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

Home > Logic > Weights and Scales
Twelve Coins and a Broken Scale (Posted on 2005-06-24) Difficulty: 4 of 5
You have 12 coins, six weigh 24 grams and six weigh 25 grams. You also have the broken scale from Five Weights and a Broken Scale.

Sort the 12 coins into the group of 24g coins and the group of 25g coins using that broken scale no more than 9 times.

See The Solution Submitted by Brian Smith    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Some thoughts | Comment 4 of 8 |
1) I note that if we balance 6 against 6, the fact that the scale is broken doesn't hurt. If the pans are of unequal weight, then there must be at least two more pounds on one side than the other. In other words, they balance if and only if there are 3 heavy and three light on each side.

2) Situations with 4 coins of 2 heavy and 2 light and 8 coins of 4 and 4 both present the same phenom as seen in (1). If we place all the coins on the scale, they will balance exactly when the weights are equal.

3) I can solve the 4 coin problem in 3 or less weighings. I think there is the possibility that I can reduce the 8 coin problem to the 4 coin problem in 3 moves. If we can reduce the 12 to the 8 in 3 moves, the puzzle is solved in 9 moves. At least that is where my thoughts have led me ...

  Posted by owl on 2005-06-30 04:06:21
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 (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

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