PCMI Post 5: Ketchup Math

Today I was sitting at a lunch table of 8 people. We somehow got on the topic of grilled cheese. You may know that I’m a vegetarian, but I think a more accurate term for me is a queso-carbotarian because I love cheese and carbs together. So I’m a real fan of grilled cheese. And growing up, when my mom made me grilled cheese made with American singles inbetween two pieces of white bread, she always served it with ketchup.

I thought that was normal. That everyone ate their grilled cheese with ketchup. I mean, yes, you can dip it in tomato soup. And you can dip it in ketchup. And maybe, just maybe, you could eat it by itself. And everyone is going to have their own opinions about what’s best.

What I wasn’t prepared for is that no one at my table of 8 had ever even heard of eating grilled cheese by dipping it in ketchup. I’m not talking about not liking it, or not doing it. They hadn’t ever heard of anyone doing it.

While I was totally certain that everyone at least must have heard of it, and I’d have guessed that most people did it except for just a few. So that fact that of the 8 of us, I was the only one who heard of it led me to believe one of two things:

I was at a very weird table that was not representative of the rest of the American/Canadian population, or that I grew up with this very unique cultural tradition of eating grilled cheese with ketchup — and that was something my mom invented or maybe it’s an Indian thing — but not widely known.

Of course I decided to double down, and claim that my lunch table was TOTALLY WEIRD and that they were the outlier — and more people had to have heard of ketchup and grilled cheese. So I get up to ask another group of around 6 teachers at a neighboring table. And what happened? They all said the combination was new to them. (And later in the day, I ran into author and mathematician Jordan Ellenberg who also said he had never heard of the combination, but understood why it would likely be good.)

Now at this point I feel like my world is crashing down. Something that I thought was so commonplace in the world wasn’t. My sense of reality was being called into question. And instead of accepting it, I double down again. Everyone at my table is interested in this — maybe because I feel totally bonkers and can’t let it go. So I put up a poll on twitter, set for 3 hours, which asks the question below and gets these results from 41 people:

Another person at the table did a similar poll on facebook, and got 25-ish results, and they said about 2/3rds of the respondants said “yes.”

What to conclude?

I figure I can think of it like this. I want to know if my two lunch tables of 14 people (where 13 hadn’t heard of eating grilled cheese with ketchup) WEIRD or if I am WEIRD for doing this. I am using the two polls to be representative of the true population… and to make things easier, I’d even argue there’s some error and so maybe I could even say about 50% of the world has heard of eating grilled cheese with ketchup, and 50% of the world hasn’t heard of eating grilled cheese with ketchup.

Then in a group of 14, for only 1 person to have heard of eating grilled cheese with ketchup IS TOTALLY WEIRD. It’s like flipping a coin 14 times, and only one time you get heads (and 13 times you get tails). Hello binomial distribution.


But… I still don’t know… tonight we had an event at 7pm where a bunch of people showed up. Maybe there were 20 people in the room and the ketchup question was asked and I think only 3 or 4 people had heard of eating grilled cheese with ketchup. So I’m not sure what’s up.

Regardless, I loved this random fun math question that popped up as I was having a mental breakdown involving the internal reality of my world. And that others got into it.

P.S. For another fun condiment digression, our lunch table then started talking about the tiktok trend where people put yellow mustard on oreos and claimed it was so so good. Even Lizzo tried it. Randomly, there was a box of oreos on a table in our classroom, and we had mustard packets from lunch . So later in the day, another person and I tried the combination. I have a screenshot of the video someone took where I tried it. It wasn’t awful at all, but it wasn’t like enhancing the flavor either for me. It was just kinda fine.



  1. I never heard of doing this before. At the same time, this is basically just a different format for pizza, right?

    I have always loved how you turn a quirky conversation topic into an adventure!

    – Elizabeth (@cheesemonkeysf)

  2. Math can be pretty amazing, as I learned from this blog post. I never knew there were so many cool details and facts about math! This website is a great resource for learning more about math, with plenty of information and tutorials. I also found some other sites , blogs and and online courses that are worth checking out for anyone who wants to learn more about mathematics. Thanks for sharing this information!

  3. If you had asked me two months ago when this was posted, I would have been in the “never heard of grilled cheese with ketchup” crowd, and the same for tomato soup. But I have frequently had grilled cheese with salsa. However, this is the second time now that I’ve encountered ketchup (and tomato soup) mentioned as a condiment for grilled cheese sandwiches. So now I have to wonder if quesadillas with ketchup is a thing, because like grilled cheese sandwiches, quesadillas with salsa rocks.

    Some food for thought: it could be that neither you nor your tables were weird! Your weirdnalysis implicitly assumes your tables have an unbiased sampling of the same population that is represented by the twitter polls. My bet would be that certain regions are nearly saturated with “never heard of” people, while other regions are nearly saturated with “have heard of” people, with relatively few regions where the two groups significantly intermingle. If so, the twitter polls probably collected data from several regional clumps.

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