CONUNDRUM | August 2023 | Counterfeit

You have 9 gold coins but one of the coins is counterfeit and weighs slightly less than the others.

You have access to a scale but it costs money every time you use it.

What’s the least number of times you can use the scale to find the counterfeit coin ?

The most efficient way to handle this problem is to separate the coins into three groups of three.

Step 1: You can determine which of those groups contains the counterfeit coin by weighing two of those three groups of coins. If the scale is uneven then the lighter group of three contains the suspect coin. If the scale is even then the unweighed group contains the suspect coin. You have now narrowed the possibilities down to just three coins.

Step 2: Choose two of the coins to weigh. If one proves to be lighter, you have the counterfeit coin! If they are the same weight then the unweighed coin is the counterfeit coin.

SOLUTION: You can determine the counterfeit coin using the scale just 2 times.