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 different flowers?
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.