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.
The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
How many ways can you arrange the bridges if the island with one
bridge joins to the island with two bridges to the second island
with two bridges (1-2-2)?
Now extend this systematic approach by altering one of the
constraints (say 1-2-3).