Question

Среди 9 одинаковых по виду монет надо найти одну фальшивую (более лёгкую).Назовите наименьшее число взвешиваний,которыми моряки могут найти эту монету,пользуясь чашечными весами без гирь.

Answer 1

2 взвешивания:
1)взвесить по 3 монеты, какая кучка оегче, в той фальш., если они одинаковы, фальш. в третьей кучке
2)взвесить по одной монете из легкой кучке, по тому же принципу найти фальшивую монету

Answer 2

Finding the Fake Coin

To find the fake coin among 9 identical-looking coins, we can use a balance scale without weights. The goal is to determine which coin is lighter than the rest. We need to find the minimum number of weighings required to identify the fake coin.

Solution

To solve this problem, we can use a divide-and-conquer strategy. Here's how it works:

1. Divide the 9 coins into three groups of 3 coins each: A, B, and C. 2. Weigh group A against group B using the balance scale: - If group A and group B balance, then the fake coin is in group C. - If group A is lighter than group B, then the fake coin is in group A. - If group A is heavier than group B, then the fake coin is in group B.

Now, let's consider the possible scenarios:

Scenario 1: Group A and Group B Balance

If group A and group B balance, it means the fake coin is in group C. We can proceed as follows:

3. Take any two coins from group C and weigh them against each other: - If they balance, the remaining coin in group C is the fake coin. - If one of the coins is lighter, that coin is the fake coin.

In this scenario, we need a total of 2 weighings to find the fake coin.

Scenario 2: Group A is Lighter than Group B

If group A is lighter than group B, it means the fake coin is in group A. We can proceed as follows:

3. Take any two coins from group A and weigh them against each other: - If they balance, the remaining coin in group A is the fake coin. - If one of the coins is lighter, that coin is the fake coin.

In this scenario, we also need a total of 2 weighings to find the fake coin.

Scenario 3: Group A is Heavier than Group B

If group A is heavier than group B, it means the fake coin is in group B. We can proceed as follows:

3. Take any two coins from group B and weigh them against each other: - If they balance, the remaining coin in group B is the fake coin. - If one of the coins is lighter, that coin is the fake coin.

Again, in this scenario, we need a total of 2 weighings to find the fake coin.

Conclusion

In all possible scenarios, we can find the fake coin among 9 identical-looking coins using a balance scale without weights in a minimum of 2 weighings.