Enigma 1652: A colourful lamp
5 December 2011
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From New Scientist #2818, 25th June 2011 [link]
My artistic nephew is making a lamp which involves using the largest possible number of regular tetrahedra – solid bodies with four faces, each an equilateral triangle – whose faces will be painted with various colours. These will float in a fluid that is agitated and then lit from beneath by a bright light to produce a sparkling effect.
Some of the tetrahedra will have all faces the same colour, some will have faces of two different colours, others three and others four, but no two tetrahedra will be identical. Having done his sums, he finds that he will have exactly the same number of tetrahedra with four different colours as have three.
How many colours will he use? And how many tetrahedra?