There are 100 closed lockers in a school. Standing in front of each locker is a student. A bell will ring 100 times. At the first ring, all students will toggle their locker (from closed to opened). At the second ring, every other student will toggle his or her locker. At the third ring, every third student will toggle his or her locker, and so on, until the 100th ring where only the 100th student will toggle his/her locker. After the 100th ring, how many lockers will be open?

By toggling you do mean from open to closed aswell right? cause otherwise they'd all be open.

Thats a progression I do not want to work out. U have to keep track of the state of every locker to work out if it will end up open or closed. Someone gonna knock up a boolean array with a hundred elements and work it out?

i think i might have missed something or you have worded it wrong because you say ALL students toggle them then EVERY OTHER student toggle them. :S

yeh wierd.

i can't figure it out properly because of the wording.
either all, none or 50 (maybe 49 or 51)

97 I reckon.

Ok the first bell rings everyone opens there locker, the second bell ring, every second person closes there locker, the third bell ring, every third person toggles there locker so if its closed they will open it and if its open they will close it

it has everything to do with the factors of each number
its quite simple

Simple maybe, but just re-reading your initial post caused some confusion.

This was a fun one! I'll save my reasoning so the other squares can have a chance of getting it! :)

Anyway, 10 will be open.

plok is right well done

while(firstvalue, <=100,firstValue++)
{
for (secondValue = firstValue,<=100, secondvalue = secondValue + firstValue, )
{
if array(secondValue) == true
{
array(secondValue) = falae
}
else
{
array(secondValue) = true
}
}end for loop
}end while loop
add up the trues and there is the answer. What a nerdy thing to do

(insert correct syntax for your fav programming language)

plok is right well done

Now please explain how you'd calculate that? :)

ok
every number has factors, consider each ring to be a test for a factor, if that ring is a factor the student toggles a door. All factors come in pairs, like 1 and itself, or 4*5 or whatever. An even number of factors will lead to a door being opened and closed again. But if a number has an odd number of factors then the door will remain open after all the factors have been tried. So the only numbers left are the squares

1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

tricky

I reckon there will be 10 left open.

Let's see what everyone else gets.

trunc(n^1/2)

:)

SPOILER

The final state of a locker depends on how many times it is toggled. If it's an odd number of times it'll be open, otherwise closed.

The lockers are enumerated and it isn't hard to see that a locker is toggled when the Nth whistle is a denominator of that locker number. For example, locker 10 will be toggled one the first blow (1), the second, fifth and tenth blows, ie all the denominators of 10 (1,2,5,10).

Now, obviously denominators come in pairs (eg 2 * 5 = 10, 1 * 10 = 10) so we would expect to always have closed lockers. There is of course one special case, that of a square number, where the denominator is multiplied by itself and doesn't have a pair. In this case the total number of unique denominators will be an odd number (all of the pairs plus the square root) and the locker will end up open.

There are 10 square numbers from 1..100 inclusive, hence the answer.

Interesting :) Any more questions like these?

1. We were born of the same mother, on the same day, at the same hour and in the same year. Yet we are not twins. How do you explain this?

2. Can you find something which has keys that open no locks, with space but no room, and allows you to enter but not to go in? (Pretty simpe)

3. I am never the first to speak but I am always the last to be heard. Who am I?

3 an echo?
2 a piano?

Number 3 is right, Number 2 isn't

answer hidden below to prevent spoilers

Number 2 is a computer keyboard

1. They're two children from a set of triplets.

We were born of the same mother, on the same day, at the same hour and in the same year. Yet we are not twins. How do you explain this?

simple, you must be a skitzo. :D
but the more likely answer is that they are triplets.

edit: dang, Tael just beat me to it

Easy one.

I am the beginning of eternity and the end of time. What am I?

are u the letter e?

number 2 is a keyboard !

yay Spook :D

Greater than God,
More evil than the devil,
The poor have it,
The rich need it
And if you eat it, you will die.

you are nothing;

i swaer you googled that :P~

Greater than God,
More evil than the devil,
The poor have it,
The rich need it
And if you eat it, you will die.


you are nothing;

? eh I don't get it?? Please explain

nothing is greater than god
nothing is more evil than the devil
poor people have nothing
rich people need nothing
if u eat nothing you will die

Nothing is great than god
nothing is more evil thant he devil
The poor have nothing
The rich need nothing (more)
And if you eat nothing, you die.

JINX
u owe me a coke;

PERSONAL JINX!

http://www.backlinah.com/n00b.jpg
that's to hold your coke with. The coke will be sent, via email, later :P~

my answer was better coz it was up first and didnt have typos :D

and yor pic is a blank page

mine was in the correct order :P~

so is mine . .. . . .

nice edit :P~

Ok I've got one:

My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?

u r 60

Spook, correct!. Would you care to show us how you worked this out?

i used maths

well done

My grandson is about as many days as my son is weeks

Therfore my son is 7 * older than my grandson.

my grandson is as many months as I am in years.

Therefore I'am 12 * older than my grandson.

