90. There are three coins that look identical, two of which are genuine and of the same weight, and one is counterfeit and lighter than the genuine ones. Can the counterfeit coin be found with a single weighing on correct balance scales without weights?
$\triangle$ Let's number the coins as $1, 2, 3$. Place the first coin on the left pan of the balance, and the second coin on the right pan. There are two possible outcomes.

![](https://cdn.mathpix.com/cropped/2024_05_21_0aa0e6ac168e80891953g-039.jpg?height=574&width=1340&top_left_y=1809&top_left_x=358)

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The balance may be in equilibrium (Fig. 29). In this case, the first and second coins are genuine. Therefore, the third coin is the counterfeit one.

The balance may be out of equilibrium. In this case, the counterfeit coin is either the first or the second. Which one exactly? The lighter one.

Answer: it is possible.