21 Mar 2013

Four Cubes Puzzle: Upper Secondary Mathematics Competition Question

This question is an extension of the Three Cubes of Three Colours that was posted earlier this week.

This time you have a number of cubes of two different colours. The diagram below has blue and yellow, but the colours themselves are obviously not important. You are required to use 4 cubes at a time and to glue them together so that two faces are perfectly joined together. You are also required to use at least one of each colour. How many distinct objects can you make with 4 cubes in two colours?

Remember, again, that these are 3-dimensional objects that you can rotate in space, so the question requires that you select just one arrangement from those that have rotational symmetry.

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