Thread: Cube Mountains
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Old 2008-05-28, 18:37   #1
davar55's Avatar
May 2004
New York City

23·232 Posts
Default Cube Mountains

Call an "N-mountain" an arrangement of unit cubes in layers,
such that the bottom layer is an NxN square (of cubes --
I hope that's clear enough), each layer has fewer cubes than
any layer below it, and cubes are stacked evenly over cubes
(so that vertices of neighboring cubes correspond) and with
no vertical gaps.

For instance, the "height" of an N-mountain (number of layers)
can range from 1 to N^2.

How many N-mountains are there, for N=1,2,3,4,5 ?

(Don't count rotationally congruent mountains as distinct.)
((That's rotation around the center of the bottom layer.))
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