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Posers and Puzzles

Joined 26 Apr '03 Moves 26509 (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?

Joined 24 Jan '09 Moves 5514 where does the line start? inside or outside the rectangle?

Joined 26 Apr '03 Moves 26509 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:
|| . =
= . ||

Joined 26 Apr '03 Moves 26509 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.

ALG

Joined 16 Dec '07 Moves 6190

Joined 26 Apr '03 Moves 26509

ALG

Joined 16 Dec '07 Moves 6190 25 is possible:
AABAABBCCA
BCBCCAADDA
BCDDBCCBBC
DAACBDDAAC
DBBCAABBDD
27 is possible:
AABAABBCC
BCBCCAADD
BCDDBCCBB
DAACBDDAA
DBBCAABBD
AADDCCAAD
Edit: cannot be hidden.

Joined 26 Apr '03 Moves 26509