and then opened every second locker, and then went back and closed every third locker, and went back and opened every fourth locker, and so on...., through alll lockers, any number of lockers...
what lockers would end up open??
2006-08-18 23:02:54 · 11 answers · asked by iandanielx 3 in Science & Mathematics ➔ Mathematics
keran; ANY number of lockers
everyone else; its a real math question...I graduated from schools with lockers more than 10 years ago.
2006-08-18 23:12:27 · update #1
Yes, I know that every second locker would be opened, and they every third would by closed, and then every fourth opened, and then every firth closed, etc....
but describe what pattern that generates. First good answer gets the 10 points.
2006-08-18 23:30:26 · update #2
If a locker is changed an even amount of times then it will go back to being closed. If it is changed an odd amount of times, then it will be open. What kind of number has an even number of factors (how many factors a locker number has determines how many times it is changed)? Most numbers have an even amout of factors, because for every factor there is a matching one that when multiplied will equal the locker number. Except for square numbers because for one of their factor pairs the numbers are the same, and so those two factors, being exact same, are only counted as one. That would make the amount of factors for those numbers be odd.
SO the lockers that are square numbers are open (ie. 1,4,9,16,25, 36, 49, 64, ...)
2006-08-19 03:29:43 · answer #1 · answered by Prakash 4 · 3⤊ 0⤋
The odd numbered lockers ouwld end up closed, and thwe evn lockers would end up opened. This is because only the last time matters that you pass by a locker. So the first locker ends up closed, because you closed every locker, then the second locker ends up opened, because you opened every second locker. Then the third locker ends up closed, and on, thgough all lockers.
2006-08-18 23:19:51 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Even lockers would end up open.
The pattern is for every locker, every 3rd, 5th, 7th, ... lockers, the action is close them, and for every 2nd, 4th, 6th, ... lockers, the action is to open them. The actions are regardless whether the locker was already opened or closed.
Thus, even lockers would end up open and odd ones would end up close.
2006-08-19 05:17:40 · answer #3 · answered by back2nature 4 · 0⤊ 0⤋
1 2 3 4 5
c o c o c
going back 4 will open 1
1 2 3 4 5 6
c o c o c o
going back 4 results in no change
the way the problem is stated the result is inconclusive.
2006-08-19 01:00:03 · answer #4 · answered by greatire 2 · 0⤊ 0⤋
the even numbered lockers would end up being open and the odd would end up closed
2006-08-18 23:14:40 · answer #5 · answered by brian f 1 · 0⤊ 0⤋
This would depend on how many lockers are in the school.
2006-08-18 23:09:06 · answer #6 · answered by amg503 7 · 0⤊ 0⤋
all of the even number lockers
2006-08-18 23:15:26 · answer #7 · answered by 【ツ】ρεαcε! 5 · 0⤊ 0⤋
go ask the locker
2006-08-18 23:08:39 · answer #8 · answered by Anonymous · 0⤊ 0⤋
the first one
2006-08-18 23:08:27 · answer #9 · answered by Anonymous · 0⤊ 1⤋
how many lockers???
2006-08-18 23:08:17 · answer #10 · answered by keran_guy 2 · 0⤊ 0⤋