How many different symmetrical shapes can you make by shading triangles or squares?
In this problem, we have created a pattern from smaller and smaller
squares. If we carried on the pattern forever, what proportion of
the image would be coloured blue?
Can you maximise the area available to a grazing goat?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
L triominoes can fit together to make larger versions of
themselves. Is every size possible to make in this way?
The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.
Herschel figured out an experiment which might have led to the
graph, and sent us a skilful analysis of the data.
Go to last month's problems to see more solutions.
In this article, read about the thinking behind the September 2010 secondary problems and why we hope they will be an excellent selection for a new academic year.
What are rich tasks and contexts and why do they matter?
A task which depends on members of the group noticing the needs of
others and responding.