Darren’s Diatribe

I recently got three metal screen doors powder coated. I just had to reassemble them.

Each screen door had five similar pieces of metal holding down the wire mesh. Each piece of metal can only go in one way around, but there are four orientations that may need to be tried (turning over, and swapping end-to-end).

By my calculations there are 60 possible choices for placement of the first piece of metal (15 pieces x 4 orientations) and 56 for the second and so on. This gives the total possible combinations to be:

N = 60 x 56 x 52 x … x 8 x 4
= 1404104661094367232000

I started to get worried. Then I realised that on average, the first piece should take around 30.5 tries (8 pieces on average; the first 7 need to try 4 orientations, the last takes 2.5 on average), the second piece around 28.5 tries and so on. So the number of tries should be:

N = 30.5 + 28.5 + 24.5 + … + 2.5
= 247.5

Much better…

It actually only took me about 10 minutes to sort them out. There were just enough differences between some of the pieces that some of the choices were significantly reduced. By doing it in the right order, I think I only needed a hundred or so tries altogether.

I think I actually spent longer doing the calculations and blogging about it than actually doing the job