When Grover Went Viral

About a month ago I walked into my office and found this problem on the chalkboard next to my desk:
Do you think Ryan should have made option "C" zero percent? ;)
My officemate, Ryan Grover, had put it there to tease us with what I quickly believed was a paradox. Having dealt with paradoxes before, I knew the first rule of paradoxes: "Don't try to reason with paradoxes." Instead, I thought I'd post it to Google+ to see if some of my math-oriented followers could have some fun with it.

Ryan will be the first to admit that he is not the creator of this problem. He told me that he had seen something like it, had given it some thought, and then searched for similar problems. Ryan found variations of the problem on Reddit, got his wording just right, and wrote it on the chalkboard. He knew it was worth sharing, just as I did. But I had a different sharing mechanism in mind.

I posted on October 20th and nothing much happened the first few days. Then things really took off. You can get a sense for some of the progress thanks to Google+ Ripples. But what really got my attention was seeing Brian Brushwood share the picture on October 27th. I follow Brian because of his work on TWiT.tv, not because I expect him to post interesting probability problems. Because the picture had made its way to Twitter, where Brian saw it, and then back to Google+, it was no longer connected to my original post. Still, Brian's post quickly got over 2000 reshares -- including one by Terence Tao. I argued to Ryan's (and my) advisor that "getting cited" by Terence Tao should satisfy Ryan's "publishable work" requirement of our PhD program, but I don't think he bought it.

The same day Brian posted the picture it hit Reddit (and again in days following), getting over 2300 comments, probably 10 times more than in previous posts. I wonder if it's the placement of the problem on the chalkboard that added to its appeal, or if it was just the right question at the right time to engage people's interest. The next day the picture appeared again in Google+, this time in Ed Yong's stream where it got over 1500 reshares and 300 comments. It was also quite a treat to see the picture show up at FlowingData.com. I'm a pretty big fan of Nathan Yau's blog and book, and in an email Nathan said the 788 comments were probably the longest thread of any post ever made on FlowingData.

There's no way to count precisely, but the picture was reshared publicly on Google+ (where an estimated two-thirds of posts are private) around 5000 times and comments on Google+, Reddit, and FlowingData also number in the several thousand. Some good things have come of this:

  1. It's been fascinating to watch people try to reason through the problems in the comments. Math teachers like to watch people who don't give up easily.
  2. I've picked up several hundred followers on Google+ from all over the world. Many of them have interests in mathematics and how it is taught and learned, and what they've shared with me is many times more valuable than even seeing the comments and shares from Brushwood, Tao, and Yau.
  3. It's bolstered my (and my colleagues') belief that if something is interesting, it should be shared. We're not in the business of keeping good ideas to ourselves.
As far as I can tell, maybe only two bad things have come from this:
  1. We've experienced a little bit of "sharer's guilt" because neither Ryan or I deserve any credit for actually coming up with the problem. Someone who shared the problem before we did, such as in those previous Reddit posts, might be feeling justifiably peeved that they aren't getting the credit they're due. We're sorry.
  2. We've avoided erasing that portion of our chalkboard, even though we could use the space. Next time Ryan has a perplexing problem he'll have to write smaller. :)