Enigma 1653: Cut-free
4 December 2011
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From New Scientist #2819, 2nd July 2011 [link]
The image, above, shows six dominoes forming a rectangle. The dotted line shows how the rectangle can be cut into two rectangles without cutting through a domino.
I started again with a standard set of 28 dominoes and used some of them to make another rectangle. This time it was impossible to find a line that cuts it into two rectangles without cutting a domino.
I then broke up that rectangle, added two further dominoes from the set, and used them all to make a new rectangle. Once again, it was impossible to find a line that cut this into two rectangles without cutting a domino.
How many dominoes did I use in this last rectangle?