Help! 7th grade math question

[jrgaudettes]

Ok, my son has this math problem and we can not figure it out. LOL.
My mind is blank.:D
Here is the problem:
On graduation day, 200 seniors lined up outside the school. As they entered the school, they passed their lockers that were numbered from 1 to 200. The first student opened all of the lockers. The second student closed every second locker. The third student changed the position of every third locker. (If the locker was open, the student closed it; if the locker was closed, the student opened it.) The fourth student changed the position of every fourth locker, and so on until the last student entered the school. Which lockers remained open after all 200 students entered the school?

[Boatcop]

All of them.
The last student through was an illegal immigrant and after all the free handouts he and his family have taken from honest taxpayers and hard working citizens, felt thet everything was free to him and helped himself to all the other student's lunch money that they had in their lockers.
What was so hard about that?

[jrgaudettes]

LOL. So your saying all of them (closed)? If so thats what I was thinking but math was not my best subject. LOL

[Cheap Thrills]

A school has 1,000 students and 1,000 lockers, all in a row. They all start out closed. The first student walks down the line and opens each one. The second student closes the even numbered lockers. The third student approaches every third locker and changes its state. If it was open he closes it; if it was closed he opens it. The fourth student does the same to every fourth locker, and so on through 1,000 students. To illustrate, the tenth locker is opened by the first student, closed by the second, reopened by the fifth, and then closed by the tenth. All the other students pass by the tenth locker, so it winds up being closed. How many lockers are open?
A~The nth locker is opened or closed by student number k precisely when k divides n. So if student k changes locker n, so does student n/k. They cancel each other out. This always holds unless students k and n/k are precisely the same person. That is, k = n/k. The lockers that are exact squares will remain open. These are lockers 1, 4, 9, 16, 25, etc. How many of these are there in a row of 1,000? You can go all the way up to 31×31 = 961, hence there are 31 lockers open.
Damned if I know :D
http://www.eklhad.net/funmath.html
C.T. :wink:

[jrgaudettes]

Ok Darn, back to drinking beer.:D
I'm being called out to do a 1 1/2 of the diving board by my son and his friends, wish me luck be right back.
So is the answer (all of them closed)?

[Baja Big Dog]

AHHHHH....Tuesday?:confused:

[Troy McClure]

So is the answer (all of them closed)?
14x14=196. So answer is 14.
n=200, k=n/k, 14x14=196, k=14... 14 lockers open.
I thinks, I was never into geography.

[ULTRA26 # 1]

Ok Darn, back to drinking beer.:D
I'm being called out to do a 1 1/2 of the diving board by my son and his friends, wish me luck be right back.
So is the answer (all of them closed)?
Well???
My Son could answer the math qusetion, but not I
jm

[ULTRA26 # 1]

It's a trick question, of sorts. The only one that will still be open is one. Every prime number will be opened by 1 and closed by it's own number. Every non prime number will have an equal number of opens and close because a number, for example 56, will always have couplets that when mulitplied make that number. 1 x 56, 2 x 28, 4 x 14, 7 x 8. 1 is the only number that would not have at least an open and close. One is the loneliest number.
I like that. I believe you are right Good thinking :)
John M

[76ANTHONY]

Ok Darn, back to drinking beer.:D
I'm being called out to do a 1 1/2 of the diving board by my son and his friends, wish me luck be right back.
So is the answer (all of them closed)?
SO DO THE FLIP BUT REMEMBER THIS, HOW MANY DOORS ON YOUR HOUSE ARE OPEN:D
and if you used beer for this question you would have figured it out in no time:D

[Troy McClure]

It's a trick question, of sorts. The only one that will still be open is one. Every prime number will be opened by 1 and closed by it's own number. Every non prime number will have an equal number of opens and close because a number, for example 56, will always have couplets that when mulitplied make that number. 1 x 56, 2 x 28, 4 x 14, 7 x 8. 1 is the only number that would not have at least an open and close. One is the loneliest number.
Student #56 would only make changes to lockers #56, #112 & #168 if I am reading the question correctly. No??
If so, your reasoning is incorrect.
AHH, what better way to spend a Friday but debating 7th grade math.
Oh well, I've got to work early tomorrow anyway.....

