HELP!!!! MATH PROBLEM

[ccppfan]

OMFG This is part of my math homework... HELP ME PLEASE my whole family can't help mee.... onegai...

Here. Fresh translated from Chinese.

Spoiler:

Mother rested at home for a certain period of time. Below is the weather during that time.

-It rained for 8 times; either in the morning or in the afternoon.
-When it is rainy in the afternoon, it is sunny in the morning.
-There are 9 sunny afternoons.
-There are 13 sunny mornings.

How many days did Mother rest for?

Well crud. That's crazy.

[Moriarty]

All you have to do is put the rain at the right times to get an equal amount of sunny mornings and afternoons leftover then add the total:

Of 13 sunny mornings 6 have rainy afternoons = 7 sunny mornings leftover
Of 9 sunny afternoons 2 have rainy mornings  = 7 sunny afternoons leftover

So, 7 completely sunny days + 2 rainy morning days + 6 rainy afternoon days = 15 days total

[Moriarty]

Mwa ha ha. . . You may bow down and call me - The Math Wizard Of The Century. . . lol That would be cool. . .

[Moriarty]

I got a math problem for ya:

How many cubic meters of dirt are in a hole 6 meters long, 2 meters wide, and one meter deep?

[Found]

I got a math problem for ya:

How many cubic meters of dirt are in a hole 6 meters long, 2 meters wide, and one meter deep?

It's a hole, there isn't supposed to be anything in there.

[Moriarty]

lol, you are right!

[scineram]

Here is a strange one to crack:


There is an island upon which a tribe resides. The tribe consists of 1000 people, with various eye colours. Yet, their religion forbids them to know their own eye color, or even to discuss the topic; thus, each resident can (and does) see the eye colors of all other residents, but has no way of discovering his or her own (there are no reflective surfaces). If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness. All the tribespeople are highly logical and devout, and they all know that each other is also highly logical and devout and they all know that they all know that each other is highly logical and devout, and so forth. (for the purposes of this logic puzzle, "highly logical" means that any conclusion that can logically deduced from the information and observations available to an islander, will automatically be known to that islander.)

Of the 1000 islanders, it turns out that 100 of them have blue eyes and 900 of them have brown eyes, although the islanders are not initially aware of these statistics (each of them can of course only see 999 of the 1000 tribespeople).

One day, a blue-eyed foreigner visits to the island and wins the complete trust of the tribe.

The evening before he leaves all the tribe gathers, and one after another they openly declare their trust and friendship toward the visitor, who then addresses the entire tribe to thank them for their hospitality.

However, not knowing the customs, the foreigner makes the mistake of mentioning eye color in his address, remarking “how unusual it is to see another blue-eyed person like myself in this region of the worldâ€

[Umandsf]

Ack! It's the gnome problem all over again! Well, since he knows his eye color, he would have to commit ritual suicide. He mentions that there is at least one blue-eyed person there along with him. Since there are 100 blue-eyed people, everyone can see that such a statement is true. Since they are unaware of the exact distribution, this info will not add anything new. So, aside from the visitor being possibly in trouble, everything will stay the same.

Yeah, it's wrong, but hopefully others can use this step.

[c-square]

What effect, if anything, does this faux pas have on the tribe?

Spoiler:

Hmm...

Say I am a native and of all the other natives, I see 99 have blue eyes.  My thought process might go like this:

"If I have brown eyes, then:
Mary (a native with blue eyes) would look around and see 98 pairs of blue eyes.  She would reason that
"If I have brown eyes, then:
George (a native with blue eyes) would look around and see 97 pairs blue eyes.  He would reason that
"If I have brown eyes, then:
Lucy (a native with blue eyes) would look around and see 96 pairs of blue eyes.  She would reason that...

...

Bob (a native with blue eyes) would look around and see 1 pair of blue eyes.  He would reason that
"If I have brown eyes, then:
Grace (a native with blue eyes) would look around and see 0 pairs of blue eyes.  She would reason that
"The foreigner must be talking about me!  I must has blue eyes!"  So she'd then kill herself.  
But Grace is not killing herself, therefore I (Bob) must have blue eyes!" and Bob would kill himself.  
But Bob is not killing himself, so therefore...

...

so therefore I (Lucy) must have blue eyes!" and Lucy would kill herself.  
But Lucy is not killing herself, therefore I (George) must have blue eyes!" and George would kill himself.
But George is not killing himself, therefore I (Mary) must have blue eyes!" and Mary would kill herself.
But Mary is not killing herself, therefore I (ME!!) must have blue eyes!" and so I would have to kill myself.

