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.

(In reply to re: One weigh or another by ThoughtProvoker)

With ammendments due to ThoughtProvoker finding obvious flaws in my first attempt.

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, 4 or 5 Heavy coins on the heavy side, and 0, 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 coin. (4 weighings)
 Misbalanced: There are 2 Heavy coins in the heavy stack of 4. (Step 3A)

Step 2B:
 Split the 8 coins containing the 3, 4, or 5 heavy coins and weigh 4 versus 4.
Results:
 Balanced: Possible - There are 2 Heavy coins in each stack of 4. (Step 3A)
 Misbalanced: The heavy side has 2, 3 or 4 Heavy coins. (Step 3B)

Step 3A:
 Weigh 2 of the coins in the heavy stack 1 versus 1
Results:
 Balanced: Both are Heavy or both are light. (Step 4A)
 Misbalanced: The heavy side is a Heavy coin.  (Step 4B)

Step 3B:
 Weigh 2 of the coins in the heavy stack 1 versus 1
Results:
 Balanced: Both are Heavy or both are light. (Step 4A)
 Misbalanced: The heavy side is a Heavy coin. (Step 4B) 

Step 4A:
 Weigh the two coins that balanced in Step 3 against the 2 that were not weighed.
Results:
 Balanced: All 4 are Heavy (4 weighings)
 Misbalanced: The heavy side contains 2 Heavy coins. (4 weighings)

Step 4B:
 Weigh the other two coins.
Results:
 Balanced: Both are Heavy (4 weighings)
 Misbalanced: The Heavy side contains the 2nd Heavy coin. (4 weighings)

Edited on November 9, 2005, 2:16 pm

Posted by Leming on 2005-11-09 14:14:12