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Posers and Puzzles

Posers and Puzzles

  1. 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 member UmbrageOfSnow
    All Bark, No Bite
    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. 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 member adam warlock
    Baby Gauss
    18 Feb '07 00:32
    1-2
    a1-a2-...-a8-b8-b7-...-b1-c1-...-g1-...-g8-h8-...-h1
  5. Standard member XanthosNZ
    Cancerous Bus Crash
    18 Feb '07 08:19 / 2 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 member adam warlock
    Baby Gauss
    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. 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. 21 Feb '07 05:20 / 3 edits
    .