But, then I'd think "Oh, wait, silly.  There's a good chance at least one of the above people is color blind.  Okay, so I can't know what color my eyes are after all.  Phew!" and no-one would die.

[Akonyl]

Ack! It's the gnome problem all over again! Well, since he knows his eye color, he would have to commit ritual suicide. He mentions that there is at least one blue-eyed person there along with him. Since there are 100 blue-eyed people, everyone can see that such a statement is true. Since they are unaware of the exact distribution, this info will not add anything new. So, aside from the visitor being possibly in trouble, everything will stay the same.

Yeah, it's wrong, but hopefully others can use this step.

this was pretty much exactly what I was gonna say, but I had to be off to class.

usually the answer to this kind of riddle is "they all kill themselves", but that requires them to be aware of the statistic of blue vs brown eyes. So, until they're told, they can't do anything about it. Heck, for all each islander knows, they could have green eyes

[Sayumi]

i think c-square was on the right track and only trailed off slightly with the colour blindness in the end... assuming that they know than none of them are colourblind the effect would be:

Spoiler:

on day 100 all the blue-eyed islanders will kill themselves

Assuming there is only one person with blue eyes:
that evening this person thinks: I've never seen anyone with blue eyes here before so ot has to be me
day1:commits suicide

Two people with blue eyes:
that evening: both of them think: i see only one person with blue eyes. if he is the only one he'll kill himself
day1: after noon they think:that other person is alive, so he has to have seen someone with blue eyes and since I see noone besides him it has to be me
day2: both of them now know that they have blue eyes and kill themselves

Three people with blue eyes
that evening each of them thinks: I see two people with blue eyes, if I don't have blue eyes they will kill themselves on day2
day2: noon passes, all three now know that they have blue eyes
day3: all three kill themselves
.
.
.
100 blue-eyed people
that evening they think: i see 99people with blue eyes from this village, if I don't have blue eyes they'll kill thmselves on day99 at noon
day99 after noon: the others are still alive so I have to have blue eyes as well
day100: they kill themselves

We had something really similar before (it might have even been me who posted it, not sure though). Of course this only works when all of them know how the others will reason, none of them are colorblind and it's necessary that there is a specific time at which they are supposed to commit suicide (here: noon)

[Akonyl]

i think c-square was on the right track and only trailed off slightly with the colour blindness in the end... assuming that they know than none of them are colourblind the effect would be:

Spoiler:

on day 100 all the blue-eyed islanders will kill themselves

Assuming there is only one person with blue eyes:
that evening this person thinks: I've never seen anyone with blue eyes here before so ot has to be me
day1:commits suicide

Two people with blue eyes:
that evening: both of them think: i see only one person with blue eyes. if he is the only one he'll kill himself
day1: after noon they think:that other person is alive, so he has to have seen someone with blue eyes and since I see noone besides him it has to be me
day2: both of them now know that they have blue eyes and kill themselves

Three people with blue eyes
that evening each of them thinks: I see two people with blue eyes, if I don't have blue eyes they will kill themselves on day2
day2: noon passes, all three now know that they have blue eyes
day3: all three kill themselves
.
.
.
100 blue-eyed people
that evening they think: i see 99people with blue eyes from this village, if I don't have blue eyes they'll kill thmselves on day99 at noon
day99 after noon: the others are still alive so I have to have blue eyes as well
day100: they kill themselves

We had something really similar before (it might have even been me who posted it, not sure though). Of course this only works when all of them know how the others will reason, none of them are colorblind and it's necessary that there is a specific time at which they are supposed to commit suicide (here: noon)

the problem with this though is if this worked, they would all be dead before the foreigner arrived in the first place, because he doesn't tell them anything they don't already know.

[c-square]

i think c-square was on the right track and only trailed off slightly with the colour blindness in the end... assuming that they know than none of them are colourblind the effect would be:

Spoiler:

on day 100 all the blue-eyed islanders will kill themselves

Assuming there is only one person with blue eyes:
that evening this person thinks: I've never seen anyone with blue eyes here before so ot has to be me
day1:commits suicide

Two people with blue eyes:
that evening: both of them think: i see only one person with blue eyes. if he is the only one he'll kill himself
day1: after noon they think:that other person is alive, so he has to have seen someone with blue eyes and since I see noone besides him it has to be me
day2: both of them now know that they have blue eyes and kill themselves

