Clan x86
General Forums => Entertainment District => Topic started by: Sidoh on August 09, 2005, 02:36:19 am
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You are considering buying 12 gold coins that look alike but have been told that one of them is a heavy counterfeit. How can you find the heavy coin in three weightings on a balance scale?
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Weigh 4 of the coins on one side, and 4 on the other.
Two possible results from this:
- One side is heavier. If this happens, take those 4 coins and throw the other 8 away.
- They are equal in weight. If so, throw those 8 coins away.
Next you have four coins. Do the same thing, but in groups of 2s. Which ever side is heavier, take those two coins. Weigh them. Which ever one is heavier, you have your counterfeit. :)
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You're on the right track, but you're using more than three weighing sessions to determine the answer.
You're so close that if it was a snake it'd bite you!
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I used three...
Let me rephrase. Seperate them into groups of 4.
1. 4 v 4 (which ever side is heavier, take those 4 coins for #2 weighing, otherwise throw all of 'em out and take the remaining 4 for #2)
2. 2 v 2 (take the side that is heavier for #3)
3. 1 v 1
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I didn't read your answer right. That'll work. Nice job. This is the answer I have, which is why I thought yours was wrong:
1) Split the 12 in half, placing 6 on each side of the balance.
2) Remove the light 6. Then split the heavy 6 in half, placing 3 on each side of the balance.
3) Remove the light 3. Then set a random one of the heavy 3 aside and split the remaining 2 in half, placing 1 on each side of the balance. If the balance is not “balanced” you will know which is heavy. If it balances, you know that these two are both the same, thus the 1 placed aside was the heavy coin