One of the most commonly asked logical puzzle in interview of tech giants is the 8 coin and a “2 pan weighing scale” problem. Suppose you are given 8 coins and a 2 pan weighing scale which can compare the weights of two items on different sides. You are also told that one of the coins among the given 8 coins is fake and slightly heavier than the other 7 equal weights coins. Then you are required two find two things :
- The minimum number of weighings required.
- A method to find the fake coin with minimum number of weighings.
Can you tell the answer? If yes, then also provide a proper method to find the fake coin. Try yourself before seeing the answer.
Explanation : Most people think that the minimum number of weighings required is THREE. But the correct answer is TWO. Exactly, only two weighings are enough to find the fake coin among the 7 other coins.
Method to find the fake coin
Put three coins on each side of the weighing scale and keep the remaining two in hand. Now, two different cases may arise while solving this logical problem, so let’s analyze them one by one.
Case 1 : If the weighing scale doesn’t tilt on any side
This means the fake coin is one among the two other coins in our hand. So we can find the fake coin by weighing just two of them by keeping each one on opposite sides of the weighing scale.
Whichever side the scale tilts signals that the coin on that side is heavier and thus the fake coin. Hence, in only TWO weighings we found out the fake coin. Now let’s take a look at the other case.
Case 2: If the weighing scale does tilt on one side
As it can be seen below, if the weighing scale does tilt on one side in the first weighing of three coins on each side, that means one of the 3 coins present in the tilted side of the scale is the fake coin.
So we can take all the three coins from that side and weigh any two of them on each side and keep the remaining one coin in hand. If the scale tilts on any side then that side is the heavier side and thus contains the fake coin.
On the other hand, if it doesn’t tilt on any side that definitely means the remaining coin in your hand is the fake one. That means again in just TWO weighings we found out the fake coin.
Hence, minimum number of weighings required is only TWO.
Did you also get the same answer? Do tell us in the comment box and also share with your friends and family to test whether the Einstein within them can solve this logical puzzle.
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