(12*X)+(7*X)+X = 100

or

100/20 = X = 5

60 + 35 + 5 = 100

i used maths

Hahha :) Also Gumby, yes your equation is correct :)

Ok then smarty pants, how about this one:

The son of a rich bullion merchant left home on the death of his father. All he had with him was a gold chain that consisted of 130 links. He rented a place in the city center with a shop at the lower level and an apartment at the upper level. He was required to pay every week one link of the gold chain as rent for the place.

The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links at the end of two weeks, three gold links at the end of three weeks and so on.

The son realized that he had to cut the links of the gold chain to pay the weekly rent. If the son wished to rent the place for 130 weeks, what would be the minimum number of links he would need to cut?

Is it 120 million apple pies?

130 links of gold = 130 weeks of rent.

He was required to pay every week one link of the gold chain as rent for the place.

but after 15 weeks 1+2+3+4+5+6 etc he would have payed 120links and would be left with 10links.

The landlady told him that she wanted one link of the gold chain at the end of one week, two gold links at the end of two weeks, three gold links at the end of three weeks and so on.

So he would have to pay 130links in 15.66666 weeks to rent the 1 link/week apartment and shop for 130 weeks. So he would have to cut the links like 1 piece for 1st week then into 2 pieces for the next then 3 pieces for the 3rd week etc etc.
so the 130links would eventually be 8515pieces. :)

I just had fricking 5 lessons of maths today, so I might just leave this thread now. :P

maths rox

yes, but not when you have 5 lessons of it in one day. (Including a test.)

Gumby, incorrect but, please try again :)

u should consider yourself lucky to have access to sooo much maths

i envy u

Gumby, incorrect but, please try again :)

@ 1 link a week for 130 weeks = 130links

@ 1 piece the first week the 2 the second etc etc = 8515pieces = 130links

what would be the minimum number of links he would need to cut

oops wording, awnser 129links

@ 1 link a week for 130 weeks = 130links

@ 1 piece the first week the 2 the second etc etc = 8515pieces = 130links

I think you've misinterpret the question, it's asking for the "minimum" amount he has to cut the chain.

The answer is:

The minimum number of cuts needed to be made is 4 for a chain with 115 links.

If the links are numbered serially from 1 to 115, then the cuts would be made on the following links:
6, 17, 38, and 79.

This would result in 4 one-link pieces, one 5-link piece, one 10-link piece, one 20-link piece, one 40-link piece, and one 36 piece.

Week:	1	2	3	4	5	6	7	8	9	10	11	12
Gold links given:	1	1+1	1+1+1	1+1+1+1	5	5+1	5+1+1	5+1+1+1	5+1+1+1+1	10	10+1	10+1+1

The table above indicates that:
at the end of the fifth week, the 5-link piece is given and the 4 one-link pieces are taken back;
at the end of the tenth week, the 10-link piece is given and the 4 one-link pieces as well as the 5-link piece are taken back.

And no I didn't worked the answer out myself, I'm not that smart :)

u should consider yourself lucky to have access to sooo much maths

i envy u

Shut up :P

more brain teasers, less math questions, thanks.

arrrh said the blind man to the deak dog, "I see now!"

I hate it when the question takes longer to comprehend than the solution.

Here's one:
"I'm a fortess with no doors (no windows either) and halls of marble, but thieves still break-in and steal the gold inside. What am I?"

I know what it is, but that's more of a far-fetched metaphor than a riddle.

rofl i do these all the time in one of my classes called Personal Enrichment ;)

anyways heres two (dunno if they have been done)

1)
Bobbie and Gena are lying dead on the floor of their apartment. Their is only one door which is locked from the inside and one window which is open, although nothing has ever been able to get up to their window whiich is 74 floors up the side of their building, how did they die ?

2) Lisa and sandra are walking through the bush. They come across a cabin. They look through a window and everyone in the cabin is dead. How did they die ?

all of these can have different solutions..but they must be sensible


Now for both of these u can ask questions, but i can only give a yes or no answer...

gl :)

1) Old age
2) Plane crash

those are more like character questions, depending on what answer you give says something about you. You could say old age & that'd probably say ur a calm person who lets nature take it's course or whatever or you could say mass murder suicide, saying that you lean towards a violent outcome to all things. Not really brain teasers.

clint

1) No
2) very good :)

i toggle every day

Hybrid, is there glass and water on the floor of the apartment as well ;) ? (if there is, you should have said that)

there is a pool 12ft across (widest part) and on a leaf, dead in the centre is a frog.
Now, if a frog can leap in two foot bounds, can the frog get out of the pond in three jumps?

Yes, because the leaf would float about.

ok let's pretend it's a rooted lilly pad, and it doesn't move around.

no teen there isnt a glass of water on the floor ;) but there is water on the floor :D

i DIDN'T SAY GLASS OF WATER, i said glass and water.
I think the wind blew into the window and knocked a fish tank over. The dead couple were suffocated goldfish.

very good :) my bad on not reading it properly :D