2D representations of 3D shapes

problem
Favourite

Hamiltonian Cube

Age

11 to 16

Challenge level

Weekly Problem 36 - 2007
Find the length along the shortest path passing through certain points on the cube.
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A City of Towers

Age

5 to 7

Challenge level

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
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The Third Dimension

Age

5 to 11

Challenge level

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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Building Blocks

Age

7 to 11

Challenge level

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?
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Guess What?

Age

7 to 11

Challenge level

Can you find out which 3D shape your partner has chosen before they work out your shape?
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Which Solids Can We Make?

Age

11 to 14

Challenge level

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?
problem
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Nine Colours

Age

11 to 16

Challenge level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
problem
Favourite

The Spider and the Fly

Age

14 to 16

Challenge level

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
problem

Christmas Boxes

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?