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Next, take two of the cubes. Put them down on the table, either separately or together. What different arrangements are there?
I've made these three arrangements with my cubes:
How many square faces can I see in each case? Have a go at using your imagination to visualise how many I can see, and try making these arrangements yourself to check your answers. Then click on the button below:
These three arrangements each showed me a different number of faces. Are there any other ways in which I could have arranged the cubes? Would these show me a different number of faces?
Think about how we can tell whether or not two arrangements are the same. For example, I could turn the second arrangement so that the red cube is pointing to the left instead - would this count as a different arrangement? Why/why not?
Finally, take all three of the cubes. Arrange these in some different ways. It might help to write or draw each arrangement to keep track of the ways that you have already tried. Here are some of my arrangements:
How many square faces can I see in each of these three cases?
Now it's your turn! Use your three cubes every time, and see how many different ways there are to arrange them. How many faces can you see each time? Try to find all the possible answers.
What happens if the faces don't line up completely? Look at the example below: