Question 5
The first 50 natural numbers will walk down a corridor containing 50 doors numbered 1 to 50, all initially locked. Number 1 goes first, then 2, then 3, and so on, with 50 last. Number n carries the keys to doors whose numbers are multiples of n. Thus 1 carries every key, 2 carries only keys to even-numbered doors, and 25 carries only keys to doors 25 and 50. Each number uses its keys to lock doors that are open and unlock doors that are closed.
a) Which doors will number 15 unlock?
b) Show that after number 50 has walked through, door 10 will be unlocked whereas door 9 will be locked.
c) After number 50 has walked through, which doors will be unlocked?
a) Which doors will number 15 unlock?
b) Show that after number 50 has walked through, door 10 will be unlocked whereas door 9 will be locked.
c) After number 50 has walked through, which doors will be unlocked?