# One-Dimensional Chess

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Everyone knows about 3-D chess, popularised by Star Trek (but actually invented in the nineteenth century and quite popular in Germany at one time).

There are many, many forms of chess, listed by Wikipedia, but they don't mention One-Dimensional chess, so I thought I'd try to create one.

Martin Gardner invented a form of 1-D chess using a standard board, where only one line of eight squares was used. Each player had a king, a castle and a knight, and the game is about as complex as Tic-Tac-Toe (or Noughts and Crosses). An exhaustive analysis of every possible game played with Gardener's rules is given in this very good six-minute video (Warning: also contains cats).

I decided that there had to be a more interesting way of implementing the concept of linear chess, hence this 'Ible.

The end result is good fun, a great conversation piece, and a good way to kill ten minutes at the start of a games night while you're waiting for folk to show up.

### Supplies:

You will need:-

(paper-based)

A printer
A pair of scissors
Sellotape/Scotch tape
The file attached to the next step

OR

(proper board)

Some scrap wood at least two inches by twenty (50mm x 500mm)
A tenon saw
Small paintbrushes
Dark and light varnishes
A cheap chess set for the pieces, unless you have more patience than I do

### Teacher Notes

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## Step 1: Defining the Game

Since there is so little information on one-dimensional chess games, I made a set out of paper which would allow me to experiment with different sizes of boards, starting line-ups, permitted moves etc.

To print the pieces, I needed to find a font which contained the symbols for chess pieces. I used this one, which is free for personal use and which downloaded and installed easily.

Only having access to a small printer, I drew several strips of board which could be cut out and joined together.

Several experimental games were played, which resulted in the decision to use a board of size 16x1, with each side comprising of a rook, king, queen, bishop and knight.

For ease of learning, I have tried to keep the movements of the pieces as close to what they are in 2-d chess, at least philosophically.

The King can only move one square in either direction. It cannot go into check.
The Rook can move or attack up to THREE squares only, in either direction.
The King and Rook, whenever beside each other, can swap places as one move. This can include when the King is in check, but cannot deliver the King into check.
The Bishop can move or attack up to THREE squares of the same colour as the one on which the Bishop is standing, only, in either direction.
The Queen moves as a combination of Rook and Bishop.
The Knight is the most changed. It must move two and then three squares. The moves can be made in either order and in either direction. The Knight can capture a piece on either the intermediate or final square, but it can only capture ONE piece per move.

Given these moves, the file attached above, and the font referenced (or another chess font on your system) you can print out the game and play it. If you have a set of chess pieces already, you can use a subset of those, but

For a much nicer board, read on.

## Step 2: Cutting Wooden Board

I had a strip of scrap plywood just under three inches (75mm) across.

Using a steel ruler, I drew a one-inch (25mm) strip up the centre of the piece, and then marked cross lines to delineate the squares. (second photograph).

I made the border allowance at one end the same as at the sides, and then marked off sixteen one inch squares. Then I marked the border allowance for the other end and cut there (third photo).

To groove the outside of the playing area, I clamped a piece of wood with a straight edge (actually the offcut from the workpiece) along the marked line and then used a tenon-saw. Holding the blade horizontal, I started at the far end of the board and dragged the blade along the guide, cutting down into the line (fourth photo). This takes a bit of care, as you want to leave a clear and quite deep line, while not cutting all the way through the ply of timber. It takes several passes to get a clean cut, so take your time. The fifth photograph shows a close-up of what the cut looks like.

Then I repeated the cut for the ends of the board.

## Step 3: Carving Squares

Using the saw to cut grooves between the individual squares would have left the border looking very rough and fragmented. To make sure that the grooves only separated the playing squares, I used a wide (20mm 3/4") wood chisel.

This was lined up on the outside of the pencil mark at one end and pushed down by hand, then moved along a fraction to join the cut up with the other side of the board.

Then I made the same cut from the opposite side of the line and levered out the matchstick of wood (third photograph).

Repeating the process (fourth photograph) produced a little pile of slivers of wood and a collection of sixteen outlined squares (first photograph).

If the grain on your scrap wood runs in the opposite direction to this piece of ply, you will need to be even more careful to sharpen the chisel.

## Step 4: Staining Squares and Edge

I rubbed off the remaining pencil lines with an eraser, then masked off everything except for every second playing square, and then used a #4 Humbrol model brush to apply a coat of a dark stain and varnish. Using the tiny brush meant that I could get right to the edge of the square without putting stain into the carved groove.

After this had dried, the same squares got a second coat which was left to cure.

N.B. Trap for young players:- the sixth photograph shows the masked board mid-staining. The masking tape was about the same width as the border of the piece, which means that it _almost_ looks as if there are NINE squares to paint. I nearly stained half of the end white square and the border before I realised, and that would have been a hard mistake to come back from.

Once the dark stain had dried, I peeled the masking tape off, masked the playing squares and used a light-brown stain to colour the border. Again, the tiny brush let me keep clear of the carved grooves (mostly).

