Dissecting to Five Rectangles

  1. 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.
  2. Find the smallest area rectangle which meets these requirements.
  3. 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.
Extension: One reader asked: "What's the next fewest number of pieces?" For example, could six smaller rectangles be found, all with different dimensions? Seven?

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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