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.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Label this plum tree graph to make it totally magic!
To make a Magic W you have to put the numbers 1, 2, ...,9, one in each circle, so that each row of three numbers has the same total. Experiment to find as many different magic totals as you can using the interactivity from the Magic W problem.
Prove that if you have a Magic W and you replace each of the numbers by 10 minus that number then the new W is also magic. What will its magic total be?