How Many Pancakes Can Fit into a Mailbox?

Jason Hall

Published On: May 14, 2020

Categories: T SQL, Community 0

The title of this blog post is weird, but bear with me while I add some context.

May is National Military Appreciation Month. This got me thinking about some special moments from my time in the US Army. We spent a lot of time on the road, and passing the time while riding in trucks and on buses could get "interesting" to say the least.

One of my best friends was Donald Hammock. He was, and is, one of the best people you could ever meet. He would give you the shirt off his back, snatch the shirt off the person next to him for you, and have all three of you laughing the whole time. I found an old picture with both of us in it.

82nd Airborne "All American Chorus" - Circa 199582nd Airborne "All American Chorus" - Circa 1995
 

One very odd game we often played on the road was seeing who could ask the most random question. The questions were never really answered. The point was to laugh at a dumb question and try to think of an even dumber question.

For some reason, one of those nutty questions has stuck with me ever since. We were driving to who knows where and Donald threw out the question, "How many pancakes can fit into a mailbox?" It's a question that just begs more questions. Why? Do they have syrup on them? How big is the mailbox? Can I just eat the pancakes instead?

So, how many pancakes can fit into a mailbox? In honor of National Military Appreciation Month, I'm finally going to answer this question using questionable math and T-SQL.

Rules

We can't answer this question without putting some rules in place because there are several "it depends" elements. Setting some ground rules will eliminate most of the ambiguity of the question.

  1. We'll use the standard mailbox size, as depicted here.
  2. We'll assume the mailbox is rectangular-ish with a curved top.
  3. We'll use the dimensions of a regular IHOP pancake, as discussed here.
  4. We won't fold or otherwise "squish" our pancakes.
  5. We'll assume the pancakes do not have syrup or butter on them.
  6. The pancakes might, of course, be stacked. Pancakes that don't stack aren't pancakes at all!

Parameters

We can get close to an answer to the question using the volumes of the mailbox and a pancake. We won't be able to figure those out without the following measurements:

  • Dimensions of a standard mailbox = m
    • *Base Height: 6 inches
    • *Top Height: 2.75 inches
    • Width: 6.25 inches
    • Length: 18.75 inches
  • Dimensions of an average IHOP pancake = p
    • Height: 0.4 inches
    • Diameter: 5.5 inches

*Estimated using a known total height of 8.75 inches.

We'll need the volume of the mailbox first, which is slightly interesting because of the curved top. I suck at math, so I'm telling you now that the Internet is helping me cheat on these calculations.

Next, we'll need to figure out the volume of a pancake, which is really a cylinder as opposed to a circle.

Now, I know this approach is the simplest possible way to get our answer. I also know that a person who actually does math would come up with something more interesting and valid here, so I invite anyone interested to do so in the comments. I think my basic approach gets us into decent seats at the ballpark, so I'm going to use simple division to determine how many @p can fit into @m.

Here are my results:

How many pancakes can fit into a mailbox: resultsHow Many Pancakes Can Fit into a Mailbox: Results
 

Finally, after many years, I have somewhat of an answer to this ridiculous question. According to my calculations, you can probably fit somewhere in the vicinity of 120 pancakes into a mailbox.

Donald Hammock, if you're out there reading this blog post for some reason, this is your fault!

 

Jason has worked in technology for over 20 years. He joined SentryOne in 2006 having held positions in network administration, database administration, and software engineering. During his tenure at SentryOne, Jason has served as senior software developer and founded both Client Services and Product Management. His diverse background with relevant technologies made him the perfect choice to build out both of these functions. As SentryOne experienced explosive growth, Jason returned to lead SentryOne Client Services, where he ensures that SentryOne customers receive the best possible end to end experience in the ever-changing world of database performance and productivity.


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