Question

Есть 7 неотличимых на вид монет. Известно, что 6 из них настоящие и весят одинаково, а одна фальшивая - она тяжелее. Найдите фальшивую монету за два взвешивания на чашечных весах

Answer 1

Пошаговое объяснение:

кладём по 2 монеты если одна сторона тяжелее значить взвешиваем их и который из них тяжелее тот фальшивый.

или кладём по 2 монеты ли они одинаковые. У нас еще есть 3 монеты взешиваем их по одной который из них тяжелее тот фаьшивый или они одинаковые значит третий фальшивый

Answer 2

Finding the Fake Coin

To find the fake coin among the 7 identical-looking coins, we can use a balance scale to compare the weights of different groups of coins. Since we know that the fake coin is heavier than the genuine ones, we need to find a way to identify the heavier group of coins.

Let's divide the 7 coins into three groups: A, B, and C, with two coins in each group, and leave one coin aside. We will then compare the weights of groups A and B.

Step 1: Weigh groups A and B on the balance scale.

- If group A is heavier, then the fake coin is either in group A or it is the coin left aside. - If group B is heavier, then the fake coin is either in group B or it is the coin left aside. - If both groups weigh the same, then the fake coin is in group C or it is the coin left aside.

Now, let's consider the possible scenarios and proceed accordingly:

Scenario 1: Group A is heavier than group B.

In this case, we know that the fake coin is either in group A or it is the coin left aside. We can proceed to the next step to identify the fake coin.

Scenario 2: Group B is heavier than group A.

In this case, we know that the fake coin is either in group B or it is the coin left aside. We can proceed to the next step to identify the fake coin.

Scenario 3: Both groups A and B weigh the same.

In this case, we know that the fake coin is either in group C or it is the coin left aside. We can proceed to the next step to identify the fake coin.

Second Weighing

Now, let's move on to the second weighing to identify the fake coin.

Step 2: Take the group that was identified in the first weighing (either group A, group B, or group C) and divide it into two individual coins. Leave one coin aside and weigh the other two coins on the balance scale.

- If one of the two coins is heavier, then that coin is the fake coin. - If both coins weigh the same, then the coin left aside is the fake coin.

By following this two-step process, we can identify the fake coin using only two weighings on the balance scale.

Please note that the specific arrangement of the coins in groups A, B, and C may vary depending on the initial weighing results. The key is to divide the coins into groups and compare their weights to narrow down the possibilities.

I hope this explanation helps! Let me know if you have any further questions.