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Can you Solve the Knight's Tour Math Problem?


  • 23 months ago · Quote · #2

    temp_ddg

    I solved this a while ago too, even for bigger boards:

    In a 15x15 board:

    https://www.youtube.com/watch?v=RaLi3xfvqXc

    24x24

    https://www.youtube.com/watch?v=NEtWctx-TU8

    49x49

    https://www.youtube.com/watch?v=eGjXzdVCn1Q

  • 23 months ago · Quote · #3

    JasonSchlotter

    Very cool

  • 23 months ago · Quote · #4

    Scottrf

    Thanks, not going to bed until I do this.

  • 23 months ago · Quote · #5

    Scottrf

    Thanks Gerry! Awesome.

    http://www.borderschess.org/KnightTour.htm

    (Disclaimer: did start trying before my first message).

  • 23 months ago · Quote · #6

    MBClevenger

    Sounds fun, don't know if I have time.

  • 23 months ago · Quote · #7

    PortlandPatzer

    Another idea is when breaking the board down into quadrants, is to also devise patterns based on easily recognizable shapes and then determine a pattern based on those shapes.

    Here is an example:

    You can envision the Knights making a diamond-shaped pattern by the moves from a8-b6-d5-c7 and a square being made from the moves a6-b8-d7-c5. Now, if these could be repeated in a particular way, you could travel in all four quadrants and reach all 64 squares from starting on a8 and ending on h6 having to familiarize yourself with only four moves at a time.

    Next think of the upper left quadrant as 1, the lower left 2, lower right 3, and upper right as 4 and the most complex of these patterns is the formation of Diamond, Square, Square, Diamond followed by Square, Diamond, Diamond, Square.

    Putting the two concepts together we get:

    [P|Q]

    D1, S1, S2, D2, S3, D4, D3, S3, D2, S2, S1, D1, S4, D3, D4, S4.

    Here is the pattern over the board:

    This is the most complex of the patterns I have found aside from the Euler's Square. I was able to work out 3 other patterns as well, those being:

    D,D,D,D,S,S,S,S

    D,D,S,S,D,D,S,S

    D,S,D,S,D,S,D,S

    See if you can find the patterns of the Knights moves into the quadrants in these.

  • 23 months ago · Quote · #8

    BorgQueen

    Nice way to understand it, thanks CN :-)

  • 23 months ago · Quote · #9

    tintin1016

    no idea!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


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