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## 'Cube Net' printed from http://nrich.maths.org/

How many tours that visit each vertex once and only once can
be traced along the edges of a cube? How many of these tours can
return to the starting point thus completing a Hamiltonian
Circuit?

How many different ways can the subsets of the set $\{a, b,
c\}$ be arranged in a sequence so that each subset differs from the
one before it by having exactly one element inserted or
deleted?