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Challenge suggestion for MAY - Domination CHESS problems ! RRS feed

  • General discussion

  • Domination CHESS problems !

    Another kind of mathematical chess problems is a domination problem (or covering). In these problems it is requested to find a minimum number of pieces of the given kind and place them on a chess board in such a way, that all free squares of the board are attacked by at least one piece

    So how minimum KNIGHTS is required or you have to put on a chess board for they all cover the 64 squares. ??

    Monday, April 18, 2016 8:24 PM
    Answerer

All replies

  • This is my first step of this challenge: CNV255-0.

    Screen shot of a program Knight's Domination 0.5

    Click to move or remove a knight.


    Nonki Takahashi


    Sunday, May 1, 2016 10:31 AM
    Moderator
  • great !! a really fun challenge for the mind !

    I found a superb website about chess algorithms:

    AI Chess Algorithms

    The program implements the following concepts and algorithms:
     1. Board Representation
     2. Min-max Searching
     3. Alpha-beta pruning
     4. Null move heuristic
     5. Quiescence searching
     6. Static board evaluation functions
     7. Optimizing board evaluation functions via genetic algorithms
     8. Opening Move Database

    Sunday, May 1, 2016 2:14 PM
    Answerer
  • As the second step, I'm trying to find symmetric pattern like this.

    Symmetric Pattern Figure

    There are 65536 patterns in this figure.  The pattern number is from 0 to 65535.

    For example, Pattern 1 has 4 knights a1, h1, h8, and a8.  Pattern 3 (= 1 + 2) has 8 knights a1, b1, h1, h2, h8, g8, a8 and a7.


    Nonki Takahashi


    Sunday, May 29, 2016 4:49 AM
    Moderator
  • My second program is still running.  But it already has two answers - pattern 78 and 3136.

    Screen shot of a program Knight's Domination 0.6

    Pattern 78 (=2+4+8+64) has 16 knights, and pattern 3136 (=64+1024+2048) has 12 knights.


    Nonki Takahashi


    Sunday, May 29, 2016 5:21 AM
    Moderator
  • After running about 8 hours, I stopped the second program (CNV255-1).  Because pattern 49152 (=32768+16384) was the last pattern that has only two knights.

    Screen shot of a program Knight's Domination 0.6 (pattern 60739)

    So, the minimum knights (in symmetric pattern 3136) is 12.

    Screen shot of a program Knight's Domination 0.51 (pattern 3136)


    Nonki Takahashi


    Sunday, May 29, 2016 9:57 AM
    Moderator
  • Fantastic !!
    Sunday, May 29, 2016 1:32 PM
    Answerer
  • Just4fUn and chess, not about dominant knights but opening a new game. ID: DBG614
    There's just to apply a single popular opening move for an h dive between tangerine and samba.
    Wednesday, June 1, 2016 9:48 PM
    Answerer
  • Cool !!! as i am a chess player, your program is great !!
    Thursday, June 2, 2016 2:09 AM
    Answerer
  • Great and who is the first sb chess Play?

    Best Regards Martin

    Thursday, June 2, 2016 5:38 AM