A Painting Conundrum

painting conundrum

From Stephen Barr’s Experiments in Topology (1989) via Miodrag Petkovic’s Mathematics and Chess (1997):

This apartment contains eight rooms, each measuring 9 square meters, except for the top one, which measures 18 square meters. You have enough red paint to cover 27 square meters, enough yellow paint to cover 27 square meters, enough green paint to cover 18 square meters, and enough blue paint to cover 9 square meters. Can you paint the eight floors in four colors so that each room neighbors rooms of the other three colors?

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The task can’t be done with the colors given, but there’s a trick: If you mix 1/3 of the red paint into the blue paint you’ll produce enough purple paint to cover 18 square meters. And now a solution is possible:

September 7, 2014September 14, 2014 | Puzzles