Once that had dried, it was re-coated, left to dry again and the masking tape was removed.

## Step 5: Finishing the Board

The sides and base of the board were still bare timber so they were sanded down to about 200 grit and then primed and given two coats of flat black paint, again, with much drying time between coats.

Once the paint had dried, I applied two coats of a clear polyurethane varnish to the board. This left the flat black looking rather gloss, but should protect the white squares from staining.

If I were making the board again, I would prepare and paint the sides and base before staining the playing surface, but I had to get a playable board to take along to a games night, hence the out-of-sequence making.

## Step 6: Examples and Strategy

The first photograph above shows (Empty, White Knight, White Bishop, Black Bishop, Empty, Empty, Black Queen, Black Rook).
In this scenario, the White Knight could leap forward two (since it can jump over intermediate squares) and take the Black Bishop, but it could _NOT_ then jump forward three and take the Black Queen since it may only take one piece per move. Therefore, the White Knight could jump forward two and take the Black Bishop and then jump back three.
The White Knight could alternatively jump forward three to an empty square, and then jump forward two to take the Black Queen.
In this photograph, the White Bishop could move forward two squares of its colour (Black) and take the Black Queen, but it could _NOT_ move forward three black squares to the other side of the Black Rook as that would involve passing through an occupied (Black) square.
If this scenario showed Black to move, then the Black Bishop could take the White Knight, or the Black Queen could take the White Bishop.

The second photograph shows (in part) (White Bishop, Empty, Empty, White Knight, Empty, Black Knight, Black Queen).
In this scenario the White Knight could take either the Black Bishop or the Black Queen. The White Bishop could take the Black Queen. The White Queen cannot take the Black Knight because that move is blocked by the White Knight.
If it were Black to move, the Black Knight COULD NOT take the White Knight. If it took the White Knight on the 2-move, then it would need to find a vacant landing spot for the subsequent 3-move, and those square are occupied by the White Bishop and the Black Queen. Similarly, the Black Bishop cannot take the White Knight because the Black knight is blocking its path. The Black Queen could take the White Bishop however.

The third photograph shows (White Queen, White Bishop, Empty, White Knight, Empty, Empty, Black Knight, Black Queen).
The White Knight could take the Black Knight, or could move +2,+3 and jump to the other side of the Black Queen.
The White Bishop cannot move because it is blocked by the White Knight.
The White Queen could take the Black Knight because the intervening squares of the same colour as the one it is currently sitting on are clear.
The Black Knight could take the White Knight with -3, +2, or the Black Queen could take the White Knight since the intervening square of the same colour as the one it is currently sitting on is clear.

The fourth photograph above shows some checking using (White Knight, White Bishop, Black Bishop, Black King, Empty, Black Queen, Black Rook.)
Here, Black King is in check, but _only_ from the White Bishop. The White Knight is not attacking the Black King, since it would not be able to complete its move (blocked by either the White Bishop or the Black Queen).
The only move in this case is for the Black King to move +1 to get out of check.

I've played fewer than a dozen games of this, so if you come across a situation not covered, then please hit me up for an authoritative ruling ;-)

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## 20 Discussions

The knight can jump over occupied squares, but no other piece can. As the bishop or queen can move on a "diagonal" then the squares which have to be unoccupied are the ones of the same colour. All of this is covered in Step 6 Examples and Strategies.
Step 6 covers every situation I could think
of. Once you've internalised the info in that then you should be well on
the way. If there's a specific example that isn't covered in Step 6,
then please post it and I'll see if its covered by the rules.

1) thank you :-)
2) because I _can_!
If you've ever done any geometry, the first question you ask when you've solved something is "does it work in higher dimensions?" So I just went the other way and asked how it would work in fewer dimensions.

I haven't studied this in depth for move combinations however, isn't it like tic, tac, toe? Knots and crosses in other words? The first player wins?

As I say in the introduction, the six-piece, eight square version defined by Martin Gardner was indeed as simple as tic-tac-toe (noughts and crosses). In that version, the first player will always win (unlike in tic-tac-toe where a draw can always be attained).
There is probably an advantage to going first In any game of complete information, and in the MG chess this is insurmountable: in tic-tac-toe it is surmountable.
With this version of 1-D chess, the situation is sufficiently more complex that the surmountability has yet to be determined. Remember that even in standard chess, there are a finite number of possible games and once they have been exhaustively enumerated it will be possible to solve standard chess. It is only the dearth of computing resource which has prevented this happening.
Draughts (checkers) is a simpler game, and it has been solved.
Since this game is simpler than checkers, it should be solvable with current technology. Fill your boots :-)

I'm reminded of a novel I once read (sorry can't remember author or title) where 2 people were imprisoned during the final ultimate battle (between interest and mediocrity) at the end of the world. One of the things they did was play one dimensional Go. I've a feeling their board was infinitely long though so you have a ways to er, go...