The Seemingly Impossible Tree Counting Escape Logic Puzzle

Excited for the August 21 eclipse? Visit our Eclipse 2017 page to explore the science, history, and myths of the event. The Curiosity team will be viewing the eclipse alongside NASA in Carbondale, Illinois. Follow us on Facebook for live videos, trivia, and interviews on the big day.

Alice and Bob are imprisoned. Alice can see 12 trees and Bob can see 8 trees. Together, they can see all the trees, but no tree is seen by them both. Neither knows how many trees the other sees, and they can't communicate with each other. Every day, Alice is asked, "Are there 18 or 20 trees?" If she passes, then Bob is asked the same thing. If he passes, the process repeats the next day. If either guesses the total number of trees incorrectly, they're both imprisoned forever. If either guesses correctly, they're set free. They both know these rules. Can they escape by giving an answer with certainty? Or is the best chance they have at escaping a random guess? Watch the videos to get the answer, and explore more challenging puzzles.

If you liked this you'll love our podcast! Check it out on iTunes, Stitcher, Google Play Music, SoundCloud, search 'curiosity' on your favorite podcast app or add the RSS Feed URL.