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

 One of Sixteen (Posted on 2015-12-29)
I have two sets of 8 coins. In one set the coins weigh 30g each, in the other set the coins weigh 31g each.
Unfortunately they got mixed together in one big pile of 16 coins. I want to identify one coin. It can be from either set.

(Easy) Using a balance scale, identify a coin in four weighings.

(Hard) Identify a coin in just three weighings.

 See The Solution Submitted by Brian Smith Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): What's the problem? (and a spoiler) | Comment 8 of 12 |
(In reply to re: What's the problem? (and a spoiler) by Brian Smith)

If it is not possible to identify a specific coin in just three weighings, then that explains why I did not come up with a method.  That, plus the fact that I only tried to do it in my head.

As expected, the easy method has fewer expected weighings (slightly more than half) when compared to the hard method.  The hard method always takes 3 weighings.

My calculations of the easy method:
1 weighing   ~53.33% of the time
2 weighings ~38.97%
3 weighings ~ 7.68%
4 weighings ~ 0.02%
expected weighings: ~1.54

Edited on January 1, 2016, 10:36 am
 Posted by Steve Herman on 2016-01-01 10:34:53

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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information