Saturday, 5 December 2020

Incrementally Challenged

Arduous, my ass, he thought, prying the key from the plate on the door and trying it first there just to be sure. It fit but didn't turn, which means it slid into the lock, the way keys in hotels might slide into the lock of any of its doors, but only access one room. Or so the convenient assumption.
This mansion's many rooms were situated like those of a hotel of ludicrous luxury, decadence around which one could wander a while, a scenic waste of time. Within each wing were wider corridors with ornately antique and uncomfortable waiting furniture, sparse if only because of the vastness of space, and passages to narrower corridors.

He decided for economy of movement's sake to move, key in hand, clockwise, wherever possible along the wall, repeating the attempt with each door in succession until, voilà, the first key turned, likewise clockwise, and unlocked the fourteenth lock he tried, which was the thirteenth door, the third door having had two locks.

This thirteenth door opened into a large empty windowless room. Arduous, my ass, he thought. He hadn't even got to the end of the first hall. Any contrary implications had not occurred at that point. Not to him.

After a cursory inspection of the thirteenth room, labeled 13 on the plate above the peephole, he determined nothing of significance and returned to the second room, leaving the first key behind in the lock, door wide open, immediately identifiable for future exclusion.

He took the key affixed to the door of the second room, labeled 2 in the plate just above the peephole, tried it in the same door's lock, again, just to be sure, and repeated the process he had the first time until he got distracted as he reached the open door of thirteenth room. A temptation, a compulsive thoroughness or just an obsession yet to be settled, to see if this second key would also unlock the room labeled 13, was one beyond his will of resistance.

And it was but for random chance, or not unlikely happenstance, that he discovered how it did not unlock this door. He had used it first to turn the cylinder smoothly counterclockwise, locking the only door he had yet unlocked, before trying, unsuccessfully, to twist they key back in the other direction.

Had his first action not been to remove the key in the door left ajar and, say, instead to close and lock the door and then remove the key, he likely would only have concluded through that alternate sequence of events that the second key didn't work in this lock.

While still mindfully mocking the suggestion of arduousness, a beautiful symmetry presented itself in which each door had but one key that would gain access to its room, and one entirely different key that would secure it from entry. So affixed to each door was a key that would rotate clockwise in one lock and counterclockwise in another. Or so the convenient assumption.

At this his eyes drifted upward, to the label 13. There, the key, if you will, the third key he'd paid any mind to, or better yet, the thirteenth key from where he had begun, or better yet still, key 13, for, indeed, it was the keys that labeled the numbers of the rooms onto which they were affixed, was neatly fitted into the plate above the peephole.

Now it was his mind being mocked for the casual way he had dismissed the suggestion of arduousness. It seeped slowly like a chemical reaction to one mental occurrence after another, each confusing the one that had preceded it, increasingly complicated, potentially convoluted, until he brushed it all aside with the thought that tediousness does not equal arduousness, and, without allowing himself to stray too far from the original plan, mapped out the following intervening sequence:

Remove key 2 from the lock, use key 1 to turn the lock to the unlocked position again, close the door, remove the key, take key number 13 from the plate on the door and see if it, too, will lock it. If not, lock the door again with key number 2, use key number 13 to, in all likelihood, surely, rule out that it will either lock or unlock the door onto which it had been affixed, and place key 13 back into the plate above the peephole. Finally, unlock the door with key 1 again and leave the door open. Mark the door with a 2, indicating the key number that can lock it again.

That sequence complete, he would then be able to proceed with the original plan, with the caveat that economy of movement would happen in two stages. First he'd circumnavigate the premises establishing which keys unlock which doors, inspecting each room in the meantime, of course. Once every door was open and identifiable for exclusion, the more tedious task of establishing which keys lock which doors would begin. The first door of stage two would be already done, if out of a certain sequence.

But a hiccup happened before he could get started. Being a second hiccup, it was a disquieting indication that he might have the hiccups, which came in the form of the key he could neither turn nor remove from the lock.

Chalk up a 1 for this door instead of a 2, he thought, trying to relieve himself with the amusing wit of a person he decided just then was too clever by half the month's worth of rooms he had yet to reach in a mansion full of four seasons. Truth in comedy, the number that now eliminates this door is the key that locks it, leaving aside for a moment the one that determines its number embedded in the plate above.

Knowing he was able to remove the key that unlocked the door without any problem, he considered position dependence: An unlocking key is removable after opening the door; a locking key is only removable if you lock it when it is closed.
Why did he have to stop at 13 again? Thoroughness?

On the one hand, it might have been the only way he'd discover, as he had, that each door had two keys, leaving aside, again, the one of its numbered sequence. On the other hand, it could be that the second key would have been able to unlock it from its normal closed and locked position.

Panic reduces the level of intelligence to mere obscurity, but the next process of elimination might eliminate the ability to use any key twice. Proceed with careful consideration.

His solution at this point is to go back to the third room, take key number 3 and continue with the original plan. Any key that unlocks shall be immediately tested to re-lock, prior to the opening of any door. Baby steps are arduous for the toddler - but only tedious for me, he thought. And then, there's a chaise lounge with my name on it.