Question

Имеется 9 листов бумаги.Некоторые из них разорвали или на 7,или на 9 частей.Некоторые из образовавшихся частей разорвали или на 7,или на 9 частей и так несколько раз.Можно ли после нескольких таких операций получить 100 частей?

Answer 1

Варианты:

1х7 + 8х9=79

2х7 + 7х9=77

3х7 + 6х9=75

4х7 + 5х9=73

5х7 + 4х9=71

6х7 + 3х9=69

7х7 + 2х9=67

7х8 + 1х9=65

 

Ответ: 100 частей не получится

Answer 2

Problem Analysis

The problem states that there are 9 sheets of paper, some of which have been torn into either 7 or 9 pieces. Some of the resulting pieces have been torn again into either 7 or 9 pieces, and this process has been repeated multiple times. The question is whether it is possible to obtain 100 pieces after several such operations.

Solution

To determine if it is possible to obtain 100 pieces after multiple operations, we need to analyze the number of pieces obtained at each step.

Let's start with the initial 9 sheets of paper. If each sheet is torn into 7 pieces, we would have a total of 9 * 7 = 63 pieces. If each sheet is torn into 9 pieces, we would have a total of 9 * 9 = 81 pieces.

Now, let's consider the subsequent tearing operations. Each piece obtained from the initial tearing can be torn into either 7 or 9 pieces. Let's assume that all the pieces are torn into 7 pieces in each subsequent operation.

After the first tearing operation, we would have a maximum of 63 * 7 = 441 pieces. After the second tearing operation, we would have a maximum of 441 * 7 = 3087 pieces. After the third tearing operation, we would have a maximum of 3087 * 7 = 21609 pieces.

As we can see, the number of pieces increases exponentially with each tearing operation. Therefore, it is highly likely that after multiple operations, we would have more than 100 pieces.

To summarize, it is indeed possible to obtain 100 pieces after multiple tearing operations.

Conclusion

Based on the analysis, it is possible to obtain 100 pieces after multiple tearing operations on the 9 sheets of paper.

Note: The analysis assumes that all the pieces are torn into 7 pieces in each subsequent operation. If some pieces are torn into 9 pieces in the subsequent operations, the number of pieces obtained would be even higher.