Question

В каждом из десяти узлов пятиконечной звёздочки (см. рисунок) лежит по монете. Среди них четыре фальшивых - они на 1 г легче настоящих и лежат на одном отрезке. ли за одно Можно взвешивание на чашечных весах со стрелкой, показывающих, какая чаша тяжелее и на сколько граммов, найти все фальшивые монеты?

Answer 1

Хз
Пошаговое объяснение:

Answer 2

Problem Analysis

We have ten nodes arranged in the shape of a five-pointed star, with each node containing a coin. Among these coins, four are fake and weigh 1 gram less than the genuine coins. The fake coins are also located on the same segment of the star. We need to determine if it is possible to find all the fake coins using a set of balance scales that can indicate which side is heavier and by how many grams.

Solution

Yes, it is possible to find all the fake coins using the balance scales. Here's how we can do it:

1. Divide the ten coins into three groups: A, B, and C, as shown in the diagram below:

          A
        /   \
       B     C

2. Weigh groups A and B against groups C and B on the balance scales. There are three possible outcomes:

a. If the scales are balanced, it means that the fake coins are in group C. Move to step 3. b. If the scales tip towards group A, it means that the fake coins are in group A. Move to step 3. c. If the scales tip towards group B, it means that the fake coins are in group B. Move to step 4.

3. Weigh any two coins from group C against each other on the balance scales. There are three possible outcomes:

a. If the scales are balanced, it means that the remaining coin in group C is fake. Move to step 5. b. If one side of the scales is heavier, it means that the heavier coin is genuine, and the lighter coin is fake. Move to step 5. c. If the scales tip towards group C, it means that both coins are genuine. Move to step 5.

4. Weigh any two coins from group B against each other on the balance scales. There are three possible outcomes:

a. If the scales are balanced, it means that the remaining coin in group B is fake. Move to step 5. b. If one side of the scales is heavier, it means that the heavier coin is genuine, and the lighter coin is fake. Move to step 5. c. If the scales tip towards group B, it means that both coins are genuine. Move to step 5.

5. Weigh any two coins from the remaining group against each other on the balance scales. There are three possible outcomes:

a. If the scales are balanced, it means that the remaining coin is fake. b. If one side of the scales is heavier, it means that the heavier coin is genuine, and the lighter coin is fake. c. If the scales tip towards the remaining group, it means that both coins are genuine.

By following this procedure, we can identify all the fake coins.

Conclusion

Using a set of balance scales, it is possible to find all the fake coins among the ten coins arranged in the shape of a five-pointed star. The procedure outlined above allows us to determine the location of the fake coins and identify them accurately.