Extended Munroe Protocol

Last Monday three of us were drinking beer at Arbor. One of us got up for a bathroom break. Like a pack of dogs, or a classroom of coughing students, the other two took the cue within a couple of seconds. And we trudged in a line to the bathroom.

The thing with Arbor is that it might be very crowded and very loud on weekends, but on rainy Monday evenings it’s remarkably empty and quiet (the music was very pleasant there, for the first time when I’ve been there). A consequence of this is that there are very few people in the bathroom at any given point of time. And last Monday, when the first of us (it wasn’t me) entered the bathroom it was absolutely empty (I was about to say “when we entered the bathroom”, but since we were walking in a line and not abreast, the bathroom wouldn’t have been empty when the second of us entered! (it’s an old Tenali Rama story that was once published in Tinkle) ).

The urinal at Arbor has five stalls, and the first guy who entered took the stall at one corner (let’s call it 1).┬áThe second guy (again not me, things are coming back to mind now) took the stall at the other corner (number 5). I go in, and see that it makes most logical sense for me to take 3, and I go. At almost the same instant, the other two guys shout “Munroe Protocol“.

Without realising it, or maybe those guys did but I surely didn’t, we had followed the Munroe protocol precisely. First guy took one corner, second took the other corner and third took the farthest away from both. As perfect as it gets. One of the benefits of the discussion that followed was that I got acquainted with the Munroe Protocol (I was aware of the protocol but not the name). And since then it’s been embedded in my head.

On Saturday at the Landmark Quiz, I went for a leak between the time the prelims finished and the answers were to be given. Again, since the answers were yet to be given, most people were in their seats, and the toilet was not too full. I approached a line of five stalls (this was a big bathroom) and found people in positions 2 and 4. “Bastards”, I thought, thinking about their utter disregard of the Munroe Protocol, and took my stand at the now uncomfortable stall 3.

As I was doing my business it occurred to my mind that the clown to the left of me and the joker to my right may not have been so evil after all. They might have been occupying stalls 2 and 4 despite following the Munroe Protocol, and for no fault of theirs. This leads us to the Extended Munroe Protocol, which can follow as an extension of the Munroe Protocol.

So here is how it could have happened. Let’s assume that people take a constant amount of time to pee. Let’s assume that the bathroom has precisely five stalls, numbered 1 to 5. First guy enters and takes 1 (as per the Munroe Protocol). Second guy takes 5. Third guy takes 3. All going well according to the protocol.

Now the fourth guy enters. What does he do? If he is of the extremely decent types, he will wait for one of the three (most likely 1, given our assumption) to finish and take his place. But most people are not that way, and so the fourth guy is likely to take one of the two empty stalls. Without loss of generality, let’s say he takes 2. The fifth guy now enters and seeing only one stall (4) empty, takes that. We have a full house now.

Let’s assume that it’s a while before the sixth guy enters. In the meantime, the first guy finishes his business, and exits stage left. The second guy (position 5) follows him soon, and he is then followed by the third guy (position 3). And at this precise moment the sixth guy enters. And what does he see?

Positions 2 and 4 taken in a five-stall urinal. “Bastards”, he thinks, without realising that this setup came about via diligent practice of the Munroe Protocol.