I was reminded of a story yesterday while I was in the bathroom.
The story came from one of my friends in grad school. She was fascinated by the existence of a hidden order in the universe, one that she had been blind to until college. She was taking a computer programming class in her undergraduate days, and each student had to write a simple computer game as a final project. One of her friends, a male, wrote a game that created a random layout of a men's room, with urinals distributed along the walls, and on some turns, with people standing at a subset. On each turn, the player had to select the single best urinal.
The game was popular in her circle of friends, and was even more popular as a conversation topic. It seems that the vast majority (let's say, 80%) of the male players were able to perform nearly perfectly at this game. While the female players didn't even know that it might be possible to rank urinals on the dimension of social acceptability. And often the male players could all agree on a single best urinal but not really articulate why it was the best. Or maybe they had totally divergent, possibly confabulated, reasons, for picking a winner, but, except in rare circumstances it was the same winner.
And all the males had the desire for the remaining 20% to play by the same rules as them, and reduce social friction in the men's room. [If you have never been in a men's room, it helps to know that talking is taboo, and so any coordination needs to be non-verbal.]
I heard my friend's this story about the computer game 10 year's ago. Although I had never thought about these rules before, I have thought about it many many times since. Pretty much any time I had to choose a urinal, which is often. And I have come to the conclusion that, except in certain degenerate cases, there is always a single best urinal, and choosing it is precognitive.
Indeed, were I an evolutionary psychologist, I would attempt to argue that there is a urinal-selecting module in our brains and genes, likely on the y-chromosome.
I have, sadly, never seen the game in person. It's limited to my friend's anecdote and my fervid imagination. I imagine it looks something like the below. As far as I know, this blog post is the first time the Men's Room Urinal Game has been shared with the internet. (Admittedly, my knowledge is limited, since I refuse to search for "Men's Room Urinal Game" in google). I present 4 of the simpler problems, with some exegesis, but no answers, below. Answers tomorrow.
This is a view of the men's room, from above. The gray squiggles are the urinals. The black shape represents the urinator(s) there when you arrive, if any. The choice of font was dictated by the intense love for comic sans among my likely readership.
Round 1 presents the "Basic 5" problem. If you look at this and say, 'how could you possibly choose?' you have already lost, and demonstrated that you are either unfamiliar with men's rooms, or possibly autistic. There is a clear hierarchy of urinal choices. Although left/right preferences may vary by individual.
Round 2 introduces the issue of the other urinator. It breaks the symmetry. And increases the complexity infinitely. But not in this simple case. There's a clear hierarchy here.
Round 3: No comments, except to say, this takes us from beginner's to intermediate level.
In my friend's telling, there were a large number of layouts, with corners, occasional support pillars, small puddles of urine on the floor, and so on. Because I am considering releasing a home board game of this, I will not present them all here, but I will provide a corner case, for your consideration and discussion.