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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)

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Solution Solution (by Visual Basic program) | Comment 7 of 8 |
My Visual Basic program produced this solution:
   
Physically label each of the coins with the letters A thru L. Then perform the following nine weighings of 6 coins against 6 coins on the broken scale:
 
Weighing 1: A C H I K L on the left, B D E F G J  on the right.
Weighing 2: A C E F G K on the left,  B D H I J L on the right.
Weighing 3: C E G H K L on the left, A B D F I J on the right.
Weighing 4: A B C D G H  on the left, E F I J K L on the right.
Weighing 5: A F G H I K  on the left, B C D E J L on the right.
Weighing 6: C D G I J K  on the left, A B E F H L on the right.
Weighing 7: B C F G I L on the left, A D E H J K on the right.
Weighing 8: A D F G K L on the left, B C E H I J on the right.
Weighing 9: A B G J K L on the left, C D E F H I on the right.
 
The ordered results of the nine weighings produce a unique
identifier for the 12 coins, so you will know which are the 24g and
which the 25g coins, by referring to a manual list of possible ordered result sets. There are exactly 924 sets of ordered results for the nine weighings, each uniquely corresponding to one of the 924 possible ways that the coins A thu L could consist of six 24g and six 25g coins.
 
For example, if the results are:
 
  Weighing 1: Equal
  Weighing 2: Equal
  Weighing 3: Right side heavier
  Weighing 4: Equal
  Weighing 5: Left side heavier
  Weighing 6: Left side heavier
  Weighing 7: Right side heavier
  Weighing 8: Left side heavier
  Weighing 9: Left side heavier
 
Then {A,D,G,I,J,K} weigh 24g, and {B,C,E,F,H,L} weigh 25g
 
 

Edited on October 20, 2007, 6:49 pm
  Posted by Penny on 2005-07-03 19:19:24

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