Problems
Simple Train Journeys
Stage: 1 and 2 Challenge Level: 
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
Reef and Granny
Stage: 2 Challenge Level:
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
Turning Granny
Stage: 2 Challenge Level:
A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?
Twisting and Turning
Stage: 3 Challenge Level:
Take a look at the video and try to find a sequence of moves that will take you back to zero.
More Twisting and Turning
Stage: 3 Challenge Level:
It would be nice to have a strategy for disentangling any tangled ropes...
Turning Tangles
Stage: 3 Challenge Level:
Look carefully at the video of a tangle and explain what's happening.
Cola Can
Stage: 3 Challenge Level:
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Featured Solution
Articles & Games
Drawing Doodles and Naming Knots
This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!
Celtic Knotwork Patterns
This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.
Tower Rescue
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
NRICH is part of the family of activities in the Millennium Mathematics Project.