Hello and welcome to our community! Is this your first visit?
Register
Enjoy an ad free experience by logging in. Not a member yet? Register.
Page 2 of 3 FirstFirst 123 LastLast
Results 16 to 30 of 43

Thread: Complex Formula

  1. #16
    Senior Coder missing-score's Avatar
    Join Date
    Jan 2003
    Location
    UK
    Posts
    2,194
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Lol.

    Next time I go onto a site where it asks for a mission, I can put: "To prove jkd wrong"

  2. #17
    Regular Coder
    Join Date
    Nov 2002
    Location
    Bristol, UK
    Posts
    932
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Originally posted by mattover-matter
    ok, im going to restate:

    My question:
    I wish to figure out how many valid positions in a chess game are possible (at one time)

    My troubles:
    1) two peices cannot be on the same square at one time
    2) bishops cannot reach every square on the board
    3) pawns cannot reach every square on the board (cannot move backwards)
    4) Whenever a pawn reaches the end, It can choose a peice that is already dead (from his side) and revive it inplace of the pawn. You cannot have 2 queens, or 3 rooks.
    5) Units cannot travel through (you must think back). A pawn cannot appear behind an enemy pawn for some reason (well, it is possible but not if the pawns have not killed anyone)

    FYI:
    1) There are 64 squares on a chessboard.
    2) There are 8 pawns, 2 rooks, 2 knights, 2 bishops, 1 queen, 1 king per side(32 in total)
    3) The dimensions for a chessboard are 8x8.
    4) A knight CAN reach every position on the board.


    Also, I asked at DR.math forum to see if anyone there knows a solution.


    re: It would be interesting to know, but probably not fun to do

    You are missing the point of this. Do you think I randomly pick things that have 0 relevency in anything I will ever do (don't take me literally)? I am doing this to learn, not to know. knowing is just a bonus. (note : what I just said applies to this problem, and this problem only [again, don't take me literally])
    good luck.

    start from the 'potential' figure I gave you (1008) and then take away whatever you want... but your question still lacks what I would call a 'point'... which means I'm probably still missing it!

    Oh yeah and your rules 4 and 5 are technically incorrect. It's possible to have 8 queens, for example, and number 5 is to be laughed at What if someone simply decided NOT to take...? Perfectly legal.

    ::] krycek [::
    ithium | SOAPI | SDP | PTPScript manual
    "ithium is a non-profit webhost, which is pretty much unique. The mission of ithium is to provide free hosting resources for worthwhile and needy non-profit projects, which otherwise may not be able to obtain such facilities. The money from commercial customers goes to maintain ithium's servers and further development."

  3. #18
    Banned
    Join Date
    Mar 2003
    Posts
    224
    Thanks
    0
    Thanked 0 Times in 0 Posts
    I think you mean number of possible games. I mean number of posible positionings

  4. #19
    jkd
    jkd is offline
    Senior Coder jkd's Avatar
    Join Date
    May 2002
    Location
    metro DC
    Posts
    3,163
    Thanks
    1
    Thanked 18 Times in 18 Posts
    Possible positions is still enormous. With *just* two kings on the board, you have something like this:

    A king on interior: 36*55 (9 squares opponent can't be in)
    A king on side: 24*59 (5 squares opponent can't be in)
    A king on a corner: 4*61 (3 squares opponent can't be in).

    Which sums to 3640. As soon as you throw any more pieces onto the board, it becomes ridiculously enormous.

    Notice 64*63 is 4032, which could be considered an upper limit for the calculation. A difference of 392 may seem significant right now, but as we get into billions of combinations, the only feasible way to calculate the number is to look at upper limits.

  5. #20
    Regular Coder
    Join Date
    Nov 2002
    Location
    Bristol, UK
    Posts
    932
    Thanks
    0
    Thanked 0 Times in 0 Posts
    ahhhhhh now I get what he is trying to do!

    the question is, why?

    oh well!

    ::] krycek [::
    ithium | SOAPI | SDP | PTPScript manual
    "ithium is a non-profit webhost, which is pretty much unique. The mission of ithium is to provide free hosting resources for worthwhile and needy non-profit projects, which otherwise may not be able to obtain such facilities. The money from commercial customers goes to maintain ithium's servers and further development."

  6. #21
    Regular Coder
    Join Date
    Nov 2002
    Location
    Bristol, UK
    Posts
    932
    Thanks
    0
    Thanked 0 Times in 0 Posts
    By the way, I worked it out, mattover-matter.

    The answer is,

    4.5e+53 (I cannot write superscript on here can I? Ah well, I will leave it like that)

    Any more accuracy, and that's up to you to work out...

    ::] krycek [::
    ithium | SOAPI | SDP | PTPScript manual
    "ithium is a non-profit webhost, which is pretty much unique. The mission of ithium is to provide free hosting resources for worthwhile and needy non-profit projects, which otherwise may not be able to obtain such facilities. The money from commercial customers goes to maintain ithium's servers and further development."

  7. #22
    Banned
    Join Date
    Mar 2003
    Posts
    224
    Thanks
    0
    Thanked 0 Times in 0 Posts
    re: why?
    I am trying to learn
    Hey, Can you kinda put that in stupider terms, I thought e was for calculating the growth in percentages...but I learned that on my own (not at school, don't give them the credit for my intelligence ). Kryckeck, can you please attempt to explain how you figured that out? I'm 13 so you guys are a wee bit ahead of me My math class is still on ratios and proportions (for 9 weeks now ) WOW, jkd I guess....my next mission will be to prove you wrong. I was getting 64*32 = 2??? I guess you proved me wrong.

