document.write( "Question 231880: I'm not sure if this question goes here, but it's about finding the sub-problems and solving them so I hope I have the right section.
\n" ); document.write( "Alright so this problem confused me. Basically I was stuck with what the question was saying. I didn't know how to form the picture based off of what the word problem was say. So here is the question:\r
\n" ); document.write( "\n" ); document.write( "\"There are nine identical-looking coins. One of the coins is counterfeit and weighs less than the other coins. The only scale available is a balance scale, on which you can weigh any number of coins against each other. Using the scale only twice, figure out a way to find the counterfeit coin.\"\r
\n" ); document.write( "\n" ); document.write( "The last sentence to the question was where I was sort of stuck. I'm only allowed to use a scale twice so you would have to find out which coin was the counterfeit by piling on five coins on one end of the scale and then four on the other? I'm not quite sure how to solve this problem and if anyone has a suggestion I was would be very grateful for it! \r
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Algebra.Com's Answer #171498 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
Start by putting three coins on one side of the balance and three other coins on the other side. This leaves three coins unused. Now two things can happen:
  • The two sets of three coins on the balance are balanced. This means that the counterfeit coin is in the set of three unused coins. Then
    1. Remove the coins from the balance
    2. From the unused set of three coins, place one coin on each side. This leaves one coin still unused. Two things could happen:
      • The two coins balance. This means the one coin that was never put on the balance is the counterfeit.
      • The two coins don't balance. This means the coin on the lighter (higher) side is the counterfeit.
  • The coins do not balance. This means the counterfeit coin is in the set of three on the lighter (higher) side of the balance. Then:
    1. Remove the coins from the heavier (lower) side of the balance.
    2. Take one of the coins from the lighter side and set it aside.
    3. Take a second coin from the lighter side and move it to the other side of the balance. Now two things can happen:
      • The two coins balance. This means the counterfeit coin is the one you set aside.
      • The two coins do not balance. This means the counterfeit coin is the one on the lighter (higher) side of the balance
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