I must say I hadn’t planned on exploring the ‘wrapping gumballs’ problem again quite this soon, but then I hadn’t planned on quite the response I got from that column either!!
I was delighted to see so many responses to the invitation to send in solutions! There were several such responses! Moreover many of them would ‘work’ in the real world!! And some submissions that wouldn’t ‘work’ incorporated some very good mathematics, but made the same easy-to-forget ‘real world’ omission, namely forgetting to account for the space between the gumballs in the container.
I guess my own favorite submission (subjective, of course) was from Michael Doss and his 12-year old daughter, Lilly. It went like this:
My 12 year old daughter and I enjoy these types of math problems, so we put our thoughts together to come up with an answer. Here is our logic.
Due to the dead space that needs to be included when stacking spheres or gumballs, we took the .5 inch diameter of each gumball and cubed it to find the volume required for each one. .5x.5x.5=0.125 cubic inches. We then multiplied that times 5000 gumballs giving us a total cubic inch requirement of 625 for the inside of the container. The cube root of 625 is 8.55 inches, so if the box had the same dimensions on all six sides it would need to be at least 8.55 inches tall, 8.55 inches wide, and 8.55 inches deep.
How marvelous! Not only did Michael and Lilly ‘nail’ the problem (though several other specific answers are possible), they remembered to account for ‘dead space’ between the gumballs (as mentioned, a common Achilles heel for other solutions, even from math types). And my own personal favorite part: A father and daughter loving and working on such problems together!!
By the way, did you note above that I avoided using the word ‘correct’ as I described answers that would ‘work’? Another thing I like about this ‘real world’ problem is that several other specific container shapes/sizes answers are possible – and indeed were received as submissions. This is an important aspect of problem-solving in the real world – ‘correct’ can be a hang-up, if different answers ‘work’ in the real world.
For those interested in my own personal version of the solution (similar to, but also different from the Doss’), you may visit this link: http://aftermathenterprises.com/nov-15-bts-campbells-bonus-solution/
By the way, I have to mention another ‘solution’ I grinned at. Diane Bailey said:
The solution is to order them from Amazon and they will figure out the size of the container and have it on your doorstep in two days.
I suppose that does ‘solve’ the problem, unless of course you already have the gumballs! And, from my perspective (which is the minority, I know), it robs you of the joy of figuring it out!
I’ve enjoyed the brief diversion from the slightly more serious columns that usually fill this space – I hope some of you have, as well. We’ll return to the task of examining educational issues of all shapes and sizes in the next column.
In the meantime, I’ve got space, so I can’t resist. Here’s another problem to solve, for those that wish to tackle it . . . e-mail submissions gladly accepted! A club with 10 members meets and each member shakes hands (once) with every other member. How many total handshakes occur? Happy Solving!
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