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Cube Nets on a Grid

While attempting the latest Internet Puzzle Solvers Test, I found I needed to
create a cube. I have graph paper with 1-inch squares, measuring 9 by 7
inches. What is the maximum number of unit cubes I could create from a
single page, by cutting out 6-square Cube Nets? Extension: What is the maximum number of unit cubes which
could be made from an MxN sheet (M<=N<=10)?

There are 11 different Cube Nets which might be used in building a cube.
I found a listing at the Cube page at MathWorld:

http://mathworld.wolfram.com/Cube.html

Source: Original.

Solution

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