Visualising and representing

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?

Find the sum of this series of surds.