Question

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

Answer 1

После разрыва листа или части листа на 7 частей, количество всех частей увеличится на 7-1=6 частей, после разрыва листа или части листа а 9 частей, количество всех частей увеличится на 9-1-8 частей. Изначально листов (частей) было 9 - нечетное, после любого разрыва на 7 или на 9 частей общее количество частей будет пополнятся на четное число, а значит суммарное число останется нечетным (нечетное+четное дает нечетное), а значит каким образом не совершались разрывы общее число при подсчете будет нечетным, 100- четное число, следовательно получить после нескольких заявленных операций 100 частей невозможно.
ответ: нет

Answer 2

Problem Analysis

We have 9 sheets of paper that have been torn into either 7 or 9 pieces. Some of these 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 through multiple iterations of this tearing process.

Solution

To determine if it is possible to obtain 100 pieces through multiple iterations of tearing, we need to analyze the possible combinations of tearing and calculate the total number of pieces.

Let's start by considering the initial tearing of the 9 sheets of paper. We know that some of the pieces have been torn into 7 parts and some into 9 parts. However, we don't have specific information about the distribution of these torn pieces.

To calculate the total number of pieces after the initial tearing, we need to consider all possible combinations of torn pieces. Since we don't have specific information about the distribution, we cannot provide an exact answer. However, we can calculate the minimum and maximum number of pieces based on the given information.

Let's assume the minimum number of pieces is obtained when all 9 sheets are torn into 7 parts. In this case, the total number of pieces would be 9 * 7 = 63.

Now, let's assume the maximum number of pieces is obtained when all 9 sheets are torn into 9 parts. In this case, the total number of pieces would be 9 * 9 = 81.

Therefore, based on the initial tearing, the number of pieces ranges from 63 to 81.

Next, we need to consider the subsequent tearing of the resulting pieces. We know that some of these pieces have been torn again into 7 or 9 parts, and this process has been repeated multiple times. However, we don't have specific information about the number of times this process has been repeated or the distribution of the torn pieces.

Without specific information, it is not possible to determine the exact number of pieces after multiple iterations of tearing. However, we can make some observations:

- Each tearing operation increases the number of pieces by a factor of either 7 or 9. - The number of pieces after each tearing operation will be a multiple of either 7 or 9.

Based on these observations, it is possible to obtain 100 pieces through multiple iterations of tearing. However, without specific information about the number of tearing operations and the distribution of torn pieces, we cannot provide an exact answer.

In conclusion, it is possible to obtain 100 pieces through multiple iterations of tearing, but the exact number of tearing operations and the distribution of torn pieces are unknown.