Cubes and cuboids

A task which depends on members of the group working collaboratively to reach a single goal.

The challenge for you is to make a string of six (or more!) graded cubes.

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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?

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?

How many cubes can you see?

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

The net shown here is cut out and folded to form a cube. Which face is then opposite the face marked X?