White Castle Word Problem
We were all heading home from the western suburbs. It was after eight and while we were hungry, we weren’t really hungry. White Castle and their “fun sized” hamburgers seemed like the perfect choice. Unlike most fast food places, White Castle burgers aren’t wrapped in waxed paper, but are housed in small open-ended cardboard boxes. To cash in on the fortune cookie trend, White Castle prints pithy sayings on the bottoms of the boxes. Some have wise sayings, others have amusing riddles. Daniel grabbed the box out of my hand as I slid my third hamburger onto my five inch paper plate.
“If you stacked all the White Castle hamburgers sold, they would stretch to the moon and back with plenty left over for lunch,” he read aloud. “Is that true?” Meka shook her head. I wiped the corner of my mouth off with a napkin and pulled out a pen to do some quick calculations. A White Castle hamburger (typically known as a “slider”) is a square patty about two inches wide. It’s wider than it is tall, so that’s why I used that measurement.
“Fudging your data?” said Meka, our resident scientist. “Your results are going to be suspect at best –” I bought her silence with a pair of jalapeno cheeseburgers and got to work. With my standard slider measurement, there were 6 sliders to a foot and it would take 31,680 sliders to stretch a mile. While that’s a lot of burgers, I worked at Burger King when I was in high school. We would typically sell a thousand Whoppers a day; thirty thousand sliders didn’t seem like all that many in the grand scheme of things.
But the moon is pretty far away. Even at the so-called “supermoon” approach back in March, it was still 221,565 miles from Earth. I started writing across the narrow edge of the napkin, but had to switch to the other side and redo my math across the long edge instead; the numbers got big pretty quickly. I came up with 14,038,358,400 sliders required to reach the moon and back.
“You forgot the ones for lunch,” said Daniel.
Oops. I came up with 14,038,358,404 sliders.
Fourteen billion is a lot of sliders, but was it an impossible number? According to the vintage poster hanging above the booth, White Castle sold 50 million hamburgers in 1941. At that rate, White Castle wouldn’t reach the moon until the summer of 2061.
“You’re just assuming one long string of hamburgers,” said Meka. “For something that tall, you’d need more of a pyramid structure in order to get the necessary strength –” I slid my box of fries across the table and she withdrew her protest.
Back in the olden days, White Castle’s motto was “Buy ‘em by the Sack”. Nowadays, you can pick up hamburgers by the case or even the crate. It took White Castle forty years to sell their first billion hamburgers, but only seven years to sell their second billion. If their sales stayed at 1968 levels, White Castle burgers would have reached the moon by now, but would have barely begun the journey back.
I felt it was a reasonable assumption their business has continued to grow since the sixties. The two White Castles I visit most frequently were built since I was born. And you don’t have to go to White Castle to get sliders anymore. Frozen White Castle hamburgers are available in the freezer section at Wal Mart (and if you stacked all the Wal Marts from here to the moon… well, that’s another story). I figured their sales had to average 96% better year-over-year since 1968 in order to get the slider trail all the way back to terra firma. White Castle is a privately owned company. I couldn’t find any hard data on their website. However, they did mention building a plant in 1992 that could make 200,000 hamburgers a day. That would have added 51% to their annual burger production capabilities, or more than 43,000 slider miles since the day it opened.
While my final numbers were incomplete, I felt I could say with some confidence to Daniel that – yes, if you stacked all the White Castle hamburgers sold, it was possible they would reach the moon and back.
“Nope, you’re wrong,” said Daniel.
“I’m wrong?” I repeated. “What do you mean?”
“It’s a trick question,” said Daniel with a laugh. “If you stacked all the hamburgers sold, it wouldn’t be a tall pile at all. They’ve all been eaten!”
“He has a point, you know,” said Meka. I gave her the last half of my shake before she could say “I told you so” and threw out my napkin in the trash.