# 6.9 100 Lockers

# There are 100 closed lockers in a hallway.
# A man begins by opening all 100 lockers.
# Next, he closes every second locker. 
# Then, on his third pass, he toggles every third locker.
# The process continues for 100 passes, such that, on each pass, the man toggles every ith locker.
# After his 100th pass in the hallway, in which he toggles only locker 100, how many lockers are open?

'''
1 2 3 4 5 6 7 8 9 10
O O O O O O O O O  O 
  C O C O C O C O  C
    C     O     C
      O       O
        C          O
          C
            C
              C
                O
                  C
'''

# 10 lockers (10 perfect squares)