Posers and Puzzles

Posers and Puzzles

  1. Joined
    20 Jan '07
    Moves
    1005
    17 Feb '07 20:30
    A chess king is placed on a 8x8 chessboard. It has to make 64 moves, visiting each (of 64) squares only once, and to return there where it started. The path has to be with no intersections (a path looking like '8' is no good). For a loop, one can count the total number of horizontal + vertical (i.e. excluding diagonal) moves; let's call this number M. 1. Give an example of at least one such loop. 2. Give an example of a loop with the largest possible M. 3. Give an example of a loop with M=28. 4. Prove that 28 is the smallest possible M.
  2. Standard memberUmbrageOfSnow
    All Bark, No Bite
    Playing percussion
    Joined
    13 Jul '05
    Moves
    13232
    17 Feb '07 21:08
    Originally posted by GinoJ
    A chess king is placed on a 8x8 chessboard. It has to make 64 moves, visiting each (of 64) squares only once, and to return there where it started. The path has to be with no intersections (a path looking like '8' is no good). For a loop, one can count the total number of horizontal + vertical (i.e. excluding diagonal) moves; let's call this number M. 1. Give ...[text shortened]... sible M. 3. Give an example of a loop with M=28. 4. Prove that 28 is the smallest possible M.
    Explain the loops and M thing more clearly, sounds like an interesting problem, but I'm not sure what you're asking yet.
  3. Joined
    20 Jan '07
    Moves
    1005
    17 Feb '07 22:49
    Originally posted by UmbrageOfSnow
    Explain the loops and M thing more clearly, sounds like an interesting problem, but I'm not sure what you're asking yet.
    M can be X or Y or A or B or C or D or E or any letter.

    It's just an unknown variable yo.
  4. Standard memberadam warlock
    Baby Gauss
    Ceres
    Joined
    14 Oct '06
    Moves
    18375
    18 Feb '07 00:32
    1-2
    a1-a2-...-a8-b8-b7-...-b1-c1-...-g1-...-g8-h8-...-h1
  5. Standard memberXanthosNZ
    Cancerous Bus Crash
    p^2.sin(phi)
    Joined
    06 Sep '04
    Moves
    25076
    18 Feb '07 08:192 edits
    That doesn't return to the starting square. If we look at not returning to the starting square the minimum number would be 15.
  6. Standard memberadam warlock
    Baby Gauss
    Ceres
    Joined
    14 Oct '06
    Moves
    18375
    18 Feb '07 10:51
    Originally posted by XanthosNZ
    That doesn't return to the starting square. If we look at not returning to the starting square the minimum number would be 15.
    oops..misread the first post. Working on the right solution right now.
  7. Sigulda, Latvia
    Joined
    30 Aug '06
    Moves
    4048
    18 Feb '07 14:07
    Ka1-a8-b8-b2-c2-c8-d8-d2-e2-e8-f8-f2-g2-g8-h8-h1-a1. 17 loops, if you count the one between finish and start. Not proof exactly but I couldn't find any way with fewer loops at the moment.
  8. Joined
    20 Jan '07
    Moves
    1005
    21 Feb '07 05:203 edits
    .
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