Starting from position 1, the knight can move to positions 18 or 11. Therefore, the motions of the piece can be thought of as increasing or decreasing in increments of 8+/-2 or 16+/-1. In this manner, the piece can be moved as far as it will go to the opposite end of the board, "upward," by making the moves 1+17, (1+17*2), and 1+17*3, where it can go no farther without surpassing 64. Moving it in one direction "to the right," 1+10, 1+10*2 and 1+10*3=31, where it stops as it approaches point 8*4.
To move in the other direction generally upward from position 31, the piece will have to move in increments of 6. Therefore, 31+6, 31+6*2, 31+6*3=49, stopping at point 8*6+1. Therefore, let's think of the game set-up as such:
Pawns:
pb1-pb8@9-16
pw1-pw8@49-56
MOVES: +8&-8, respectively; non-continuous
KILL: +1 or -1 after move
SPECIAL: secondary move IF @origin
SPECIAL: If @>56 replaced by any missing piece
Queens:
qb@4
qw@60
MOVES:
+/-1 between multiples of 8; continuous between self
+/-8 between 1 and 64; continuous
+/-8+/-1; between 1 and 64; continuous
KILL: stops after kill, and may not kill same side
Kings:
kb@5
kw@61
MOVES:
+/-1 between multiples of 8; non-continuous
+/-8 between 1 and 64; non-continuous
+/-8+/-1 between 1 and 64; non-continuous
KILL: simple, and may not kill same side
Bishops:
bba@3
bbb@6
bwa@59
bwb@62
Moves:
+/-8+/-1 between multiples of 8; continuous
Knights
kba@2
kbb@7
kwa@58
kwb@63
Moves:
+/-8+/-2 but not crossing multiples of 8; non-continuous
+/-16+/-1 but not crossing multiples of 8; non-continuous
Rooks
rba@1
rbb@8
rwa@57
rwb@64
+/-8; continuous between 1 and 64 but not over obstructions
+/-1; continuous between multiples of 8 but not over obstructions
SPECIAL: a+4 or b-2 AND k+/-1 but not over obstructions
I think that pretty much sums up the rules of chess except the weird stuff about the king. However, to make things a lot easier, let's just list all of these pieces in accordance with their starting positions and then alter the numbers in our set according to their positions. Furthermore, let's divide them up into 8 sets, four of them for either side.
{1,2,3,4} for rook through queen on the black side and {5, 6, 7, 8} for king through rook. The others will follow the same pattern. Therefore:
a{01,02,03,04}, b{05,06,07,08}
a{9,10,11,12}, b{13,14,15,16} for the pawns. We can call them "queen's pawns" and "king's pawns."
a{49,50,51,51}, b{53,54,55,56} PAWNS!!! lol
a{57,58,59,60}, b{61,62,63,64}
Now, at the outset of the game, we know that certain pieces can't move. The way we'll think of this is to say, for example, we wanted to move the rook at position 01. We couldn't perform the maneuver +1 because that would create a duplicate at position 02. Same for the maneuver +8.
However, the knight at 02 wouldn't create a duplicate by moving 16+/-1, and any of the pawns could move either +8 or +16 from the origin. Now, I'm going to show right now how I'm going to start figuring out how to move these babies!
kba up and in: 01020304, 02+16+01=16+3=19, 01190304 ((Here, I eliminated the commas)
kwb down and in: 61626364, 63-16-01=63-17=46, 61624664
Okay, maybe that's comprehensible, maybe it isn't. However, I'm going to make a shorthand especially for representing moves by the knight. Therefore, for the same move, consider this:
kba++ means that for the set represented by 01020304, I calculate the addition of (8*2+1*1)*10^4.
Therefore, kba++ is code to perform EXACTLY that operation for the set that's in! When I write kba++, I WITHOUT VARIATION perform that operation on that set. So here is a cause and effect picture in simple language:
cause: kba++
effect: black queen back-row {01020304} => 01190304
For the black queen, here is how a move three spaces down and to the right would look: qb3+-
qb3+-=01020344
44: next multiple of 8 is 48, and 48-44=4, which is greater than 3, which gives me space
44+3-8*3=23
0<23<64 therefore there is no vertical inhibition
However, now I have to complete it as a SERIES of operations. Therefore, if anything in my SERIES of one-step operations creates a duplicate, I must either make a kill or stop, depending on whether it's in the black set or the white set. The easiest way to do this would be to consider the number of spaces it would move with each duplication and just remember that.
Therefore, for the +- operation, I would ALWAYS be subtracting by 9. ALWAYS
You can see where this is going. Now, I'm going to use indicators h and v to indicate horizontal v. vertical movement, so I'll have qbh+3 for three spaces right, qbv+3 for three spaces down, etc.
How about I make up the rules for moving the other ones as I go along. Let's play!
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a{01,02,03,04}, b{05,06,07,08}
a{09,10,11,12}, b{13,14,15,16} pawns
a{49,50,51,51}, b{53,54,55,56} pawns
a{57,58,59,60}, b{61,62,63,64}
kbb+-05060708--05062208
kwb--61626364--61624664
kba++01020304--01190304
kwa-+57585960--57425960
Updated board:
a{01,19,03,04}, b{05,06,22,08}
a{09,10,11,12}, b{13,14,15,16} pawns
a{49,50,51,52}, b{53,54,55,56} pawns
a{57,42,59,60}, b{61,62,46,64}
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Now I'll do that sequence of moves using the method of treating the whole board as just one number.
0119030405062208091011121314151649505151535455565742596061624664
Operations:
kbb+-: (05060708+16*10^2-1*10^2)*10^(8*6)
0000000005062208000000000000000000000000000000000000000000000000
kwb--: (61626364-16*10^2-1*10^2)*10^(8*0)
0000000000000000000000000000000000000000000000000000000061624664
kba++: (01020304+16*10^4+1*10^4)*10^(8*7)
0119030400000000000000000000000000000000000000000000000000000000
kwa-+: (57585960-16*10^4+1*10^4)*10^(8*1)
0000000000000000000000000000000000000000000000005742596000000000
Therefore, adding them together
+0119030400000000000000000000000000000000000000000000000000000000
+0000000005062208000000000000000000000000000000000000000000000000
+0000000000000000000000000000000000000000000000005742596000000000
+0000000000000000000000000000000000000000000000000000000061624664
Plus add in the pawn rows:
+0000000000000000091011121314151649505151535455560000000000000000
=0119030405062208091011121314151649505151535455565742596061624664
And, as tedious as that was, it is clearly a waste of time to try using the method of treating the board as one number. However, the point has been proven that it can be done. It is very well possible to input a series of computations on one number and consider that series of computations to be the game. Anyway, let's get back to the game.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
a{01,19,03,04}, b{05,06,22,08}
a{09,10,11,12}, b{13,14,15,16} pawns
a{49,50,51,52}, b{53,54,55,56} pawns
a{57,42,59,60}, b{61,62,46,64}
pb3+09101112--09101812 pawn move
pw8--53545556--53545540 pawn move, this time double
Updated board:
a{01,19,03,04}, b{05,06,22,08}
a{09,10,18,12}, b{13,14,15,16} pawns
a{49,50,51,52}, b{53,54,55,56} pawns
a{57,42,59,60}, b{61,62,46,40}
This is turning out to be an interesting project, and my real interest is in trying to see how I can determine how the math involved in chess actually works. However, I might at some point construct a full length game based on this method, using a spreadsheet program. This would allow me to study the mathematics of the game more easily, and perhaps I can begin developing a concept of strategy that goes beyond just instinct and gut reaction.
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