![Which spinners?](/sites/default/files/styles/medium/public/thumbnails/content-id-6123-icon.jpg?itok=orBOhseL)
![circles in quadrilaterals](/sites/default/files/styles/medium/public/thumbnails/circles-in-quadrilaterals.png?itok=X4IAfJLW)
problem
circles in quadrilaterals
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
![Track design](/sites/default/files/styles/medium/public/thumbnails/content-id-7359-icon.png?itok=SoM9Ko59)
problem
Track design
Where should runners start the 200m race so that they have all run the same distance by the finish?
![Nutrition and Cycling](/sites/default/files/styles/medium/public/thumbnails/content-id-7571-icon.png?itok=7GvnTgar)
problem
Nutrition and Cycling
Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?
![Steel Cables](/sites/default/files/styles/medium/public/thumbnails/content-id-7760-icon.png?itok=iTS5VCIy)
problem
Steel Cables
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
![Picturing the world](/sites/default/files/styles/medium/public/thumbnails/content-id-10464-icon.png?itok=pFECGSV1)
problem
Picturing the world
How can we make sense of national and global statistics involving very large numbers?
![Box plot match](/sites/default/files/styles/medium/public/thumbnails/content-id-11002-icon.png?itok=M3HX5Gr3)
![Attractive Tablecloths](/sites/default/files/styles/medium/public/thumbnails/content-03-03-six1-icon.gif?itok=SiNNF02K)
problem
Attractive Tablecloths
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
![Painted Cube](/sites/default/files/styles/medium/public/thumbnails/content-id-2322-icon.png?itok=r3fcelpR)
problem
Painted Cube
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
![Nicely Similar](/sites/default/files/styles/medium/public/thumbnails/content-id-5635-icon.png?itok=H87VLq-O)
problem
Nicely Similar
If the hypotenuse (base) length is 100cm and if an extra line
splits the base into 36cm and 64cm parts, what were the side
lengths for the original right-angled triangle?
![Surprising Transformations](/sites/default/files/styles/medium/public/thumbnails/content-id-6544-icon.jpg?itok=48Xkr569)
problem
Surprising Transformations
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
![Same length](/sites/default/files/styles/medium/public/thumbnails/content-id-11134-icon.png?itok=0lXl0Dnd)
problem
Same length
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
![A Chance to Win?](/sites/default/files/styles/medium/public/thumbnails/content-id-5611-icon.png?itok=FWukIbfG)
problem
A Chance to Win?
Imagine you were given the chance to win some money... and imagine
you had nothing to lose...