Can You Join the World’s Biggest Zoom Call?

Another week, another riddler. This one came from Jim Crimmins:

One Friday morning, suppose everyone in the U.S. (about 330 million people) joins a single Zoom meeting between 8 a.m. and 9 a.m. — to discuss the latest Riddler column, of course. This being a virtual meeting, many people will join late and leave early.

In fact, the attendees all follow the same steps in determining when to join and leave the meeting. Each person independently picks two random times between 8 a.m. and 9 a.m. — not rounded to the nearest minute, mind you, but any time within that range. They then join the meeting at the earlier time and leave the meeting at the later time.

What is the probability that at least one attendee is on the call with everyone else (i.e., the attendee’s time on the call overlaps with every other person’s time on the call)?

As a quarantine experiment I solved this live on in what I called a “speedrun”. About 50 people joined over the two and half hour broadcast — some familiar faces and some people I’d never met.

After cleaning up a bit of the work the next few days we got a solution of 2/3.

Overall, it was a fun experiment. As I noted after, I don’t think live streaming the solving process is the best method — hosting and solving is very taxing and a “worst of both worlds” situation… but one I wanted to try. Stay tuned for new forays into content creation 😂 – face with tears of joy emoji

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