Painting a Pyramid


by Henry E. Dudeney

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There are seven primary colors of the solar spectrum - violet, indigo, blue, green, yellow, orange, and red (or "Vibgyor").

This puzzle concerns the painting of the four sides of a tetrahedron, or triangular pyramid. Each time no more than four colors from the solar spectrum can be used to paint a pyramid.

The question is in how many unique ways may the triangular pyramid be colored, using in every case one, two, three, or four colors of the solar spectrum? A side can only receive a single color, and no side can be left uncolored. The crucial point of the challenge is careful selection of the painting scheme in order to avoid the repetitions of the pyramids. In other words if a colored pyramid cannot be placed so that it exactly resembles in its colors and their relative order another pyramid, then they both are different. Otherwise they are the same. Remember that one way would be to color all four sides red, another to color two sides green, and the remaining sides yellow and blue; and so on.

Posted: April 30, 2009
PDF Version (89 KB)

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