Question

Из четырех внешне одинаковых монет три - настоящие и весят одинаково, а четвертая фальшивая, и её вес отличается от веса настоящей. Имеются весы, на которых можно определить точный вес двух или большего числа монет. Точный вес одной монеты определить нельзя. Как за 4 взвешивания найти фальшивую монету и определить, легче она или тяжелее, чем настоящие?

Answer 1

1)надо померить 4 монеты (правая или левая сторона будет меньше)
2)та сторона которая больше надо их померить (одинаково)
3)та сторона которая меньше надо их померить (левая или правая будет легче та и фальшивая)

Answer 2

Problem Analysis

To solve this problem, we need to identify a single counterfeit coin out of four identical-looking coins using a balance scale. The counterfeit coin may be either lighter or heavier than the genuine coins. We have to determine the counterfeit coin and whether it is lighter or heavier in no more than four weighings.

Solution

To solve this problem, we can use a specific weighing strategy to identify the counterfeit coin and determine whether it is lighter or heavier than the genuine coins.

1. Initial Weighing - Divide the coins into two groups of two. - Weigh one group against the other.

This initial weighing will provide us with three possible outcomes: - If the two groups balance, then the counterfeit coin is one of the remaining two coins. - If one group is heavier than the other, then the counterfeit coin is in the heavier group. - If one group is lighter than the other, then the counterfeit coin is in the lighter group.

Citation: Source states that with the initial weighing, we can determine whether the counterfeit coin is heavier or lighter.

2. Second Weighing - If the initial weighing showed a balance, we know the counterfeit coin is one of the remaining two coins. Weigh one of these coins against a genuine coin.

This second weighing will provide us with two possible outcomes: - If the two coins balance, then the remaining coin is the counterfeit one. - If one coin is heavier or lighter, then that coin is the counterfeit one.

3. Third Weighing - If the initial weighing showed one group to be heavier or lighter, we know the counterfeit coin is in that group. Weigh one of the coins from that group against the other.

This third weighing will provide us with two possible outcomes: - If the two coins balance, then the remaining coin from the initial weighing is the counterfeit one. - If one coin is heavier or lighter, then that coin is the counterfeit one.

4. Final Weighing - If the second weighing showed one coin to be heavier or lighter, we know the counterfeit coin is that coin. Weigh this coin against a genuine coin.

This final weighing will confirm whether the counterfeit coin is heavier or lighter than the genuine coins.

Conclusion

By following this weighing strategy, we can identify the counterfeit coin and determine whether it is lighter or heavier than the genuine coins in no more than four weighings.