In the past two columns, we’ve had fun with an anecdote centered on Marilyn vos Savant and we’ve taken a related side trip into teaching/encouraging creativity in general. It’s now time to put a final bow on this whole 50Coins/Marilyn/problem-solving/creativity discussion and move on, don’t you think?
Perhaps you’ll recall that this whole adventure started with two almost-identical Marilyn vos Savant columns, some twenty years apart. The challenge given in those columns was to put 50 coins into 10 envelopes in such a way that each envelope had a different number of coins. Marilyn had claimed this isn’t possible and had loosely referred to solutions which put envelopes inside of others (as I had seen done years before) as ‘cheating’.
This led into educational discussions of ‘thinking outside the box’ and encouraging creativity among students while simultaneously providing them needed structure as they struggle to learn those hard-to-teach qualities.
Some final loose ends to get some closure:
1. Reader Responses. I had several fun and varied responses to the ‘Marilyn’ column. At least two of those focused on another push-the-boundary solution, namely allowing zero coins in an envelope. The justifications ranged from ‘0 is a number, too’ to wordier e-mails involving the meaning of ‘putting coins into envelopes’. These were fun, generated good discussions, and in general, from my perspective, exhibited praiseworthy thinking. But I was beginning to see how some of us with ‘creative’ solutions were perhaps a minor pain to Marilyn. More below.
2. The Educational Crux of the Matter. There’s more than semantics or ‘tricks’ going on here, from an educational angle. We’re dealing with the whole idea of ‘conditions’ (or parameters, or limits) in a problem. It’s a bugaboo that’s plagued students in math classes forever, but it’s more far-reaching than that.
It’s important for students to learn that all problems (math or otherwise) have conditions, and that they need to be noticed (or defined) and worked with. It doesn’t do any good to perfectly solve a minor algebra problem asking for ‘consecutive integers’, if in fact the problem called for ‘consecutive EVEN integers’!
Simultaneously, however, it’s also important for problem posers, be they teachers in schools, or engineers on the job, or branch managers in a business, to successfully make conditions/limitations clear. You can’t ask your business team to solve a problem for a client, and days later add ‘oh yeah, we only have $5000 to work with, and can’t use palm oil’!
Technically, of course, it’s that last circumstance which caused the trouble for Marilyn. She assumed (perhaps reasonably?) that her intended conditions ruled out things like nested envelopes or even empty ones. But of course, she didn’t state those restrictions.
3. In Partial Defense of Marilyn. Based on all this, I’m willing to offer some words in Marilyn’s defense. She writes a column designed to grab readers and hold interest. I know, first-hand, that columns have word limits, and words accumulate quickly. I can understand Marilyn thinking that she shouldn’t have to specify every last detail in a riddle, while she’s trying to grab readers, especially when wordy problems turn most solvers off. That’s not meant to be a free pass, but I can see her thinking.
4. Final Thoughts. Moving on, the overall educational issues remain, and teachers must deal with them daily. How do we encourage good solutions to problems of all kinds, while learning to work with – perhaps even define! – conditions and boundaries? And how do we encourage ongoing creativity while building the right amount of structure within which to create? They are not easy dilemmas.