[ Weighings ]

Two weighings. There are 7 visually identical coins, among which 5 are genuine (all of the same weight) and 2 are counterfeit (of the same weight to each other, but lighter than the genuine ones). How can you use two weighings on a balance scale without weights to select 3 genuine coins?

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Number the coins $1,2, \ldots, 7$. The first weighing - on one side coins $1,2,3$, and on the other $-4,5,6$.

a) In the case of equality among the groups of coins 1, 2, 3 and 4, 5, 6, there is one fake coin, so 7 is genuine.

The second weighing of coins 1 and 2. If the scales are balanced, 1, 2, 7 are genuine. If 1 is heavier than the second, then 1, 3, 7 are genuine.

b) If there is no balance in the first weighing, then the heavier group of three coins consists of genuine coins.