Question

Дедка вдвое сильнее Бабки. Бабка втрое сильнее Внучки. Внучка вчетверо сильнее Жучки. Жучка впятеро сильнее Кошки. Кошка вшестеро сильнее Мышки. Дедка, Бабка, Внучка, Жучка, и Кошка вместе с Мышкой могут вытащить репку, а без мышки-не могут. Сколько надо позвать Мышек чтобы, они сами смогли вытащить репку???

Answer 1

Сила мышки = х (или, допустим, 1), тогда

Кошка = 6х

Жучка = 5*6х=30х

Внучка = 4*30х=120х

Бабка = 3*120х=360х

Дедка = 2*360х=720х

Чтобы достать репку, нужна сумма силы всех, т.е. 1237х или 1237 мышек.

Answer 2

Problem Analysis

In this problem, we are given a series of relationships between different characters and their relative strengths. We are also told that together, these characters can pull out a turnip (referred to as "репка" in Russian), but they cannot do it without the mouse (referred to as "Мышка" in Russian). We need to determine how many mice are needed for them to be able to pull out the turnip on their own.

Solution

Let's analyze the given relationships step by step to determine the relative strengths of the characters involved:

1. The grandfather (Дедка) is twice as strong as the grandmother (Бабка). 2. The grandmother (Бабка) is three times as strong as the granddaughter (Внучка). 3. The granddaughter (Внучка) is four times as strong as the dog (Жучка). 4. The dog (Жучка) is five times as strong as the cat (Кошка). 5. The cat (Кошка) is six times as strong as the mouse (Мышка).

Based on these relationships, we can calculate the relative strengths of each character compared to the mouse (Мышка):

- The grandfather (Дедка) is 2 * 3 * 4 * 5 * 6 = 720 times as strong as the mouse. - The grandmother (Бабка) is 3 * 4 * 5 * 6 = 360 times as strong as the mouse. - The granddaughter (Внучка) is 4 * 5 * 6 = 120 times as strong as the mouse. - The dog (Жучка) is 5 * 6 = 30 times as strong as the mouse. - The cat (Кошка) is 6 times as strong as the mouse.

Now, let's consider the scenario where the characters can pull out the turnip on their own. We know that the combined strength of all the characters is equal to the strength of the mouse multiplied by the number of mice needed to pull out the turnip.

Let's assume that we need "x" mice to pull out the turnip. In this case, the equation becomes:

720x + 360x + 120x + 30x + 6x = x

Simplifying the equation, we get:

1236x = x

Dividing both sides by "x", we get:

1236 = 1

This equation is not possible to solve, as it leads to an inconsistency. Therefore, there is no number of mice that can allow the characters to pull out the turnip on their own.

Answer

No number of mice can be called to allow the characters to pull out the turnip on their own.