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Cubicle Stack #2


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Question

Suppose 27 identical cubes are glued together to form a cubical stack, as illustrated below.

image.png.1d35379223509669e07e1659355d1797.png

If one of the small cubes is omitted, four distinct shapes are possible. If two of the small cubes are omitted rather than just one, twenty-two distinct shapes are possible (see previously submitted Cubicle Stack at BrainDen.com).

Now, if three of the cubelets are omitted, how many distinct shapes are possible?

 

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