Help me work out this question...
You are in the hallway, you open every locker. The second time you walk through the hallway, you close every second locker. The third through, you change every third locator this means that you open it (if it Is closed) or close it (if it is open). The fourth time through you change every fourth locker. This patten continues until the 100th walk through. The hallway, where the 100th is changed how many locker are left open?

Question

Help me work out this question...
You are in the hallway, you open every locker. The second time you walk through the hallway, you close every second locker. The third through, you change every third locator this means  that you open it (if it Is closed) or close it (if it is open). The fourth time through you change every fourth locker. This patten continues until the 100th walk through. The hallway, where the 100th is changed how many locker are left open?

directrix · Answer

This is one of the "classics" in mathematics. 

Start with a smaller case of 10 lockers and go through the motions. 
At the conclusion of the 10 locker openings and closings, the lockers numbered 1, 4, and 9 are left ajar.

From 10 lockers, move to a case of, say, 40 lockers. Continue until you see a pattern for the 100 lockers.