All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Logic
3 Hats (Posted on 2023-12-19) Difficulty: 3 of 5
The wizard has placed hats on the heads of three logicians. He explains that he has written a positive integer on each hat, and that one of the numbers is the sum of the other two numbers. Each person can see only the numbers on the other people's hats.

The wizard offers a prize to the first person who can logically determine the number. The wizard starts questioning the logicians in order, starting over again if nobody can state the number with certainty. No guessing is allowed.

(1) Prove that someone will always determine the number.
(2) Prove that will always be the person with the highest number.
(3) Find an explicit formula for the number of rounds needed until the number is found.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( You must be logged in to post comments.)
  Subject Author Date
No SubjectK Sengupta2024-02-07 00:31:16
fffThebausi2024-02-06 12:49:36
Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information