Cubes and cuboids

problem

More Christmas Boxes

Age

7 to 11

Challenge level

What size square should you cut out of each corner of a 10 × 10 grid to make the box that would hold the greatest number of cubes?
problem

Dicey

Age

7 to 11

Challenge level

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?
problem

Painted Faces

Age

7 to 11

Challenge level

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
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

Little Boxes

Age

7 to 11

Challenge level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?
problem

Presents

Age

7 to 11

Challenge level

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?
problem

Green Cube, Yellow Cube

Age

7 to 11

Challenge level

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

Three Cubed

Age

7 to 11

Challenge level

Can you make a 3×3 cube with these shapes made from small cubes?
problem

All Wrapped Up

Age

7 to 11

Challenge level

What is the largest cuboid you can wrap in an A3 sheet of paper?
problem

Cuboid-In-A-Box

Age

7 to 11

Challenge level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?