Stage: 5 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?
Inequality/inequalities. Manipulating algebraic expressions/formulae. Combinatorics. Number theory. Sets. Stage 5 - Reviewed 2012. Mathematical reasoning & proof. Algorithms. Optimisation. Networks/Graph Theory.
Published July 2004,August 2004.
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