A set of 17 coins contains five 35g coins and twelve 30g coins. Using a balance scale at most four times find at least two of the 35g coins.

Step 1:
 Take 16 coins and weigh them against each other. 8 versus 8 with 1 coin on the side
Results:
 Balanced: There are 2 Heavy coins in each stack and 1 Heavy coin on the side. One Heavy coin found.(Step 2A)
 Misbalanced: There are 3 Heavy coins on the heavy side, and either 1 or 2 on the light side. (Step 2B)

Step 2A:
 Split the 8 coins containing 2 Heavy coins and weigh 4 versus 4.
Results:
 Balanced: There is one Heavy coin in each stack of 4. Lable one stack of coins ABCD. Weigh A vs B and C vs D. The one coin of ABCD that is Heavy is the second Heavy coin. (4 weighings)
 Misbalanced: There are 2 Heavy coins in the heavy stack of 4. (Step 3)

Step 2B:
 Split the 8 coins containing the 3 heavy coins and weigh 4 versus 4.
Results:
 Balanced: Not possible (odd number of heavy coins)
 Misbalanced: The heavy side has 2 Heavy coins. (Step 3)

Step 3:
 Weigh 2 of the coins in the heavy stack 1 versus 1
Results:
 Balanced: Both are Heavy or both are light. Weigh both against the other two to find 2 Heavy coins. (4 weighings)
 Misbalanced: The heavy side is a Heavy coin.  Weigh the other two coins to find a second Heavy coin. (4 weighings)

Posted by Leming on 2005-11-09 13:14:02