If you haven't done any of the other
coin problems, then you might want to go back and try those now, this one is very difficult, even if you have figured out the other ones.
This time, as the title implies, there are 39 coins, and one is fake. You have a balance scale, which can be used 4 times.
How would you find the fake coin?
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Submitted by Jonathan Waltz
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Rating: 4.1250 (8 votes)
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Solution:
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First, as always, split the coins into three seperate groups. lets label the three groups as A, B, and C. First weigh all of A vs. all of B. If they are equal, this is the easy situation. Then, with three weighings left, you have 13 coins. So take nine coins from C, and weigh it against nine coins from A or B, which we know are not fake.
Then, which ever way the dcoins from C go, up or down, that is what the fake coin is. I will go back to the equal case later. So if the fake coin is in the 9 from C, and is heavier, then take three C against three C, both from the nine we just weighed. If they are equal, it is in the third group, and if one side goes the same way as it did in the second weighing, then it is in that group.
Then weigh one vs one from whichever group was like the second weighing or the third group of three from the third weighing. |
