Single Comment

I have expanded Fischer's mathematics system to cater for Capablanca's
chess variations.

Capablanca84000 is a variant of Fischer Random Chess (Chess960), based
on the Capablanca (10x8) variation.
The light (for white. dark squared for black) squared bishop may start
on one of 5 files (b,d,f,h,j). the dark (light for black) squared
bishop may similarly begin on one of 5 files (a,c,e,g,i).
The archbishop may then be placed on any of the remaining 8 files.
The chancellor may then be placed on any of the remaining 7 files.
The queen may then be placed on any of the remaining 6 files.
The two knights may be placed within the remaining 5 files in 10 ways:
1+2, 1+3, 1+4, 1+5, 2+3, 2+4, 2+5, 3+4, 3+5, 4+5.
The remaining 3 files are filled in the order of rook-king-rook to
allow for castling on both sides of the king.
Multiplying the quotients gives the number of combinations: 5 x 5 x 8
x 7 x 6 x 10 = 84,000

By taking the random number, 12345, we can calculate the combination
for white (black is mirrored from white through 4th/5th rank).
Placement of light squared bishop: 12345/5 = 2469 with no remainder.
the light squared bishop goes in it's first possible file, b.
Placement of the dark squared bishop: 2469/5 = 493 with remainder of
4. The dark squared bishop goes in it's last possible file, j.
Placement of the archbishop: 493/8 = 61 with remainder 5. The
archbishop goes into its 6th (note, lowest remainder is 0, not 1)
possible file. b and j are already taken, so the archbishop goes into
file g.
Position of the chancellor: 61/7 = 8 with remainder 5. The chancellor
goes into the 6th available file. b, g and j are taken, so the
chancellor goes into file h.
Placement of the queen: 8/6 = 1 with remainder 2. The queen goes into
the 3rd possible file. b, g, h and j are taken so the queen goes into
file d.
Placement of the two knights: The last integer result, 1, indicates
that the two knights occupy the 2nd possible combination of files,
1+3. b, d, g, h and j are taken, so the knights occupy files a and e.
The remaining three files (c, f and i) are filled by the two rooks and
the king, with the king inbetween the two rooks. Thus, the rooks go
into files c and i. The king goes into file f.
The set up for combination 12345 is:
knight-bishop-rook-queen-knight-king-archbishop-chancellor-rook-bishop.

One of the current most popular chess variants on the market today is
Gothic Chess, 'designed' by Edward Trice. The pieces row in Gothic chess
is as follows (from left(a-file) to right(j-file)):
rook-knight-bishop-queen-chancellor-king-archbishop-bishop-knight-rook on
a 10x8 board.
How to calculate the equivalent Capablanca84000 combination: The light
squared bishop is in the 4th possible file. We use the quotient 3.
The dark squared bishop is in the second possible file. For this we
use the quotient 1.
The archbishop is in the 6th possible file, quotient = 5.
The chancellor is in the 4th available file, quotient = 3.
The queen is in the 3rd available file, quotient = 2.
The knights are in the 6th possible orientation, quotient = 5.
Using these numbers we calculate backwards. The last quotient is 5.
The number 5 is achieved after dividing 30 by 6. 30 + 2 is the
previous number. 32 is achieved After dividing 224 by 7. 224 + 3
should be the previous number. 227 is achieved After dividing 1816 by
8. 1816 + 5 should be the previous number. 1821 is achieved After
dividing 9105 by 5. 9105 +1 should be the previous number. 9106 is
achieved by dividing 45530 by 5. The final calculation is to add the
first quotient, 3, to 45530 to give 45533.

The first Capablanca84000 combination is 00000. The last combination is
83999.

Capablanca84000 and its calculating system are intended to be made the
property of the public domain and may be used or improved by any entity,
or hosted for free on any internet website. The reason for designing
Capablanca84000 was to give something to the world of chess. It took under
an hour to design and I would not feel comfortable for receiving anything
more than acknowledgemnt of contribution, since no novel idea was
employed. I wish that no third party may charge or be charged for using
Capablanca84000. I wish for it to be public domain. I wish that the design
ownership belong to José Raúl Capablanca and Robert James Fischer.
I have 'designed' my own personal combination which I believe is unique
and the best set-up. Currently, I choose to keep this combination secret,
until I am the recognised 'designer' of it.