Transcript If all the lockers are closed at the beginning, how

Hint:
consider one
particular
locker – what
condition must
be met for it to
be open at the
end?
At Mathschool, the staff have a very
odd tradition:
After each of the 100 pupils has been
given their locker number, they all, in
turn, walk down the whole row of 100
lockers, and any lockers with numbers
that are a multiple of their number
they either open it if it’s already closed,
or close it if it’s already open.
If all the lockers are closed at the
beginning, how many are open
after the 100th person has finished?
How many times will these be opened or closed?
4
5
6
7
1, 5
9
1, 2, 4, 8
1, 2, 3, 6
1, 2, 4
8
1, 7
1, 3, 9