There are 10 similar coins, but 2 of them are fake. The fake ones are lighter than the real ones, but both have the same weight. You are give a balance scale, and you should determine which coins are fake. At least how many weighings do you need to find the fake coins?
Hmm. I think you'd need 3. Say you got the two fake ones in a row. You can't really go off of that since you have nothing to compare it to. So, you'd have to weigh a third to see if they were the real coins or the fake ones. Make sense?
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To determine the fake coins, you can follow this strategy:
1. Divide the 10 coins into three groups, with three coins in each group and one group of four.
2. Weigh two of the three groups of three coins against each other using the balance scale.
3. There are three possible outcomes:
a. If the two groups balance each other, then the fake coins are in the group of four.
b. If one group is lighter than the other, then the fake coins are in the lighter group.
c. If one group is heavier than the other, then the fake coins are in the heavier group.
4. Now, take the identified group (either the group of four or the lighter/heavier group) and select any two coins from it.
5. Weigh these two coins against each other on the balance scale.
6. Again, there are three possible outcomes:
a. If the two coins balance each other, then the remaining two coins in the group are the fake ones.
b. If one coin is lighter than the other, then the fake coin is the lighter one.
c. If one coin is heavier than the other, then the fake coin is the heavier one.
In total, you would need at least two weighings to determine which coins are fake using this strategy.