# 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.

## Recommended Posts:

- Puzzle 1 | (How to Measure 45 minutes using two identical wires?)
- Puzzle 2 | (Find ages of daughters)
- Puzzle 3 | (Calculate total distance travelled by bee)
- Puzzle 4 | (Pay an employee using a 7 units gold rod?)
- Puzzle 13 | (100 Prisoners with Red/Black Hats)
- Puzzle 5 | (Finding the Injection for Anesthesia)
- Puzzle 6 | (Monty Hall problem)
- Puzzle 7 | (3 Bulbs and 3 Switches)
- Puzzle 8 | (Find the Jar with contaminated pills)
- Puzzle 9 | (Find the fastest 3 horses)
- Puzzle 10 | (A Man with Medical Condition and 2 Pills)
- Puzzle 11 | (1000 Coins and 10 Bags)
- Puzzle 12 | (Maximize probability of White Ball)
- Puzzle 14 | (Strategy for a 2 Player Coin Game)
- Puzzle 15 | (Camel and Banana Puzzle)

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.