The Color Dilemma

We bought a house giving in to dreams of belonging, growing roots, and making a style statement of our own. We fantasized using latest decorating trends from the premium home design catalogs. As our dreams came true, so did the nightmares of home ownership. The romanticism of Home Depot commercials turned into ridiculous fights over color selection. I love bright warm colors. My husband, on the other hand, is stuck in the retro age, plus he definitely wants at least one dark brown room – a dungeon perhaps. A decorator professional called in to mediate our color disagreements, rescued us by suggesting we use our brightly colored Nelson clock for the color palette. So, how many colors do we need to satisfy everyone? What is the minimum number of colors that we have to compromise on? This reminded us of an old map coloring problem. Most children at some point discover that at most four colors of crayons, markers or chalk are enough to paint any drawing so that no areas of same color share a common edge. Mathematicians battled for centuries proving that this always works and that any map can be painted with up to four colors so that no two neighboring countries will have the same color. Take a look at the four-color map of United States:


But wait, a top view plan of our house looks very much like a map. It means that four colors should be enough to paint all the rooms with no two adjacent rooms having the same color:



So, among four members of my household, we only need to choose four colors. One each. That's doable!




For more household adventures with math, try Cheap and Hip but Assembled by You