[Troy McClure]

You're reading it correctly, I read it incorrectly. However, I believe the rationale of couplets still prevails. I'm pretty sure only 1 would remain open.
This whole situation is ridiculous because on my graduation day, I think I was out drinking (or trying to) rather than opening and closing lockers. :D
The issue is one of the perfect square numbers. For instance 18 (even #) has an even number of factors.. 1,2,3,6,9,18. However 16 (also even #) has an odd number of factors... 1,2,4,8,16.
Hence for #18 it would be open, close, open, close, open, close.
for #16, open, close, open, close, open.
Door 18 would be closed, door 16 would be open as would all other perfect square numbered doors. ie. 0, 1, 4, 9, 16, 25....etc.
DONE. I really don't know know what I'm talking about anyway.. Most of the time on this website I BS my way though it.:eek: :D

[scooooter7]

Subject: Schooling
Perhaps this is one of the reasons for the deterioration of standards
since the 1940's
Last week I purchased a burger and fries at McDonalds for $3.58.
The counter girl took my $4.00 and I pulled 8 cents
from my pocket and gave it to her. She stood there,
holding the nickel and 3 pennies. While looking at the
screen on her register, I sensed her discomfort and
tried to tell her to just give me two quarters, but
she hailed the manager for help. While he tried to
explain the transaction to her, she stood there and cried.
Why do I tell you this?
Because of the evolution in teaching math since the 1950s:
Teaching Math In 1950
A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price. What is his
profit?
Teaching Math In 1960
A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price, or $80. What
is his profit?
Teaching Math In 1970
A logger sells a truckload of lumber for $100. His
cost of production is $80. Did he make a profit?
Teaching Math In 1980
A logger sells a truckload of lumber for $100. His
cost of production is $80 and his profit is $20 Your
assignment: Underline the number 20.
Teaching Math In 1990
A logger cuts down a beautiful forest because he is
selfish and inconsiderate and cares nothing for the
habitat of animals or the preservation of our
woodlands He does this so he can make a profit of
$20. What do you think of this way of making a living?
Topic for class participation after answering the
question: How did the birds and squirrels feel as the
logger cut down their homes? (There are no wrong
answers.)
Teaching Math In 2005
Un ranchero vende una carretera de madera para $100.
El cuesto de la produccion era $80. Cuantos tortillas
se puede comprar?

[yopengo]

Ok, my son has this math problem and we can not figure it out. LOL.
My mind is blank.:D
Here is the problem:
On graduation day, 200 seniors lined up outside the school. As they entered the school, they passed their lockers that were numbered from 1 to 200. The first student opened all of the lockers. The second student closed every second locker. The third student changed the position of every third locker. (If the locker was open, the student closed it; if the locker was closed, the student opened it.) The fourth student changed the position of every fourth locker, and so on until the last student entered the school. Which lockers remained open after all 200 students entered the school?
Only locker #1 will remain open. It is the only locker that is opened and never touched again. With an even # of students all the other lockers should end up closed.

[Cheap Thrills]

door 16 would be open as would all other perfect square numbered doors. ie. 0, 1, 4, 9, 16, 25....etc. :D
Seems I've read this somewhere before :idea:
Wait ! Hold the press... Are the lockers on a treadmill ? :D and is Crazy Bitĉh hiding in any of them ? That'll make a difference ya know :D
LMAO
C.T. :wink:

[BIGRRNU]

Subject: Schooling
Perhaps this is one of the reasons for the deterioration of standards
since the 1940's
Last week I purchased a burger and fries at McDonalds for $3.58.
The counter girl took my $4.00 and I pulled 8 cents
from my pocket and gave it to her. She stood there,
holding the nickel and 3 pennies. While looking at the
screen on her register, I sensed her discomfort and
tried to tell her to just give me two quarters, but
she hailed the manager for help. While he tried to
explain the transaction to her, she stood there and cried.
Why do I tell you this?
Because of the evolution in teaching math since the 1950s:
Teaching Math In 1950
A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price. What is his
profit?
Teaching Math In 1960
A logger sells a truckload of lumber for $100. His
cost of production is 4/5 of the price, or $80. What
is his profit?
Teaching Math In 1970
A logger sells a truckload of lumber for $100. His
cost of production is $80. Did he make a profit?
Teaching Math In 1980
A logger sells a truckload of lumber for $100. His
cost of production is $80 and his profit is $20 Your
assignment: Underline the number 20.
Teaching Math In 1990
A logger cuts down a beautiful forest because he is
selfish and inconsiderate and cares nothing for the
habitat of animals or the preservation of our
woodlands He does this so he can make a profit of
$20. What do you think of this way of making a living?
Topic for class participation after answering the
question: How did the birds and squirrels feel as the
logger cut down their homes? (There are no wrong
answers.)
Teaching Math In 2005
Un ranchero vende una carretera de madera para $100.
El cuesto de la produccion era $80. Cuantos tortillas
se puede comprar?
LMFAO! Sad :( BUT Unfortunately TRUE!!

[OCMerrill]

Trick question...
Lockers removed...students carry backpacks.:)

[jrgaudettes]

Thanks for all the help.
You should have seen it. We had a 5th grader, 6th grader(daughter and friend), five 7th grader's and three 8th graders plus my wife and I could not figure it out. :eek: :D