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A Curious Collection of Bridges
Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!
Topology
problem
Torus patterns
Age
16 to 18
Challenge level
How many different colours would be needed to colour these
different patterns on a torus?
problem
Painting by Numbers
Age
16 to 18
Challenge level
How many different colours of paint would be needed to paint these
pictures by numbers?
problem
The Bridges of Konigsberg
Age
11 to 18
Challenge level
Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
problem
Tourism
Age
11 to 14
Challenge level
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
problem
Travelling Salesman
Age
11 to 14
Challenge level
A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start.
How many Hamiltonian circuits can you find in these graphs?
problem
Königsberg
Age
11 to 14
Challenge level
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
problem
Earth Shapes
Age
16 to 18
Challenge level
What if the Earth's shape was a cube or a cone or a pyramid or a
saddle ... See some curious worlds here.
problem
Icosian Game
Age
11 to 14
Challenge level
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.