ZS Associates: You Have 12 Coins And One Is Weight-Deformed. Use A Measuring Balance Just Three Times To Find The Right One.

Applicants for the Operations Associate position at ZS Associates, which is the brainchild of professor Andris A. Zoltners and Prabhakant Sinha, had to answer this grueling question to make the cut in March 2013.

This brainteaser is the harder variation of the typical ‘balance problem’ and the key here is to have a normal coin for reference.

As per a user from Math forum.org, you also solve this problem by distributing the 12 coins over the three measurements in such a way that no coin participates in the three measurements in the same way as any other coin. One of the possible distributions out of the many that fulfill this requirement is given below:

1, 2, 7, 10 against 3, 4, 6, 9

1, 3, 8, 11 against 2, 5, 6, 7

2, 3, 9, 12 against 1, 4, 5, 8

In the words of the user from Math forum.org, “If the measurements results disproportionately, then it can be seen from this distribution that coin 8 is lighter than the other coins. No other coin can explain the disproportionate outcome”, as reported by Business Insider.

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