Twelve coins

Logic Level 2

You have 12 identical-looking coins, one of which is fake - either heavier or lighter than the rest (it is not known). The only scale you have to use is a simple balance and no measure weights.

How many measurements do you need to perform to find the fake coin?

2 6 4 3 5

2 solutions

Pranav Rao
Nov 18, 2015

I had once seen this question so i remembered the answer. But I don't know the method correctly. Please correct my solution. I don't know if it's correct. We divide 12 coins in 3 groups of 4. Now we take two groups and put them in the weighing pan. Case 1: We get that both the pans are balanced. Then the third group surely contains the fake coin. We now remove the 8 coins present in the pan and put 2 coins of the third group into the pans. Case 1.1 If they balance then remove only one of them and put another of that same group. If again they balance then the remaining coin is fake. Or else the third coin is fake. Case 1.2 If they didn't balance then remove one of the coins and put another coin. If they balance then the removed coin is fake. If they don't then the coin which was not removed first is fake. I couldn't work further properly. Please help

Praful Jain
Oct 4, 2015

We can just have 6 coins in both the hands and we can keep dropping one coin from each hand at a time and when we find an imbalance we can take back the both the coin which caused the imbalance and measure each of them separately with the real coins which were balancing while dropping . So the one while dropping and the two other measures for find which of the two are fake. Thus the answer is 3

Each time you drop coins the scale is performing a new measure to determine should it stay in balance or not. So with your "method" you will actually have 7 measurements.

Krassimir Kondarev - 5 years, 4 months ago

Twelve coins

2 solutions

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