McMinion Math

Update:  Below is the contents of the email I received back from McDonald's.  At this point I'm assuming the puzzle is a misprint.  Even so, if you happen to see 96 triangles, I'd love to know the solution.
  
Thank you for contacting McDonald's and sharing your comments with us. We greatly appreciate this opportunity to address your concerns.

I'm sorry you were disappointed recently with the puzzle on our Minion themed Happy Meal box . At every McDonald's we strive to deliver 100-percent Total Customer Satisfaction. However, it appears as though we've failed to deliver these standards to you. I apologize that I do not have a solution to the puzzle to share with you.

Because you are a valued customer, I have shared your comments with our Quality Assurance team. They work closely with our suppliers to ensure that all of our products meet our quality standards. Your complete satisfaction is one of our top priorities.

Again, thank you for bringing this matter to our attention. We hope to have the opportunity of serving you again.


Well, I have to admit to being  Mc-stumped.  I ordered the tweens, McDonald's Happy Meals for lunch - sort of as a joke, since they outgrew Happy Meals some time ago.  (Okay, maybe it was because I wanted to hear what the Minion toys actually had to say).


Original Post:
Anyway, the puzzle at the top of this page was printed on the side of the box.  The kids took a couple of seconds counting triangles, and then turned back to their burgers and fries, content to trust the Minion (Phil? or Tom?) that the "pyramid" was made up of 96 triangles.

I wanted proof.  So, I copied the triangle, made up of 16 small triangles, 96 times to make a worksheet...

...to color in, so it would be easy to see that we weren't getting any duplicate triangles in our count.  I figured I'd work on it alone, find the solution, and then challenge the tweens to take an real stab at it.  The only problem was that I didn't find 96 triangles, I only found 27.

Of course, the Minion said there were 96 triangles in the "pyramid" not the "big triangle".  So, I tried again working with the shape as a four sided pyramid (or tetrahedron)...

...which would flatten out as in the picture below.  However, 27 triangles on each side, times 4 sides, equals 108 - not 96.

And, I briefly considered a five sided, square bottomed, pyramid, but that would take figuring the area of the square bottom divided by the area of the smallest triangles, and not only did that come out uneven, and greater than 96 (something like 101 triangles), it seemed a little convoluted for the target age of children normally ordering Happy Meals.

My children are content to believe it is probably supposed to be more of a "how many licks does it take to get to the center of a Tootsie Pop" sort of question - one meant to be enjoyed, and fudged, rather than solved.  Just to be sure, I emailed McDonald's and ask for a solution.

While I'm waiting, what do you think?  Is the pyramid made of 96 triangles, or not?