Random Problem Idea: The Perfect S’more
I was scrolling through Twitter a few days ago when I saw this tweet from John Scammell (@thescamdog):
It caught my eye because I’ve had the same problem before – all excited about these new, crazy marshmallows only to be disappointed with the results.
The Problem Idea(s)
You bought the giant marshmallows because you thought it would be cool; then you realized it “messes up the chocolate to marshmallow ratio.” So, assuming that the “perfect s’more” consists of two graham cracker halves, one normal marshmallow, and three “pieces” of chocolate (or 1/4 of a bar)…how do we fix it with these jumbo things?
At this point, there are so many different directions we could take this:
Option 1) Do we just cut the marshmallow? Where do we cut it?
Option 2) Without cutting it, can we add graham cracker and chocolate and find just the right number to make the ratios work out correctly? Taking the problem this direction makes it very similar to Dan Meyer’s “Nana’s Chocolate Milk” problem – which I’ve used in class.
Option 3) On the jumbo bag, there’s this gem:
They are doubling the graham cracker and doubling the chocolate. How close are they?
Option 4) Alright, why don’t we just send someone back to the store to get smaller marshmallows. Uh oh…they got the wrong kind again! Now how do we fix it?
Option 5) There is another consideration here: the perfect amount of marshmallow roasteyness (that’s a real word, right?). Dan Anderson (@dandersod) brought this up:
Now the relationship between surface area and volume comes into play. Assuming that the perfect roasteyness is a golden brown outer layer of the regular sized marshmallow, how can we get the same surface-area-to-volume ratio with the giant (or small) marshmallows?
We could also complicate things further by using my favorite s’more-making method: catch the outside on fire, blow it out, then take that charred layer off. I then eat it that way, but couldn’t you now roast what’s left? Alright, I think I’ve gone far enough with this.
I’ve said it before: I like messy problems, and this one fits the bill. There are certainly multiple – if not infinite – solutions to most of these questions. And, you get to eat the results (I’m full now). Enjoy.