May 5 Day 58: First Approximation

The puzzle presented on May 2, Day 55: Small Start gives a first approximation to the participant placement algorithm in a Zoom meeting room. Provided all participants use their cameras, placement seems dependent on the order in which we signed into the meeting except that each person appears in the “second” position of their own display.

I wanted produce a larger collection of simultaneous screenshots with more participants to confirm. Unfortunately, my collection is imperfect; I took my screenshot but neglected to save it from the clipboard. Given the images I do have, can I verify the conjecture? I would say yes, based on just two images:

The first gives the entrance order for all but Ander: Jenny, Sasha, Duong, Olga, and Erik. The second clearly places Ander between Duong and Olga. So the final order should be Jenny, Sasha, Duong, Ander, Olga, and Erik. I can confirm this is in fact the order that people arrived to the meeting and Sasha, as the second person to log in, has the screenshot that represents the proper order.

Not every pair of screenshots is this decisive. For example:

As previously noted, first image confirms the entrance order of Jenny, Sasha, Duong, Olga, and Erik. From the second we conclude that Ander arrived between Sasha and Olga. So Duong and Ander are both between Sasha and Olga but their relative order is not completely determined. A third screenshot should break the suspense, right?

So what happened here? Are we all wrong?

Maybe, as Richard Guy would have us believe, we ask too much of small numbers. His Strong Law of Small Numbers proclaims that “There aren’t enough small numbers to meet the many demands made of them.” Perhaps the pattern that we concluded for four participants doesn’t generalize to larger numbers. Or maybe our first approximation is on track and there are other variables in play still to uncover.

I will need to take greater care and gather more data. Anybody out there want to help?