Super Safi’s Monday Morning Math Mayhem 03 – Narcissistic Number

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)


Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.

And what better way to start your week, then by discussing math Monday morning?

So let’s get started this week by continuing our discussion from last week about Perfect numbers and move on to Narcissistic numbers.

In the finale of Season 17, Marge and Homer Turn a Couple Play (Season 17, Episode 22), the Springfield Isotopes’s star first baseman Buck “Home Run King” Mitchell is having marital problems with his pop star wife Tabitha Vixx (voiced by This Is Us star Mandy Moore). So when he sees Homer and Marge kissing on the Jumbotron, he asks them for advice. But when Homer is later caught giving a neck massage to Tabitha, both couples break up again – and it is hard for Homer and Marge to give advice when they are not talking to each other themselves.

Towards the end of the episode, Tabitha appears on the Jumbotron asking the stadium crowd to guess the evening’s attendance. At first glance, it appears as though the three numbers are just random numbers. However, as we saw the last two weeks and will see today, these three numbers are more than just random numbers.


The third number on the Jumbotron is 8,208.

8,208 is a narcissistic number, which is a number that is the sum of its own digits each raised to the power of the number of digits.

8,208 is the 16th narcissistic number in the base 10 decimal system. The first ten are the ten single digit numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), as anything raised to the power 1 is itself. So all one-digit numbers are narcissistic numbers. The following 6 narcissistic numbers are:

153 = 13 + 53 + 33

370 = 33 + 73 + 03

371 = 33 + 73 + 13

407 = 43 + 03 + 73

1,634 = 14 + 64 + 34 + 44

8,208 = 84 + 24 + 04 + 84

In 1985, mathematician D. Winters proved there are only 88 narcissistic numbers in the base 10 decimal system. The 88th and largest narcissistic number has 39 digits and is 115,132,219,018,763,992,565,095,597,973,971,522,401.

115,132,219,018,763,992,565,095,597,973,971,522,401 = 139 + 139 + 539 + 139 + 339 + 239 + 239 + 139 + 939 + 039 + 139 + 839 + 739 + 639 + 339 + 939 + 939 + 239 + 539 + 639 + 539 + 039 + 939 + 539 + 539 + 939 + 739 + 939 + 739 + 339 + 939 + 739 + 139 + 539 + 239 + 239 + 439 + 039 + 139


Now that we know the secret behind the third number on the Jumbotron, one has to wonder why did the writers of the episode select these three numbers and why did I start this series of post with these three numbers? It could be argued the both Tabitha and I are perfect, in our prime, and narcissistic.  🙂

Be sure to come back next week when we talk about a different concept of math.

Do you remember this episode? Did you catch the number 8,208 on the Jumbotron? Did you recognize the number 8,208 as a narcissistic number? Are you familiar with Narcissistic numbers? Sound off in the comments below. You know we love hearing from you.

14 responses to “Super Safi’s Monday Morning Math Mayhem 03 – Narcissistic Number

  1. Another cool and math filled learning journey, keep them coming Safi, it’s the best part of monday mornings now!
    As math filled as The Simpsons is (are?) there’s even more cool math in music. Fibonacci sequence anyone?

  2. Dear Safi

    Once again, Sir, you have proven to be a ‘master of mathematics’ … I’m convinced that you truly could master the ‘mathematics of chaos’ ! 😀👍

    • OMG! I haven’t heard Killing Joke in forever! I stumbled onto this very album in the early-mid 90’s and just about wore out the CD.

  3. I was watching “Bart the Genious” and the had another math joke. Although this time it was a calculus joke (But what was written on the board isnt correct).
    Find the rate of change in y=r^3/3
    D'(y)=r*dr*r (har-dee-har-har)

  4. I liked your post, Math Genius Safi 🙂 I’m amazed at how brilliant these Simpsons writers are… I hope you keep catching these Easter eggs. I like thinking of the Simpson’s as an intelligent satire of society packed with smart allusions and references- it makes me feel better about binging hours of what my family calls only “cartoons” lol

  5. I did notice that the number 8.191 because it’s almost a power of 2 number.

  6. Ooooooh boy.
    Cheers for Mr. Winters for his proof, and to Super Safi for this post! You’re the best! 💪

  7. Dude….you’re, like, some kind of mathemagician…

  8. They do a daily task every day so the last task in kwik mart and when they are done they go back and repeat the same task

    • Count you blessings and make some donuts off it for a day or two. Tap the Thumbs up and let the cash XP splash out. Then tap on the friends button and go to the friends screen. After that come back to your Springfield. Your cash and XP will have been added to your total and if there is enough XP you will get a chance at donuts. Free your characters again and repeat.

      Once you are bored with this or when you need some of these characters for the next event store the building they are doing their task in and they will be freed permanently. Then go into storage and put the building back in your Springfield.

      This is the one glitch in the game that you can take advantage of instead of feeling like you are being taken advantage of. It happened to me just before this last mini-event. I made about a 100 million cash and around 800 donuts off it, then freed my characters to do the mini-event. I’d feel bad about this, but I’ve been on the crap end of so many glitches I figure there is nothing wrong with taking advantage of the one that worked out in my favor.

  9. My game is stuck all my characters repeat the same job

    • Not sure what you mean by this, how is it stuck? What are they repeating?

      I’m not playing your game so I need more information to go off of…

    • Are they stuck in the same building? If so, store the building and that *should* break the cycle. I’ve had it a couple times, as well as my sister who plays the game.

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