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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!
Side Note
My new favorite YouTube search phrase is Alex Gendler puzzle.
Comments 5
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Hi Michael! We used this exact problem at the beginning of the year to establish a collaborative problem solving culture in our classroom! Video was engaging. I used edpuzzle to slow the video down for my students and had them take stock of all the important information as it went by.
Then my students presented their findings to the rest of the school at our community assembly and teachers came up to me afterwards asking for the link so they could do it on their own time.
Math FTW!
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Here’s a link to the edpuzzle I made: https://edpuzzle.com/media/55fff305324882bb178b4265
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Yes, his are my favorites…I posted about this and the Einstein one as well the set daily puzzle I see you wrote about, on my blog http://eatplaymath.blogspot.com. Fun stuff!! Stay tuned for a new Ted Ed puzzle coming out soon!
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I do “Math Movie Monday” most weeks with my high school classes, and we watched this video way back earlier in the year. My classes loved it! We paused the video at the right spot and took time to work independently. Then we acted it out. They begged for more, and I have done my best to throw some like this into the MMMs periodically. (I also do a similar search to your new favorite YouTube search, and we have looked at some of the riddles as well. As a side note, there’s also a lovely treatment of Hilbert’s Hotel.)
What’s especially great about this, though, is that after begging for more “bridge problems,” every time I find one that’s a twist, I get the inevitable “this is just like the …!” reaction, and my students have the confidence to begin to attack whatever new twist they encounter. And that confidence overflows into a million other little wonderful places. It’s been a fabulous find. I am definitely going to take your “what if” scenarios and add them to our mix. Thank you!
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