Dissecting to Five Rectangles
Extension: One reader asked: "What's the next fewest number of pieces?"
could six smaller rectangles be found, all with different dimensions?
Find the smallest square which can be dissected into five
non-overlapping rectangles with integer sides, such that the ten dimensions
of the five rectangles are all unique. That is, the length
and width of each piece is different from the length or
width of any other piece.
Find the smallest area rectangle which meets these requirements.
- Extra Credit. The smallest rectangle above is MxN, but one of
the smaller rectangles has N as one of its dimensions. Can you find the
smallest area MxN rectangle such that M and N are different from the 10
dimensions of its divided rectangles.
Source: Denis Borris and Joseph DeVincentis.
Problem 2 was published by Frank Rubin in the Journal of Recreational Math
under the name "Temple of Heterodoxy" a few years ago.
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