Posted by: rdkpickle | 03.13.2017

favorite problems 3 – dartboard

[previously: favorite problems 1 ā€“ pirates, favorite problems 2 – triangles]

This one came from the “#MTBoS,” before it was named such a thing.

These were early days, when I was still kinda geeking out over the fact that I was tweeting with k8, and Dan, and Sam. There was this energy about the whole thing for me – I’m a competitive person, and realizing there was this group of whip-smart, motivated, brilliant teachers to learn from and look up to – I wanted to impress, to be impressive.

I’m pretty sure I could use my internet skills to figure out who first posed the square dartboard problem, but it’s a Monday night with a long week ahead and you’ll forgive my delinquency, here. What’s more important is what I haven’t forgotten – that I spent a long Greyhound bus ride to New York City sketching notes in a small Moleskine notebook (the same one I used to sketch tiny maps of Metro stops + the cross streets I’d find upon riding the escalator up up up and emerging onto the D.C. sidewalk). The problem posed was a challenge. I wanted to be in with the in crowd, wanted to solve the problem and share that I’d done so. Brain buzzing, headphones on, I jotted down my ideas, ignoring the seatmate eyeing my mathematical scribbles with furtive, skeptical glances.

The question: “There is a square dartboard, and a dart has equal probability to land anywhere on the board. What is the probability that the dart will land closer to the center than to the edges?”

It wasn’t until the ride back that I solved the thing. I don’t think I tweeted about it. I did, however, save the work. It was posted proudly in the “cubes” at my first school, traveled with me to Nashville to get laminated and hung near my desk. Still have it, somewhere. Years and miles separate me from the girl who experienced this problem as a test of her authenticity as a math nerd, who saw a solution as signal that I was worth being invited to the table.

Still something kinda magical about it, though.

So. Scrolling down invites spoilers.



[Worth mentioning – I posed this problem to students, years ago. Kids I didn’t even teach, who hung out in my room to talk math and after an hour or so filled my whiteboard with the work below. None of us back down from a challenge. All of us want to feel like we earned our way to the table.]


[[edit: @dandersod points me to the original question, as posed by infinigons. his work: here. “you were the nerds i wanted to accept me!”]]


  1. This series is great. I’m getting a nostalgic kick recalling when each one of these problems took over the mtbos for a couple of weeks each.

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