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Magic W Wrap Up

Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.

Instant Insanity

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Tree Graphs

A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.

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?