What if I told you that for the price of one salad you could get 170 sandwiches? Any God-fearing man would tell you that's impossible, but I fear no God. There are many fools who spend all day arguing over whether a type of food is a sandwich. They've never considered how many sandwiches are in a food. Today, we're going to find out how many sandwiches are in a salad. I'm sure you have questions. A salad's not a sandwich is it? Wrong. Of course it is. For our salad, we'll take a very easily quantifiable one, the McDonald's Chicken Seas or Salad. We'll restrict ourselves to the most stringent square in this chart. Ingredient and structural purism. Looking at the ingredient rules, this salad easily passes. It has meat, cheese, lettuce, and condiments. Structurally, you wouldn't think this is a classic sandwich. Unless you had any brain cells at all. McDonald's Chicken Seas or Salad contains croutons, which are bread. Can you take grilled chicken, lettuce, some condiments, and put it together between two slices of bread? What do you call that? A sandwich. No time for questions. So, a salad. Idealized here is a three-dimensional sphere with all of its ingredients randomly and evenly distributed within. If there are at least two croutons in the salad and there is an even ingredient mush of all the salad ingredients between the two croutons, it will contain at least one sandwich. So, we can easily conclude a salad is or contains a sandwich. And don't even try to argue with me. I know a lot more about sandwiches than you do. And anyway, that's not even what we're here for. We're here to find out how many sandwiches is a salad. Any simple tone can tell you that generally there's more than two croutons in a salad. If there are three croutons, then not only does that create two two bread sandwiches, it creates one three bread sandwich. I'll add the big math. Four croutons in a salad would create three two bread sandwiches, two three bread sandwiches, and one four bread sandwich for a total of six sandwiches. Five croutons would create 10 and so on. So, if you didn't croup and pee your way through great school, you would know this is the triangular number sequence. Express by the formula n times n plus 1 over 2, where n is the number of croutons in a salad. Now, all we need is to find out how many croutons are in the average salad. OpenFoodFacts.org says there's 88 calories in the croutons that come in a McDonald's serving and eat this much.com says there's 35 calories in seven croutons. This means there are about 18 croutons in a McDonald's chicken Caesar salad. Expanding the triangular number sequence to n equals 18, we conclude that there are 153 sandwiches in a McDonald's chicken Caesar salad. This is the hyper-type. A perfect mathematical and culinary beauty. Now, a fool might stop here and be satisfied. 171 sandwiches, that's good enough for me. And I can't wait for them to starve with their meager sandwich rations. Going back to three croutons, if three croutons all link together, that creates three two bread sandwiches. Not just two, for higher order sandwiches, we postulate that a sandwich starts at any crouton and then ends at any other crouton. Considering the linking in between each crouton and the modalities, the higher order croutons, the number of possible sandwiches in our salad increases dramatically. Put down that pencil, you're already too far behind. I wrote an algorithm to calculate this because clearly I have to do all the work around here. We first construct a graph where each crouton is a node and the edges between them are the inter-sandwich ingredients. The algorithm performs a depth first search from each node and records each possible path from length one to the number of croutons and minus one. These are the possible sandwiches. We ensure that the path is a cyclic, meaning sandwiches don't reuse croutons. And at the end, we deduplicate sandwiches that are just the same sandwich but in reverse because counting them would be dishonorable. I ran the sandwich simulation algorithm for crouton numbers 1 through 10, getting the following results. I didn't run it for any higher number of croutons because running it for 18 croutons would have taken 226 years far beyond your attention span. So instead, I fit the results of 1 through 10 on an exponential regression plot, shown here. Plugging an 18 for the crouton count gives us approximately 12 trillion, 324 billion, 630 million, 629,453 total and possible sandwiches contained within a hyper sandwich that is the McDonald's chicken Caesar salad. That's 41 times the number of stars in our galaxy. You could give every human being alive 1,600 sandwiches and still have 200 billion sandwiches left over for your own greed and waste. If you could eat a sandwich every single second and never tire and the military never took you down for being that powerful, it would still take you 5,868 human lifetimes to eat all of those sandwiches. For $6 at McDonald's, why settle for one sandwich when you could have trillions?