Living Permutations

Tonight, while rearranging my living space, I started thinking about math. Specifically, my mind fell on the topic of combinatorics because all my tasks seemed to center around accounting for all of my items (objects) and then bringing order to them to attain the most favorable conditions (uncluttered closet, specficic drawers for specific types of items, etc). While I didn't take the time to figure the exact number of ways I could dress myself in the morning, I did think about the order in which my living room furniture must be arranged. I have a couch, a loveseat, three small tables, a lampstand (table on which my lamp must specifically go-really, it doesn't look right sitting atop anything else), and a bookcase (n=7). I cannot duplicate the objects in my living room, therefore there are only 5,040 ways in which I could arrange the items in my living room (n! = 7!).

...I think at least 30 of those arrangements were attempted.

One would think that with over a thousand ways of arranging a space, it would be easy to select an arrangement, execute it, and then return to watching the Grammy Awards (Yeah! Ursher was robbed man, Ursher was robbed!). However, there is no way that I know of which allows one to calculate which order is the most asthetically pleasing, offers the best flow of energy (yes, I'm riding on the feng shui bandwagon), and an unobstructed view of the television. True, one could look at the list of possibilities and cross out the ones which are impractical for the purpose. But then I suppose that would eliminate all the fun associated with spending two hours moving furniture, inspecting the work, reattaching the leg to the couch, and once again moving furniture. So with all the numbers floating around...the only pertinent score of the evening ended up being Couches, 2. Movers, 0.