EX10.21.py

# 10.21 (Game: locker puzzle) A school has 100 lockers and 100 students. All lockers
# are closed on the first day of school. As the students enter, the first student,
# denoted S1, opens every locker. Then the second student, S2, begins with the
# second locker, denoted L2, and closes every other locker. Student S3 begins
# with the third locker and changes every third locker (closes it if it was open,
# and opens it if it was closed). Student S4 begins with locker L4 and changes
# every fourth locker. Student S5 starts with L5 and changes every fifth locker,
# and so on, until student S100 changes L100.
# After all the students have passed through the building and changed the lockers,
# which lockers are open? Write a program to find your answer.
# (Hint: Use a list of 100 Boolean elements, each of which indicates whether a
# locker is open (True) or closed (False). Initially, all lockers are closed.)

lockers = [0] * 100

for s in range(100):
    for l in range(s, len(lockers)):
        lockers[l] = 1 if lockers[l] == 0 else 0

print(lockers)
open = []
for l in range(len(lockers)):
    if lockers[l] == 1:
        open.append(l)

print("The open lockers indices are:",open)