You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
First weigh three coins against three others. If the weights are equal, weigh the remaining two against each other. The heavier one is the counterfeit. If one of the groups of three is heavier, weigh two of those coins against each other. If one is heavier, it’s the counterfeit. If they’re equal weight, the third coin is the counterfeit.
3 Comments on "Which Coin is Counterfeit?"
Camden says
August 13, 2015 @ 23:18
(SPOILER ALERT) That would be luck, what would happen if 3 of the coins weighed more than the other 3
Jerome says
August 12, 2016 @ 04:05
@Camden No luck is needed. 8 coins, 7 are real and 1 is fake. Fake coin weighs more. We will give the Real coins a weight value of 1 and the fake a weight value of 2.
Take any six coins of the eight coins, put 3 on the left side and three on the right side.
If both sides equal 3, remove all six and weigh the remaining two. One of the two will be the fake coin and the second weighing will reveal it.
If in the first weighing one side equals 4, set aside the side that weighed less, they are all legal as are the two that weren’t weighed, take all 3 from the heavier side, place any 1 of them on the left, a different 1 of those 3 on the right, if they weigh the same, the one you are still holding is the counterfeit one, if one weighs more than the other, it is the counterfeit one… simple logic, no luck needed.
Adam says
December 14, 2016 @ 23:32
Yeah this is not luck. This is process of elimination. Unfortunately their explanation is bad… Eliminate 1 of the 7 and set it aside. Weigh the 3v3. If they’re equal, then the one you set aside is counterfeit.
If they’re not equal, then discard the lighter side. With the remaining 3 coins, take one coin and set it aside. Weigh 1v1. If they’re equal then the one you set aside is counterfeit. If they’re not equal then the heavier one is counterfeit.
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