Can you Solve the Knight's Tour Math Problem?

  • #1

    Solving the "Knight's Tour" math problem involves moving the knight about the chessboard such that each square is visited exactly once.

    Visualizing the chessboard as 4 quadrants, memorizing a small group of patterns within each quadrant, and following a few simple principles while calculating the knight moves will allow you to find a solution to this fun mathematical problem.

    It's an intuitive puzzle to challenge a friend, math teacher, or even a math classroom with.

    I've provided a solution to this math problem in this video: http://www.youtube.com/watch?v=9fSFC00ZKPg

  • #2

    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

  • #3

    Very cool

  • #4

    Thanks, not going to bed until I do this.

  • #5

    Thanks Gerry! Awesome.

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

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

  • #6

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

  • #7

    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.

  • #8

    Nice way to understand it, thanks CN :-)

  • #9

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

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