please empty your brain below

You're taking the piss today
Some of us apply the 'go opposite end but one' and 'ok to stand next to someone if it is an end space' rules.

It is also complicated further by the time dimension, whereby it's ok to start standing by someone who's clearly about to depart, a factor that becomes more important as the urinal gets larger.
Any female reading today's post who has spent the interval queuing for the loo in a theatre will be screaming "Nooo"...
This sequence does appear in the OEIS, however the submission refers to a row of payphones, not urinals.
The behavioural assumption inherent in this post most likely applies in the main to UK males. When holidaying abroad I've witnessed men at adjacent urinals engaged in animated chat! I only saw this from a distance while waiting, due to inherited Britishness that compels observance of U(n).
This feels like a taste of "back to school"...
The notable exception that should be mentioned here, is half time at a football stadium. There, no one cares and every urinal slot is immediately filled as soon as one becomes available such is the pressure of hundreds of people all wanting to have a wee.
Consider the horror of the re-designation of Gents as Ladies at some events.

Venues with predominantly male visitors such as Sandown Park or Alexandra Palace often do this for craft events. Unfortunately the facilities are not always hosed down with bleach beforehand. The queues for the Ladies are still huge and only a few hardy souls venture to try the door of the `gents before recoiling.

Decent stalls for everyone is the only acceptable arrangement.
Well said Richard, you got there first. As a female I was wondering why men queue for a slot at the urinals if there were a chance of using a sit down loo?
DG,have you a similar formula worked out for those really old urinals which consisted of a long ceramic wall with a gutter to the drain?
You must try to get out and about more,DG,or you'll go stir crazy. 😂
Not just football matches have intervals which generate congestion: the same effect can be seen in theatres and at the Royal Albert Hall, with a lot of squeezing past others to reach the only vacant stall. (More accurately "could be" seen pre-lockdown.)
That's interesting maths - but round here those rules only apply until adjacent spaces only are left, at which point it's OK to use them.

Alarmingly, our new (university) building is to be equipped with gender-neutral facilties. This is for an engineering faculty. I suspect the ladies will prefer to head over to art and design.
The formula is further complicated if early gentleman in their optimum locations leave a puddle that successor gentlemen don't want to stand in. Etc.
I have never seen a queue for urinals develop when there are stalls available.
The rule of "maximise distance from other users" also fails to match my observations. The rule I see is "go to the nearest stall to the entrance which is not next to an occupied one".
My own pee-shyness means that I can pee next to an adult stranger, but next to a relative, friend, acquaintance or boy is quite impossible, no matter how urgent.
There are two kinds of mathematician, those who argue about what the rules are and those who go ahead and solve the problem.
This also applies with current usage of tube trains, albeit with an interval of every 3rd or 4th seat being required, and trying not to line up with anyone directly opposite at the same time.
Until relatively recently I had always assumed that blokes didn't mind doing it in front of/in close proximity to one another. Given that they obviously do (and that they run the world), how on earth has this design persisted for so long? When, you know, some contiboard partitions would solve it. I am genuinely mystified.
I believe what you're looking for is a 'ceiling function'.

(Or more strictly speaking, a floor function)
Aha, just to prove there's nothing new, here's xkcd on 'Urinal protocol vulnerability' from 2009, complete with formula and graph.
What a shock. Men stand together or nearby each to urinate thereby publicly exposing themselves. Men need to stop this untoward behaviour of exposure with possible sexual connotations and use cubicles as I do on the rare occasions when I need a public facility.

You can be sure if every man has to use a cubicle, the shortage of cubicles for women will evaporate.
But when you've got to go, you've got to go...
Standing next to someone at a urinal is not something that would bother me in the slightest but I am deeply concerned by the drastic reduction in public toilet facilities that are available these days, when I was a young man there were public conveniences located at every local shopping area which were usually maintained in a spotless condition by a locally employed attendant, these days you can walk miles and miles without seeing a single public toilet available for use, looking at old maps I can see that there were four located within a mile of my home, now there are none.
The analysis misses several other factors:

- The amount of pressure in the bladder
- The distance from the entrance, the formula looks to assume an even spread
- The layout of the toilets
- The size of the/any puddle in front of any individual urinal

I'm sure I've missed a few more.
"Practically speaking you wouldn't install a row of urinals 25 stalls long": I am pretty sure the toilets below the Barbican hall are this long, but I guess that I cannot go today to check.

When I had training about being accommodative towards people with autism, a potential lack of awareness of some unwritten social rules was described, and urinal choices specifically covered.
This is the content I come here for. More posts with links to the encyclopaedia of integer sequences, please.

(I conjecture that Pisser One heads in real life for a space one away from the end, because standing unnecessarily next to the wall is also yielding personal space. But this just moves your sequence along by 1, without affecting the maths of it).
Medford: a ceiling function requires muscular pressure beyond the capacity of man; and a floor function is just disgusting. Aim properly.
But where is the location of the title photo? It looks a bit like the Princess Louise in Holborn.

dg writes: hover over it.
Sarah - I suppose the issue with partitions may be related to splashback, you wouldn't want to be surrounded by a build-up of splash marks either side.

My beige walking trousers are very good at visualising this normally less detectable phenomenon. Good incentive for optimising your technique, although the shape of the urinal also plays a big role.
Honestly surprised there's not a "leave your I hate urinals comments here" box hahaha
Is this theoretical pisssics?
I look forward to a sequel examining the usage of urinals which do not have any form of partition - these are not uncommon, I think. Where the spacings are completely at the discretion of users, I wonder if more people might actually be accommodated? Certainly where partitions are in use, they are close enough to "rub shoulders" with your neighbour. Also, is there any study of the phenomenon of mobile phone use whilst at the urinal?
I'm guessing the problematic urinals were built 50 or more years ago and men weren't so squeamish then.

dg writes: guess again.
Searching for urinal function mathematics produces lots of further reading! Including a paper from the "Fun with Algorithms" conference and this activity specifically designed for teaching students about the floor & ceiling functions here.
Re the Barbican: There was a suggestion that, by an oversight, the architects’ plans originally omitted any loos at all for the concert hall and theatre, hence a last-minute decision on the deeply inconvenient location of both ladies’ and gentlemen’s facilities in a long service tunnel under the hall, rather than higher up the building. And, yes, the gents’ is a long, unbroken trench-style urinal; ghastly.
There was something similar mentioned in the book Dave Barry's Complete Guide to Guys that was published in 1988.
Useless fact: I once used British Rail's northernmost urinal. Must go to Penzance some time..
As a female, I would be interested in a survey of how many men wash their hands before leaving the public toilets. My husband is often shocked how many just zip up and walk out. He often complains, and says it’s not just the old blokes.

It’s very rare to see a woman not wash her hands.
Having an enlarged Prostate, when the moment strikes ... the desperate need to wee has a far greater influence than the social norms described here!

Anywhere within reach is a blessing.

(Hmmm. Maybe I could have phrased that better???)
You could call today's post a uninary tract

An additional factor at my football club's urinals (and indeed many others), is that they are of the rectangular metal design without any partition, so that you can fit (in each section) 3 "wider" or more private men, or 4 if they are slimmer and happy to have less personal space LOL
I'm pretty sure the yellow colour used in this post is not just a coincidence.

TridentScan | Privacy Policy