One of the most memorable problems I got to work through at the OGAP (Oklahoma Geometry and Algebra Project) workshop I attended was the Camel Crossing the Desert Puzzle.
A week before attending the workshop, I had saw the problem in a copy of Discovering Advanced Algebra. I read the problem, and I thought it sounded interesting. But, I didn’t really take any time to solve it.
The version we attempted reads as follows:
A camel is sitting by a stack of 3000 bananas at the edge of a 1000 mile-wide desert. He is going to travel across the desert, carrying as many bananas as he can to the other side. He can carry up to 1000 bananas at any given time, but he eats one banana at every mile. What is the maximum number of bananas the camel can transport across the desert? How does he do it? Be prepared to present your solution to the class. (Hint: the camel doesn’t have to go all the way across the desert in one trip.)
My group got right to work and figured out a way to transport 500 bananas across the desert on our first try. Linda, one of the facilitators, looked at our solution and told us that we could do better than that. We tried, but every subsequent strategy ended up transporting less than 500 bananas!
One group was able to arrive at the solution during the 45 or so minutes we were given to work on the problem. The rest of us had to take the problem home for homework. At home, I tried to solve the problem by employing simpler cases. But, I never did make the breakthrough I needed.
The next day, they provided us the solution. I kinda wish I had left the room during the explanation so I could have figured it out for myself. Oh well… There are plenty of other math problems out there for me to solve!
Fawn Nguyen gives her students a version of this problem that involves transporting 45 watermelons across a 15 kilometer desert. I think this problem would be much more approachable for my students. Plus, you can easily represent 45 watermelons with manipulatives. I wouldn’t want to try to represent 3000 bananas! I definitely want to work this problem into my curriculum next year!
I think it would make a great task to give students at either the beginning or end of the school year!
I intentionally do not share solutions to the puzzles I feature on my website because I strive to provide learning experiences for my students that are not google-able. I would like other teachers to be able to use these puzzles in their classrooms as well without the solutions being easily found on the Internet.
However, I do recognize that us teachers are busy people and sometimes need to quickly reference an answer key to see if a student has solved a puzzle correctly or to see if they have interpreted the instructions properly.
If you are a teacher who is using these puzzles in your classroom, please send me an email at firstname.lastname@example.org with information about what you teach and where you teach. I will be happy to forward an answer key to you.
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