Skip to main content

Can you solve the prisoner hat riddle? - Alex Gendler


51,069 Questions Answered

TEDEd Animation

Let’s Begin…

You and nine other individuals have been captured by super-intelligent alien overlords. The aliens think humans look quite tasty, but their civilization forbids eating highly logical and cooperative beings. Unfortunately, they’re not sure whether you qualify, so they decide to give you all a test. Can you solve this hat riddle? Alex Gendler shows how.

Additional Resources for you to Explore

The ‘prisoners and hats puzzle’ is a classic logic problem with many variants, some of which are described and summarized here. Like other puzzles where each player has information about the other players but not about themselves, they rely on inductive logic and the hierarchy of beliefs to figure out the other players’ thought processes to deduce the missing information.

Just remember – if you try to stump other people with this kind of puzzle, make sure you have the right answer yourself.

Love the challenge of this riddle? Take a look at these other puzzling lessons from TED-Ed!

Can you solve the bridge riddle? : Alex Gendler
The famously difficult green-eyed logic puzzle: Alex Gendler
How many ways can you arrange a deck of cards? Yannay Khaikin

Next Section »

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 Gendler
  • Director Outis
  • Composer Cem Misirlioglu
  • Narrator Addison Anderson

More from Math In Real Life