Visualising and representing

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

Mary is driving to Birmingham Airport. Using her average speed for the entire journey, find how long her journey took.

Can you form this 2010-digit number...

Can you find ways of joining cubes together so that 28 faces are visible?

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

What is the smallest number of ferry trips that Neda needs to take to visit all four islands and return to the mainland?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

How much of the square is coloured blue? How will the pattern continue?