
possibilities of movements of the pieces by equations.

**2.1.1- Hexagonal chess boards don't have files**
(** REX**,

**Initial
position:**
(x, y)

**Final
position:**
(x_{f}, y_{f})

**Rook**

Horizontal
direction: (x_{f}, y_{f}) = (x ±
2n, y)

Diagonal
direction: (x_{f}, y_{f}) = (x ±n, y ±n)

n=[1, 2, 3, …)

**Bishop**

Vertical
direction: (x_{f}, y_{f}) = (x,
y ±
2n)

Diagonal
direction: (x_{f}, y_{f}) = (x ±
3n, y ±n)

n=[1, 2, 3, …)

For
example: Bishop on ** REX** chess board
is on

**Question:**
Which are all moves bishop can do?

**Answer:**
Initial position: **d3**=
(4, 3)

Vertical direction:

n = 1
==>
(x_{f},
y_{f})
= (4, 1) =
**d1** or (4, 5) = **d5**;

n = 2
==>
(x_{f},
y_{f})
= (4, 7) =
**d7**;

n = 3
==>
(x_{f},
y_{f})
= (4, 9) =
**d9**;

Diagonal direction:

n = 1
==>
(x_{f},
y_{f})
= (1, 2) = **a2**, (1,
4) = **a4**, (7, 2)
= **g2** or (7, 4) = **g4**;

n = 2
==>
(x_{f},
y_{f})
= (10, 1) = **j1** or (10, 5) = **j5**;

n = 3
==>
(x_{f},
y_{f})
= (13, 6) =
**n6**;

n = 4
==>
(x_{f},
y_{f})
= (16, 7) =
**q7**;

n = 5
==>(x_{f},
y_{f})
= (19, 8) =
**t8**;

**
**

**2.1.2- Hexagonal chess boards don't have ranks**
(**Glinski**, **Hexabeast** and others)

**Initial
position:**
(x, y)

**Final
position:**
(x_{f}, y_{f})

**Rook**

Vertical
direction: (x_{f}, y_{f}) = (x,
y ± 2n)

Diagonal
direction: (x_{f}, y_{f}) = (x ±n, y ±n)

n=[1, 2, 3, …)

**Bishop**

Horizontal
direction: (x_{f}, y_{f}) = (x ±
2n, y)

Diagonal
direction: (x_{f}, y_{f}) = (x ±n, y ±
3n)

n=[1, 2, 3, …)

For
example: Bishop on **Glinski** chess board is on **eh** (initial position,
**see the figure below**)

**Question:**
Which are all moves bishop can do?

**Answer:**
initial position **eh**= (5, 8)

Horizontal direction:

n = 1
==>
(x_{f},
y_{f})
= (3, 8) = **ch **or (7, 8)
= **gh**;

n = 2 ==>
(x_{f},
y_{f})
= (1, 8) = **ah** or (9, 8)
= **ih**;

n
= 3 ==>
(x_{f}, y_{f}) = (11,
8) =
**kh**;

Diagonal direction:

n
= 1 ==>
(x_{f},
y_{f})
= (4, 5) = **de**, (4,
11) = **dk**, (6, 5)
= **fe** or (6, 11) = **fk**;

n = 2
==>
(x_{f},
y_{f})
= (3, 14) = **cn**, (7, 2)
= **gb** or (7, 14) = **gn**;

n
= 3 ==>
(x_{f}, y_{f}) = (2,
17) = **bq** or (8, 17) = **hq**;

2.2- **No
Cartesian Notation **
**(based on 2 non orthogonal axes)**

**Initial
position:**
(x, y)

**Final
position:**
(x_{f}, y_{f})

**For
Chessex** (see
Figure below)

**Rook**

Horizontal
direction: (x_{f}, y_{f}) = (x ±n, y)

Diagonal
direction: (x_{f}, y_{f}) = (x,
y ±n), (x - n, y - n)
or (x +n, y +n)

n=[1, 2, 3, …)

**Bishop**

Vertical
direction: (x_{f}, y_{f}) = (x -n
, y -
2n) or (x +n
, y +
2n)

Diagonal
direction: (x_{f}, y_{f}) = (x -n,
y + n), (x - 2n,
y - n), (x +n,
y - n) or (x + 2n,
y + n)

n=[1, 2, 3, …)

For
example: Bishop on an empty **Chessex** chess board is on **9M** (initial
position, **see the figure above**)

**Question:**
Which are all moves bishop can do?

**Answer:**
initial position **9M**= (9, 13)

Vertical direction:

n = 1
==>
(x_{f},
y_{f})
= (8, 11) = **8K**
or (10, 15) = **10O**;

n = 2
==>
(x_{f},
y_{f})
= (7, 9) =
**7I**;

n = 3
==>
(x_{f},
y_{f})
= (6, 7) =
**6G**;

n = 4
==>
(x_{f},
y_{f})
= (5, 5) =
**5E**;

n = 5
==>
(x_{f},
y_{f})
= (4, 3) =
**4C**;

n = 6
==>
(x_{f},
y_{f})
= (3, 1) =
**3A**;

Diagonal direction:

n = 1 ==>
(x_{f},
y_{f})
= (8, 14) = **8N**, (7,
12) = **7L**, (10, 12)
= **10L** or (11, 14) = **11N**;

n = 2
==>
(x_{f},
y_{f})
= (5, 11) = **5K**, (11, 11)
= **11K** or (13, 15) =
**13O**;

n = 3
==>
(x_{f},
y_{f})
= (3, 10) = **3J** or (12, 10) = **12J**;

n = 4
==>
(x_{f},
y_{f})
= (13, 9) =
**13I**;

n = 5
==>
(x_{f},
y_{f})
= (14, 8) =
**14H**;

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Written by Arnaldo Rodrigues D'Almeida.

WWW page created: September 23, 2002.