A school has a strange math teacher. On the first day, he has his students of class VIII perform an odd opening day ceremony. There are hundred students in the school in that class. The teacher asks the first student to go to every locker and open it. Then he asks the second student to go to every second locker and close it. Then he asks the third student to go to every third locker and, if it is closed to open it, and if it is open to close it, and so on. After the process is completed with the hundredth student, how many lockers are open?
Answers
Answer:
50 lokers will be opened . Hope it will help you!
Answer:
Here is the answer for the question.
Step-by-step explanation:
The only lockers that remain open are perfect squares (1, 4, 9, 16, etc) because they are the only numbers divisible by an odd number of whole numbers; every factor other than the number's square root is paired up with another. Thus, these lockers will be "changed" an odd number of times, which means they will be left open. All the other numbers are divisible by an even number of factors and will consequently end up closed.
So the number of open lockers is the number of perfect squares less than or equal to one thousand. These numbers are one squared, two squared, three squared, four squared, and so on, up to thirty one squared. (Thirty two squared is greater than one thousand, and therefore out of range.) So the answer is thirty one.