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

Home > Logic
The Logician's Birthday (Posted on 2004-11-17) Difficulty: 2 of 5

A logician invites 6 of his logician friends to help him celebrate his birthday. Each of the 6 guests is wearing a hat which is either red, yellow, or blue, and the logician host informs them all that there is at least 1 of each color. After they eat the cake, the host stands up and exclaims there is a special party prize for the first person who can deduce what color hat is on their head. The party guests all looked around the room at each other but no one claimed the prize immediately. Suddenly all 6 guests stood up and correctly identify what color hat was on their head.

What were the colors of their hats and how did they know?

See The Solution Submitted by Erik O.    
Rating: 3.5417 (24 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution | Comment 50 of 75 |
Alright, so if no logician says anything, then none of them sees 0 of one color (3 of one and 2 of another, 4 of one, and 1 of another). This has to be the case with all of them, or one of them would have realized what color was on his head. Therefore, the 4:1:1 situation cannot exist, or else two people would immediately know. Moreover, the 3:2:1 situation cannot exist, or one person would immediately know. Thus, there must be two of each color.
  Posted by Yom on 2004-12-15 00:32:16
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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