# Puzzle | Cat, Mice and 4 Boxes

**Puzzle:**

There are 4 **boxes** numbered **1, 2, 3, and 4**. Initially, there are **41 mice** inside **Box 1**. A **Cat** comes and eats **X** number of **mice** from **Box 1** and destroys it. The remaining **mice** from **Box 1** go into **Box 2** and multiply **2 times**. The **Cat** returns in a few days and eats **X** **mice** again, destroying the **Box 2**. Again the leftover **mice** will go into **Box 3** and multiply **3 times**. The terror of **Cat** hits again. She returns and eats **X** **mice** again, and the process repeats. The **mice** go into **Box 4** and multiply **4 times**. But this time, when the **Cat** returns and eats **X** **mice**, there are no **mice** left in the box.

We have to find out **X**, i.e. the number of **mice** the **Cat** eats each time.

__Solution:__

**Box 1**:**=>**Number of**mice**in the box initially = 41 (given)

**=>**Number of**mice****Cat**eats =**X**(given)

**=>**Therefore, Number of**mice**left = 41 –**X****Box 2**:**=>**Number of**mice**in the box initially = 2(41 –**X**) = 82 – 2**X**

**=>**Number of**mice****Cat**eats =**X**(given)

**=>**Therefore, Number of**mice**left = 82 – 2**X**–**X**= 82 – 3**X****Box 3**:**=>**Number of**mice**in the box initially = 3(82 – 3**X**) = 246 – 9**X**

**=>**Number of**mice****Cat**eats =**X**(given)

**=>**Therefore, Number of**mice**left = 246 – 9**X**–**X**= 246 – 10**X****Box 4**:**=>**Number of**mice**in the box initially = 4(246 – 10**X**) = 984 – 40**X**

**=>**Number of**mice****Cat**eats =**X**(given)

**=>**Therefore, Number of**mice**left = 984 – 40**X**–**X**= 984 – 41**X****Result:**

**=>**Since, given that there is no**mice**left in the**Box 4**after**Cat**eats**X****mice**from it.

**=>**Therefore, Number of**mice**left = 0

**=>**But from last equation, it can be seen that,

Number of**mice**left = 984 – 41**X**

**=>**Therefore, 984 – 41**X**= 0

**=>**Upon solving,**X**= 24

Therefore, the

Cateats24miceeach time.

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