Posers and Puzzles

Posers and Puzzles

  1. Joined
    26 Apr '03
    Moves
    26509
    08 Jul '11 22:561 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. Joined
    24 Jan '09
    Moves
    5514
    08 Jul '11 23:37
    where does the line start? inside or outside the rectangle?
  3. Joined
    26 Apr '03
    Moves
    26509
    08 Jul '11 23:522 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. Joined
    26 Apr '03
    Moves
    26509
    09 Jul '11 15:272 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. ALG
    Joined
    16 Dec '07
    Moves
    6190
    09 Jul '11 17:321 edit
    Reveal Hidden Content
    The answer is 27.
  6. Joined
    26 Apr '03
    Moves
    26509
    09 Jul '11 19:24
    Nice one - proof?
  7. ALG
    Joined
    16 Dec '07
    Moves
    6190
    09 Jul '11 19:391 edit
    25 is possible:

    AABAABBCCA
    BCBCCAADDA
    BCDDBCCBBC
    DAACBDDAAC
    DBBCAABBDD

    27 is possible:

    AABAABBCC
    BCBCCAADD
    BCDDBCCBB
    DAACBDDAA
    DBBCAABBD
    AADDCCAAD

    Edit: cannot be hidden.
  8. Joined
    26 Apr '03
    Moves
    26509
    09 Jul '11 20:34
    Very good!
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