There is a wall with 1000 closed lockers on it. A person walks down the hall opening every other locker. Then the next person opens every 3rd locker. The next opens every fourth locker. The next every fifth locker.
Once this has been done, how many lockers are still closed?
(In reply to
Solution Plus Assumption by np_rt)
missing something in your process.
Person 1 who opens every other locker opens 2,4,6,8 etc.(lockers in the form 2n), which I agree opens 500 lockers.
Person 2 who opens every third locker opens 3,9,15,21 etc. (lockers in the form 3+6n), which I agree opens 166 lockers.
Person 3 who opens every fourth locker won't open any locers because person 1 already opened all of theirs!
Person 4 who opens every fifth locker opens 5,25,35,55,65 etc. (lockers in the forms 5+30n and 25+30n), which I count to be 66.
This leaves 268 lockers still closed.
I can't see how person 3 opens any, no matter the assumptions (as long as the assumptions are consistent from person to person).
re: Solution Plus Assumption
