In a recent fit of New Year’s optimism, I started bringing my running shoes with me to work the two days a week I write science news for the University of Colorado Cancer Center. The thing is, as I’ve learned these six months since moving to Boulder, CO, from Ojai, CA — it’s fricking *cold* in this state. And so instead of jogging around the golf course like any sane human, I’ve been running the Cancer Center stairs.
Okay, “running” is an overstatement.
You see, the other thing about Denver is it’s at altitude. Unlike Safeco Field or Monster Park or Chase Field, it turns out “Mile High” doesn’t imply sponsorship by, like “Mile High Communications” or “Mile High Bank” or, perhaps more appropriately in Colorado, “Mile High Hydroponics.” It’s actually a mile high — in fact, more than a mile high in some spots.
Like the eighth floor of the University of Colorado Cancer Center.
So here’s my dilemma: I’m a little shy to be seem huffing my flatlander self up and down said stairs. So I’d like to know how many people I’ll see during my run so that I can mentally and emotionally prepare myself for this number of encounters.
Let’s imagine that everyone in the stairwell, me included, travels a constant one floor per 15 seconds, either up or down. I start from the top, eighth floor, run to tag floor #1 (the ground floor) and then immediately go back up, like hell’s own yo-yo. And during the half hour I run, everyone’s going to lunch and so they travel ONLY down the stairs — they enter at a certain floor and walk all the way to floor #1 (the ground floor), where they exit.
Here’s the tricky part: people enter the stairwell at every minute multiple of the level they enter. For example, one person enters on the 6th floor at minutes 6, 12, 18, 24 and 30 (and they walk from the 6th floor, down); likewise a person enters from the 8th floor at minutes 8, 16, and 24 — again walking down. (Fugheddabout anyone entering at the first, ground floor because that would be silly.)
You get the point.
Assuming no one slows down to offer me cardiac paddles or speeds up for fear I’ll fall down the stairs and crush them, how many people will I meet during my half-hour jog?