Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Squares in a Square
Age 11 to 14 Short Challenge Level
In the diagram, all the small squares are of the same size.
What fraction of the large square is shaded?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.