8 Coins puzzle
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There are 8 identical coins.One of these coins is counterfeit and is known to be lighter than the genuine coins. What is the minimum number of weightings needed to identify the fake coin with a two-pan balance scale without weights?
Select two groups of three coins each from the given coins and put them on the opposite cups of the scale. If they weigh the same, the fake is among the remaining two coins, and weighing these two coins will identify the lighter fake. If the first weighing does not yield a balance, the lighter fake is among the three lighter coins. Take any two of them and put them on the opposite cups of the scale. If they weigh the same, it is the third coin in the lighter group that is fake; if they do not weigh the same, the lighter one is the fake.Thus we can identify the fake coin in only two weighings.
Here are some variants of this puzzle :
1.Minimum number of weighing required to find the fake coin when it is not known whether the fake coin is heavier or lighter.
2.Find lighter fake coin from a set of 12 identical coins.
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