Cubes and cuboids

problem
The solid

Age

11 to 16

Challenge level

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

Age

7 to 11

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Crawl around the cube

Age

11 to 14

Challenge level

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?
problem
28 - upward and onward

Age

7 to 11

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Cubic vision

Age

14 to 16

Challenge level

How many cubes can you see?
problem
Summing squares

Age

14 to 16

Challenge level

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

Age

5 to 11

Challenge level

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?
problem
Net result

Age

11 to 14

Challenge level

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