It’s not about number of urinals, it’s about the space they are in

There’s a post on the packing efficiency of urinals on XKCD. In summary, assuming that

  • first male to use a urinal picks a corner urinal
  • a male picks his urinal that’s furthest away from all other urinals in use
  • a male will keep at least 1 urinal between him and another male

then the best number of urinals in a row are of the form 2^k + 1, where k=1, 2, 3, …

Or if you’re not in the mood for math, 3, 5, 9, 17 and so on. I’m not listing more because, WHAT KIND OF ARCHITECT BUILDS 17 URINALS IN A ROW!?! But I digress…

What I want to emphasise is that the last assumption is the overriding one. The first 2 assumptions are corollaries of the third. It’s the buffer urinal that the self-conscious male is worried about.

Let’s look at the trivial case of 2 urinals. Based on the assumptions, there will only ever be 1 urinal in use at any one time. In effect, it’s no better than just putting 1 urinal. So why build 2 urinals?

Bonus thought experiment: One of the 2 urinals is probably used more often than the other. Based on reasons such as it’s the one furthest from the main toilet door, it’s the one most hidden from view, it’s the cleaner (for whatever reason).

However, if you build 2 urinals with 1 urinal’s space in between them, then both are more likely to be used at the same time when there are at least 2 males needing to release their liquid waste. Based on that specification, a 5-urinal-in-a-row setup is no better than a 3-urinal-with-1-urinal-space-in-between-them setup.

It’s not about the number of urinals in a row. It’s about the available space they were built in.

And I think I’m done talking about urinals for the rest of my life… (I counted 22 uses).