What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Follow the diagrams to make this patchwork piece, based on an octagon in a square.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
A huge wheel is rolling past your window. What do you see?
Which hexagons tessellate?
A design is repeated endlessly along a line - rather like a stream of paper coming off a roll. Make a strip that matches itself after rotation, or after reflection
When a strip has vertical symmetry there always seems to be a second place where a mirror line could go. Perhaps you can find a design that has only one mirror line across it. Or, if you thought that. . . .
I noticed this about streamers that have rotation symmetry : if there was one centre of rotation there always seems to be a second centre that also worked. Can you find a design that has only. . . .
Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.
Make a footprint pattern using only reflections.
Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."