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 – 2X
  => Number of mice Cat eats = X (given)
  => Therefore, Number of mice left = 82 – 2X – X = 82 – 3X

• Box 3:

  => Number of mice in the box initially = 3(82 – 3X) = 246 – 9X
  => Number of mice Cat eats = X (given)
  => Therefore, Number of mice left = 246 – 9X – X = 246 – 10X

• Box 4:

  => Number of mice in the box initially = 4(246 – 10X) = 984 – 40X
  => Number of mice Cat eats = X (given)
  => Therefore, Number of mice left = 984 – 40X – X = 984 – 41X

• 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 – 41X
  => Therefore, 984 – 41X = 0
  => Upon solving, X = 24

Therefore, the Cat eats 24 mice each time.