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Can you solve the rogue submarine riddle? Difficulty level: Master - Alex Rosenthal

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  • 277 Questions Answered
  • TEDEd Animation

Let’s Begin…

Smuggling yourself aboard the rogue submarine was the easy part. Hacking into the nuclear missile launch override — a little harder. And you’ve got a problem: you don’t have the override code. You know you need the same numbers that were used to authorize the launch, but one wrong answer will lock you out. Can you figure out what numbers to enter to stop nuclear war? Alex Rosenthal shows how.

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About TED-Ed Animations

TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here »

Meet The Creators

  • Educator Alex Rosenthal
  • Director Igor Coric
  • Narrator Addison Anderson
  • Storyboard Artist Igor Coric
  • Animator Igor Coric
  • Compositor Igor Coric
  • Art Director Igor Coric
  • Composer Cem Misirlioglu, Amit Peled
  • Sound Designer Cem Misirlioglu
  • Director of Production Gerta Xhelo
  • Editorial Director Alex Rosenthal
  • Producer Bethany Cutmore-Scott
  • Production Coordinator Abdallah Ewis
  • Puzzle Author Brian Chen, Jon Schneider
  • See more creators
Additional Resources for you to Explore
This riddle was adapted with permission (and help from) Brian Chen and Jon Schneider, who created the original as a part of their fantastic puzzle Ignorance from the 2021 MIT Mystery Hunt. If you're looking for more puzzles like this, that’s the perfect place to go. Whether (the third puzzle from the bottom there) is a personal favorite, on account of the exchange:

“Bernard: I know whether you know whether I know whether you know whether I know whether you know whether I know whether you know whether I know whether you know whether I know whether you know whether I know whether you know my number.Albert: I don’t know your number."

But be warned…these are really difficult!

Generally speaking, logic puzzles attempt to bridge the gap between often complicated theorems and fictional scenarios to engage a variety of thinkers in deep mathematical and philosophical inquiry. Logician, mathematician, and creator of Alice’s Adventures in Wonderland, Lewis Carroll, introduced these riddles to the general public in 1887 in his book The Game of Logic. For a brief history of logic puzzles and several famous problems to work through yourself, check out this article from Mathigon. For a more in-depth exposition on mathematical logic, see this entry in the Stanford Encyclopedia of Philosophy, which includes a bibliography for further reading.

The sum and product puzzle presented in this “Submarine Riddle” is a type of ignorance problem (also known as a dynamic epistemic logic problem) in which one or more parties makes an ambiguous statement that reveals key information to the reader, allowing them to eliminate possible answers and arrive at a solution. In 2015, another example of an ignorance problem went viral after TV host Kenneth Kong posted a photo of the logic puzzle on social media. Created by Dr. Joseph Yeo Boon Wooi of Singapore's National Institute of Education, Cheryl’s Birthday Puzzle quickly swept the internet, with more than 5,000 shares in a matter of days. Several follow-up puzzles appeared soon after the original “Cheryl’s Birthday” riddle, including “Cheryl’s Age” and “Denise's Revenge.”

Want more riddles? TED-Ed has lots of fun and challenging brainteasers in our Riddles Series.

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Create and share a new lesson based on this one.

About TED-Ed Animations

TED-Ed Animations feature the words and ideas of educators brought to life by professional animators. Are you an educator or animator interested in creating a TED-Ed Animation? Nominate yourself here »

Meet The Creators

  • Educator Alex Rosenthal
  • Director Igor Coric
  • Narrator Addison Anderson
  • Storyboard Artist Igor Coric
  • Animator Igor Coric
  • Compositor Igor Coric
  • Art Director Igor Coric
  • Composer Cem Misirlioglu, Amit Peled
  • Sound Designer Cem Misirlioglu
  • Director of Production Gerta Xhelo
  • Editorial Director Alex Rosenthal
  • Producer Bethany Cutmore-Scott
  • Production Coordinator Abdallah Ewis
  • Puzzle Author Brian Chen, Jon Schneider
  • See more creators