    52*Y

    like that kryckeck?

    [ s u b ] [ / s u b ] [ s u p ] [ / s u p ]

    nope, i guess these avatarless forums are jes' weird

  8. #23
    Senior Coder
    Join Date
    Jun 2002
    Location
    UK
    Posts
    1,137
    Thanks
    0
    Thanked 0 Times in 0 Posts

    Macintosh

    you say calculating the possible positions to move too at any one time in a game.
    do you mean you want to calaculate the possible positions to move too at one ponit and later recalculate at another time. or just calculate them once?

    would it be an idea that some produces a chessboard overview so that when calculating all the possible moves everyone is working on the same game board.

    Depending on positions depends on the possible moves.

    scroots
    Last edited by scroots; 04-15-2003 at 10:21 PM.
    Spammers next time you spam me consider the implications:
    (1) that you will be persuaded by me(in a legitimate mannor)
    (2)It is worthless to you, when i have finished

  9. #24
    jkd
    jkd is offline
    Senior Coder jkd's Avatar
    Join Date
    May 2002
    Location
    metro DC
    Posts
    3,163
    Thanks
    1
    Thanked 18 Times in 18 Posts
    Originally posted by mattover-matter
    I thought e was for calculating the growth in percentages...but I learned that on my own (not at school, don't give them the credit for my intelligence ).
    That's not e as in lim n-> infinity (1+1/n)^n, it is e as in the scientific notation shortcut.

    4.5e+53 = 4.5 * 10^53

    Which isn't actually the right answer either... it should be significantly larger than that.

  10. #25
    Banned
    Join Date
    Mar 2003
    Posts
    224
    Thanks
    0
    Thanked 0 Times in 0 Posts
    but..number of grains of sand on earth??? That is like....
    for (i=0;i++;200{document.write(",999")}

  11. #26
    Regular Coder
    Join Date
    Nov 2002
    Location
    Bristol, UK
    Posts
    932
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Originally posted by jkd
    That's not e as in lim n-> infinity (1+1/n)^n, it is e as in the scientific notation shortcut.

    4.5e+53 = 4.5 * 10^53

    Which isn't actually the right answer either... it should be significantly larger than that.
    I'll take your word for it... as you know, it was just a quick estimate

    I still think that 450,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 is big enough!

    ::] krycek [::
    ithium | SOAPI | SDP | PTPScript manual
    "ithium is a non-profit webhost, which is pretty much unique. The mission of ithium is to provide free hosting resources for worthwhile and needy non-profit projects, which otherwise may not be able to obtain such facilities. The money from commercial customers goes to maintain ithium's servers and further development."

  12. #27
    Mega-ultimate member
    Join Date
    Jun 2002
    Location
    Winona, MN - The land of 10,000 lakes
    Posts
    1,855
    Thanks
    1
    Thanked 45 Times in 42 Posts
    Originally posted by mattover-matter
    ok, im going to restate:

    My question:
    I wish to figure out how many valid positions in a chess game are possible (at one time)

    My troubles:
    1) two peices cannot be on the same square at one time
    2) bishops cannot reach every square on the board
    3) pawns cannot reach every square on the board (cannot move backwards)
    4) Whenever a pawn reaches the end, It can choose a peice that is already dead (from his side) and revive it inplace of the pawn. You cannot have 2 queens, or 3 rooks.
    5) Units cannot travel through (you must think back). A pawn cannot appear behind an enemy pawn for some reason (well, it is possible but not if the pawns have not killed anyone)

    FYI:
    1) There are 64 squares on a chessboard.
    2) There are 8 pawns, 2 rooks, 2 knights, 2 bishops, 1 queen, 1 king per side(32 in total)
    3) The dimensions for a chessboard are 8x8.
    4) A knight CAN reach every position on the board.


    Also, I asked at DR.math forum to see if anyone there knows a solution.


    re: It would be interesting to know, but probably not fun to do

    You are missing the point of this. Do you think I randomly pick things that have 0 relevency in anything I will ever do (don't take me literally)? I am doing this to learn, not to know. knowing is just a bonus. (note : what I just said applies to this problem, and this problem only [again, don't take me literally])
    Heres a possible hint:

    try to define the possible move at a given point in the game as an equation. Obviously, the total moves available to a player at any given moment changes based on the position of all the pieces on the board at that moment. For example, when you start the game there are 20 possible moves, each pawn can move 1 or 2 spaces, and 2 knights can move to 2 different spaces each. so we get something like

    total moves = total pawns * 2 possible moves + total knights * 2 possible moves or 8 * 2 + 2 * 2 or 16 + 4 = 20.

    Now, once you move a pawn, you total possible moves for the next turn increase based on the provious move. So everything is now dependant on the first move. This means you should be able to express the second move as a function of the first move. Hope this helps.

    Good luck. I think this could be an SA article if you figure it out. (SA = Scientific American)

  13. #28
    Banned
    Join Date
    Mar 2003
    Posts
    224
    Thanks
    0
    Thanked 0 Times in 0 Posts
    i think you guys were trying to calculate the possible games(entire game) which is infinite.

  14. #29
    Senior Coder missing-score's Avatar
    Join Date
    Jan 2003
    Location
    UK
    Posts
    2,194
    Thanks
    0
    Thanked 0 Times in 0 Posts
    No, Not infinate. A hell of alot, but not infinate.

  15. #30
    Banned
    Join Date
    Mar 2003
    Posts
    224
    Thanks
    0
    Thanked 0 Times in 0 Posts
    Yes, infinite. Moves can be retraced over and over


 
Page 2 of 3 FirstFirst 123 LastLast

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •