Dominos

iamatiger
Posers and Puzzles 08 Jul '11 22:56
1. 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. 08 Jul '11 23:37
where does the line start? inside or outside the rectangle?
3. 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. 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. 09 Jul '11 17:321 edit
6. 09 Jul '11 19:24
Nice one - proof?
7. 09 Jul '11 19:391 edit
25 is possible:

AABAABBCCA
BCDDBCCBBC
DAACBDDAAC
DBBCAABBDD

27 is possible:

AABAABBCC