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# Cube Net

##### Age 16 to 18 Challenge Level:
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?