Last weekend I was at the Interface conference in Osage Beach, MO. While attending a session on Saturday morning, a fellow participant shared this lovely problem with me.
(WARNING: The video poses the problem and solves it. Be sure to stop in the middle so you can give it a try for yourself. It’s way more fun that way. I promise.)
It took me a little while to figure it out, but eventually I did. And it felt pretty great to shave off those last couple of minutes that seemed impossible to shed during my first few attempts.
Then I got to wondering…
- Imagine the janitor and professor are even slower (say, 6 and 12 minutes to cross, respectively). How long would it take the group to cross?
- Imagine everyone is slower (say, T1 < T2 < T3 < T4 minutes to cross). How long would it take the group to cross? And what’s the winning strategy?
- Imagine there are only three folks who needed to cross (to simplify the scenario, let’s say A/B/C who take 1/2/3 minutes to cross, respectively). What’s the fastest they could cross, and what sequence would yield that time?
- Imagine there are five who need to cross (A/B/C/D/E who take 1/2/3/4/5 minutes, respectively). What’s the fastest? What’s the sequence?
- Imagine there are “n” people who need to cross (A1/A2/…/An who take 1/2/…/n minutes, respectively). Fastest? Sequence?
Some of these questions I’ve answered in my own mind, and some I have not. If you answer one or more of them (or create another extension of your own) I’d love to hear about it in the comments. Cheers!
My new favorite YouTube search phrase is Alex Gendler puzzle.