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The sultan has 100 prisoners and 100 prison guards. Today is the Sultan's birthday and he wants to release some prisoners on this occasion. He gives the following direction to his guards. The 1st guard must open all the doors. After that, the 2nd guard closes every even door (2,4,6,8..), then the 3rd guard open-closes every third door (3, 6, 9,....) depending on which one is open and which one is closed. He will open the doors that are closed and close the doors that are open. The 4th guard similarly open-closes every fourth door (4, 8, 12,...). The 5th, 6th, 7th ... and all subsequent guards will continue the same pattern, opening- closing every nth door starting with the nth door until the last guard open-closes the 100th door. The Sultan announces at the end that whoever has an open door can go free. Which prisoners are released on the Sultan's birthday?

The sultan has 100 prisoners and 100 prison guards. Today is the Sultan's birthday and he wants to release some prisoners on this occasion. He gives the following direction to his guards. The 1st guard must open all the doors. After that, the 2nd guard closes every even door (2,4,6,8..), then the 3rd guard open-closes every third door (3, 6, 9,....) depending on which one is open and which one is closed. He will open the doors that are closed and close the doors that are open. The 4th guard similarly open-closes every fourth door (4, 8, 12,...). The 5th, 6th, 7th ... and all subsequent guards will continue the same pattern, opening- closing every nth door starting with the nth door until the last guard open-closes the 100th door. The Sultan announces at the end that whoever has an open door can go free. Which prisoners are released on the Sultan's birthday?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The sultan has 100 prisoners and 100 prison guards. Today is the Sultan's birthday and he wants to release some prisoners on this occasion. He gives the following direction to his guards. The 1st guard must open all the doors. After that, the 2nd guard closes every even door (2,4,6,8..), then the 3rd guard open-closes every third door (3, 6, 9,....) depending on which one is open and which one is closed. He will open the doors that are closed and close the doors that are open. The 4th guard similarly open-closes every fourth door (4, 8, 12,...). The 5th , 6th , 7th .. and all subsequent guards will continue the same pattern, opening- closing every nth door starting with the nth door until the last guard open-closes the 100th door. The Sultan announces at the end that whoever has an open door can go free. Which prisoners are released on the Sultan's birthday?
Transcribed Image Text:The sultan has 100 prisoners and 100 prison guards. Today is the Sultan's birthday and he wants to release some prisoners on this occasion. He gives the following direction to his guards. The 1st guard must open all the doors. After that, the 2nd guard closes every even door (2,4,6,8..), then the 3rd guard open-closes every third door (3, 6, 9,....) depending on which one is open and which one is closed. He will open the doors that are closed and close the doors that are open. The 4th guard similarly open-closes every fourth door (4, 8, 12,...). The 5th , 6th , 7th .. and all subsequent guards will continue the same pattern, opening- closing every nth door starting with the nth door until the last guard open-closes the 100th door. The Sultan announces at the end that whoever has an open door can go free. Which prisoners are released on the Sultan's birthday?
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