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Posers and Puzzles

Posers and Puzzles

  1. 08 Jul '11 22:56 / 1 edit
    (thanks to the New Scientist Magazine)


    I have a standard set of 28 dominos. I take some and arrange them into a rectangle. The rectangle has the property that no horizontal or vertical straight line can be drawn across it, which doesn't bisect at least one domino. I take this rectangle apart, add two more dominos and make another rectangle with the same property. How many dominos are in my second rectangle?
  2. 08 Jul '11 23:37
    where does the line start? inside or outside the rectangle?
  3. 08 Jul '11 23:52 / 2 edits
    The line must be horitontal or vertical and start and finish outside the rectangle.

    For instance

    ||=
    =||

    (where || is a vertical domino, and = is a horizontal domino)

    ... cannot be one of my rectangles because it can be divided neatly by both a horizontal cut:

    ||=
    .....
    =||

    and a vertical one:

    || . =
    = . ||
  4. 09 Jul '11 15:27 / 2 edits
    sorry , that was very confusing, only worked if = and || each denoted two dominos.

    Hopefully this is clearer:

    axoo
    axax
    ooax

    where two adjacent pieces with the same letter compromise each domino.

    can be cut like this:

    ax oo
    ax ax
    oo ax

    So it is not a possible rectangle.
  5. 09 Jul '11 17:32 / 1 edit
    The answer is 27.
  6. 09 Jul '11 19:24
    Nice one - proof?
  7. 09 Jul '11 19:39 / 1 edit
    25 is possible:

    AABAABBCCA
    BCBCCAADDA
    BCDDBCCBBC
    DAACBDDAAC
    DBBCAABBDD

    27 is possible:

    AABAABBCC
    BCBCCAADD
    BCDDBCCBB
    DAACBDDAA
    DBBCAABBD
    AADDCCAAD

    Edit: cannot be hidden.
  8. 09 Jul '11 20:34
    Very good!