Rotations

problem
National flags

Age

7 to 11

Challenge level

This problem explores the shapes and symmetries in some national flags.
problem
So it's times!

Age

7 to 14

Challenge level

How will you decide which way of flipping over and/or turning the grid will give you the highest total?
problem
Poly plug pattern

Age

5 to 7

Challenge level

Create a pattern on the small grid. How could you extend your pattern on the larger grid?
problem
Attractive tablecloths

Age

14 to 16

Challenge level

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?
problem
Rose

Age

16 to 18

Challenge level

What groups of transformations map a regular pentagon to itself?
problem
Attractive rotations

Age

11 to 14

Challenge level

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
problem
Stereoisomers

Age

16 to 18

Challenge level

Put your visualisation skills to the test by seeing which of these molecules can be rotated onto each other.
problem
HexPentas

Age

5 to 11

Challenge level

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
problem
Flagged up

Age

11 to 14

Challenge level

Weekly Problem 31 - 2008
The flag is given a half turn anticlockwise about the point O and is then reflected in the dotted line. What is the final position of the flag?
problem
Tiles in a public building

Age

7 to 11

Challenge level

What is the same and what is different about these tiling patterns and how do they contribute to the floor as a whole?