Advanced Math/Chess Indoor Game - Reinventing - Maths Application.
Expert: Scott A Wilson - 9/27/2011
QuestionQUESTION: Dear Scott
Re engineered Chess Board Layout.
where the Total Number of squares will be 144 i.e. 12 square instead of 64
i.e 8 square.
Instead of 32 pieces altogether i.e 16 total pieces for white and 16 total pieces for black, there will be total 48 pieces i.e 24 total pieces for white and 24 total pieces for black.
Rooks - 2 nos (same nos because of the short/long castle)
Pawns - 12 nos (instead of 8 nos)
Knights - 4 nos (instead of 2 nos)
Bishops - 4 nos (instead of 2 nos)
Queen - 1 no (same no)
King - 1 no (same no)
12 11 10 9 8 7 6 5 4 3 2 1
P P P P P P P P P P P P
R K B K B Q KI B K B K R
R -> Rook
K -> Knight
B -> Bishop
KI -> King
Q -> Queen
P -> Pawn
Awaiting your inputs, views
Thanks & Regards,
Prashant S Akerkar
ANSWER: This sounds like a whole new game that would be fun to play.
For example, the bishops could guard each other and
having four knights on your side could make the game much more interesting.
I have sometimes played different games of chess as well.
One had only the king in the back row and all eight pawns up front.
Others have been found by not having some of the pieces,
like all but queen, all but rooks and bishops, no pawns (that was deadly, short, and unfair for black). It can also be played where there are no other pieces but the king and pawns and pawns must become bishop or pawns must become knights.
I have also palyed chess like it was on a cyllinder, even though it was still square.
In this game, rooks start out guarding each other or a bishop could start from just ahead of the rook's pawn and end up on the other side of the board a square in front or behind of where she was. This would really be interesting for an odd number of squares, for there would be no white bishops or black bishops since going off one side and onto the other would change their color.
That brings up something else. What about a board with an odd number of squares each way and the king in the center of the row of men with no queen? What about a game with two boards that had a doorway between them? Or maybe more boards with a teleportation square? What about if chess was played in a board that resembled a house? In the hall, you could move as chess men. If the result of your movement was just past a door, you would end up in that room.
What about a chess game with land and water and a small boat?
Boy, this is getting complicated ...
What input are you looking for?
---------- FOLLOW-UP ----------
QUESTION: Dear Prof Scott
Thank you.
I worked in the following way.
64 is a perfect square.
Square of a Even Number is a Even Number.
2 square = 4, 4 square = 16, 6 square = 36, 8 square = 64 .............
Square of a Odd Number is a Odd Number.
1 square = 1, 3 square = 9, 5 square = 25, 7 square = 49 ...............
Area of a square = side * side
8 square = 64
its white and black pieces , if i take 9 square to increase the area,
it will be 81 then where extra one square i will create on the board
which will be white or black ?
so i have to have a even perfect square to increase the area of the chess
board. it will be 10, 12, 14, 16 ........
i took 12 square = 144 total squares evenly divided with 72 white and 72 black squares.
Finally with more area i have to add major and minor pieces to the chess board.
Rooks - 2 nos (same nos because of the short/long castle)
Pawns - 12 nos (instead of 8 nos)
Knights - 4 nos (instead of 2 nos)
Bishops - 4 nos (instead of 2 nos)
Queen - 1 no (same no)
King - 1 no (same no).
We can have 100, 144, 196, 256, 324, 400 square pieces chess board manufactured with additional number of bishops, knights and pawns added to the chess board.
isn't it ?
Thanks & Regards,
Prashant S Akerkar
ANSWER: Yes, this is true that is the board has an odd number of squares in both directions,
there is a difference between the white and the black squares of 1.
To fix that, if the board is, say, 7 units wide (R K B Ki B K R, with pawns in front).
if it was made, like, 8 or 10 long it would still had and even number of squares.
The problem here is that white would have two bishops on red squares and black would have two bishops on black squares (or is it the other way around?) For an odd number of squares, the easiest piece to drop would be the queen from both sides, but it could also be a rook from each side of a knight from each side.
The number of squares is now even, and to fix the B color, making it R K B Ki K B R
would give either side on black and one white bishop.
By the way, what do you think about three way chess on a hexagonal board?
I think it would be kind of interesting in that bishops and rooks would be the same,
so they might be called roops or books or bics ... or rishies?
What about a piece that blew up on command, making the square it is on impassable?
Maybe these pieces could be called radioactive pieces?
---------- FOLLOW-UP ----------
QUESTION: Dear Prof Scott
Can we add a New Piece named Jack on the Chess Board similar to Jack Card in Card Games ?.
This is possible for Area of a chess board being increased i.e instead of 64, it will be a 256 square board manufactured.
i.e.
Rooks - 2 nos (same nos because of the short/long castle)
Pawns - 16 nos (instead of 8 nos)
Knights - 4 nos (instead of 2 nos)
Bishops - 4 nos (instead of 2 nos)
Jacks - 4 nos (instead of 2 nos)
Queen - 1 no (same no)
King - 1 no (same no)
Jack's Piece Movement on the chess board will be a combination of Rook + Bishop but can move only two steps in either Horizontal, Vertical Direction
similar to Rook and move Diagonally as a Bishop but only two steps.
Jack Piece
------------
it is not as powerful as Queen Piece.
It is less powerful than Rook Piece.
It is powerful similar to a Bishop and Knight Piece.
1 -> Rook
2 -> Knight
3 -> Bishop
4 -> Jack
5 -> Knight
6 -> Bishop
7 -> Jack
8 -> Queen
9 -> King
10 -> Jack
11 -> Bishop
12 -> Knight
13 -> Jack
14 -> Bishop
15 -> Knight
16 -> Rook
Thanks & Regards,
Prashant S Akerkar
AnswerThis looks like a game that would be of great interest.
I like the new piece, the jack.
I can say that since the board is twice as long and wide, it would be 4 times as large.
I hope this does not mean it takes 4 times as long to play.
Rooks: just like regular chess, the rook is not guarded at the start.
Pawns: Also similar to regular chess is that at the start, all of the pawns are covered.
In this style of chess, the 4 move game where the king's pawn is taken by the queen with a backup will not work, for the pawns are even more convered here than in an 8x8.