# Can someone help solve the following logical problem?

There are 100 windows in a bus, all closed. Passenger #1 decides to open half of them. Passenger #2 closes half of the windows opened by Passenger #1. They go on to repeat opening and closing the windows in the same pattern for 100 times. How many windows are open at the end of the 100th time?

### 3 Answers

- 2 months ago
A Logical Problem Solving Strategy. Introduction. At one level, problem solving is just that, solving . result is that experts follow a general strategy for solving . Write down the relationships between the quantities which will help you determine.

- Anonymous2 months ago
It's a recursive problem:

First define the base case: P(0) = 100 windows closed

Then the recursive case: P(x) = P(x-1) - P(x-1)/2 + P(x-1)/4 = 3P(x - 1)/4

So you just have to figure out P(100) to find out the windows closed after 100th time, and do 100 - P(100).

I would do it myself, but I'm lazy so I'll let you do it.

could you kindly elaborate?