rocdocmac

Back to square 1!

Thank you Bonanova for your input! To all participants ... The 3-cubelet removal question has now been submitted as a separate new entry called "Cubicle Stack #2" since the thread sort of "got lost" in the original Cubicle Stack discussion after having been solved!

∫1/(2x) = ½ln|x| + c. ln|2x| = ln|x| + ln(2), where ln(2) is a constant

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

My final answer:

Does anyone want to attempt figuring out the number of patterns if three of the cubelets are omitted rather than one or two?

What is the sum of the unit volumes of n-dimensional spheres for the infinite series 1, 2r, πr² , ⁴/₃ πr3, ...

My question and image seem to have disappeared! Suppose 27 identical cubes are glued together to form a cubical stack, as illustrated below. If one of the small cubes is omitted, four distinct shapes are possible: one in which the omitted cube is at a corner of the stack, one in which it is in the middle of an edge of the stack, one in which it is in the middle of a side of the stack, and one in which it is at the core of the stack. If two of the small cubes are omitted rather than just one, how many distinct shapes are possible?

Reason for giving 12: