How many loops of string have been used to make these patterns?

How many pieces of string have been used in these patterns? Can you describe how you know?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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?

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?

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?

Take a look at the video and try to find a sequence of moves that will take you back to zero.

It would be nice to have a strategy for disentangling any tangled ropes...

Look carefully at the video of a tangle and explain what's happening.

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

This short question asks if you can work out the most precarious way to balance four tiles.

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

Which parts of these framework bridges are in tension and which parts are in compression?

West Lodge pupils explained the thinking behind this problem very clearly and Sakib drew a diagram which really helps us picture what is happening.

Dmitri from Cork and others offered a neat way to visualise this process and to reason how one result leads to the next.

This article for students gives some instructions about how to make some different braids.

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

This article for students introduces the idea of naming knots using numbers. You'll need some paper and something to write with handy!

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!