Problem of the Week #34: Monday August 28th, 2023 As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems.
We want to flatten the outer shell of a cube without tearing or stretching the surface. For example, the common way of cutting the cube along the edges and flattening it as 6 squares would involve tearing its surface along 7 edges. Both of the ways shown below would involve tearing the cube’s surface along 4 edges:
a). The video below shows one solution. Find another solution.
b). In the example above, the surface of the cube extends outside the top square when flattened. Can this solution be modified so that the surface of the cube stays under the top square?
c). Can every solution that extend outside the top square when flattened be modified so that the surface of the cube stays under the top square?
d). How many solutions are there in total?
e). Share your own problem inspired by this one.
f). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.