Doodles
Age 14 to 16
Challenge Level
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
Network Trees
Age 14 to 18
Challenge Level
Explore some of the different types of network, and prove a result about network trees.
Magic Caterpillars
Age 14 to 18
Challenge Level
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
Stringing it Out
Age 14 to 16
Challenge Level
Explore the transformations and comment on what you find.
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.
Maximum Flow
Age 16 to 18
Challenge Level
Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.
Some Circuits in Graph or Network Theory
Age 14 to 18
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Production Equation
Age 16 to 18
Challenge Level
Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?
Flow Chart
Age 11 to 14
Challenge Level
The flow chart requires two numbers, M and N. Select several values for M and try to establish what the flow chart does.
Procedure Solver
Age 16 to 18
Challenge Level
Can you think like a computer and work out what this flow diagram does?
Zeller's Birthday
Age 14 to 16
Challenge Level
What day of the week were you born on? Do you know? Here's a way to find out.
Painting by Numbers
Age 16 to 18
Challenge Level
How many different colours of paint would be needed to paint these pictures by numbers?
Torus Patterns
Age 16 to 18
Challenge Level
How many different colours would be needed to colour these different patterns on a torus?
Mad Robot
Age 16 to 18 Short
Challenge Level
Can you work out what happens when this mad robot sets off?
Happy birthDay
Age 16 to 18
Challenge Level
Can you interpret this algorithm to determine the day on which you were born?
The Olympic Torch Tour
Age 14 to 16
Challenge Level
Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
Drug Testing
Age 16 to 18
Challenge Level
How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?
Sorted
Age 14 to 18
Challenge Level
How can you quickly sort a suit of cards in order from Ace to King?
Simply Graphs
Age 16 to 18
Challenge Level
Look for the common features in these graphs. Which graphs belong together?
NRICH is part of the family of activities in the Millennium Mathematics Project.