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davar55 · 2008-05-28, 18:37

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.))

2008-05-28, 18:37	#1
davar55 May 2004 New York City 2³·23² Posts	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.))