Three people with blue eyes
that evening each of them thinks: I see two people with blue eyes, if I don't have blue eyes they will kill themselves on day2
day2: noon passes, all three now know that they have blue eyes
day3: all three kill themselves
.
.
.
100 blue-eyed people
that evening they think: i see 99people with blue eyes from this village, if I don't have blue eyes they'll kill thmselves on day99 at noon
day99 after noon: the others are still alive so I have to have blue eyes as well
day100: they kill themselves

We had something really similar before (it might have even been me who posted it, not sure though). Of course this only works when all of them know how the others will reason, none of them are colorblind and it's necessary that there is a specific time at which they are supposed to commit suicide (here: noon)

That's kind of where I was going, though there are a couple points I have with your deduction:

Spoiler:

First, if it works for 100 people with blue eyes in 100 days, why wouldn't it work for 100 people with blue eyes and one person with brown eyes in 101 days.  The brown-eyed person has no clue that (s)he's different than the others, and so would use the same reasoning as the one you laid out.  And if it works for 100 people with blue eyes and one person with brown eyes, why not 100 people with blue eyes and 900 people with brown eyes in 101 days.  Again, they don't know they have brown eyes, so they could use the same logic to think their eyes are blue.

Second, why do they have to wait a day before moving on to the next step?  Reasoning is usually pretty quick, and since they they all know that each other is highly logical, it would probably be quicker than a day.  And if it is, then as soon as one blue-eyed person committed suicide, the chain would stop, because everyone else would say, "Aha!  Since that person figured out (s)he has blue eyes, that means I can't know about myself!"  Of course there might be one or two brown-eyed casualties first (as they might reason they have blue eyes using the logic above).

OR, if they all reason and move at exactly the same speed (if they're robots, for example), they'd all reason using your logic above, then all begin the ritual of committing suicide.  But then they'd all stop because they'd see someone else beginning the suicide ritual.  But then they'd all start again because everyone had stopped.  And they'd continue in a loop, starting and stopping the ritual forever, or until they all died of hunger.

[Sayumi]

the problem with this though is if this worked, they would all be dead before the foreigner arrived in the first place, because he doesn't tell them anything they don't already know.

Spoiler:

No they wouldn't. There has to be someone who tells them: there are some people with this (insert any color) eye color, otherwise the whole process wouldn't start. imagine 499blue-eyed people, 499brown-eyed people and 2green eyed people.
Both of the green-eyed people will think: i can can see 499 blue-eyed, 499brown-eyed and 1green-eyed person. But no matter how long he waits he isn't going to figure out which eye color he has. As far has he know he might have purple eyes.
A green eyed person will think: either the other guy (I'll just make guys out of all of them for conveniece) doesn't know that that there are people with green eyes at all or I also have green eyes.
But both of them will never fugure out which one it is.
As soon as there is someone who tells them: "There are green-eyed people." He will think: either the green-eyed guy i can see is the only one-then he will figure that out immediately and commit suicide the next day, or I have green eyes as well, he can see me and is still alive after noon the next day, since he expected me to kill myself. In that case i have to kill myself on day2 at noon since i will know my own eye-color (green).

As ridiculous as it sounds there has to be someone who tells them there are people with this eye-color, even though they all know that beforehand. That is the time when they start "counting" (see answer to c-square)

(If you want a quick way to kill them all tell them there are people with red eyes. They will all kill themselves the next day  ;) )

-why wouldn't it work for 100 people with blue eyes and one person with brown eyes in 101 days.  

-why do they have to wait a day before moving on to the next step

(sorry that I shortened your post so much I hope i got the central points)

Spoiler:

If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness.

Basically all the blue-eyed villagers will think: I can see 99blue-eyed people. Either they can only see 98blue-eyed people, figure out that they have blue eyes on day98 and commit suicide on day99, or if they are still alive after noon on day 99, they also see 99blue-eyed people and I have blue-eyes as well.

Respectively every brown eyed person will think: if I don't have blue eyes the 100 blue-eyed people i can see will kill themselves that noon on day100, if they are still alive after that time i have to kill myself at noon on day101.

It is vital that there is a specific time at which they have to commit suicide and as soon as they figure it out they have to kill themselves at the next time possible (if you want to speed the whole process up, make every solid hour or every minute instead of every day at noon). By having that specific time they can "count" how many other blue-eyed people the others can see (either 98 or 99) and it is necessary, that they all "count" at the speed (same peroid of time-here every day at noon).
By this all the islanders can think: if the "blue-eyes" I can see are still alive at this specific time I have blue eyes myself, if they are not I don't.
Like this there are no casualties at all. if they couldn't "count" noone would ever be 100% sure of their own eye-color and they would all stay alive (unless there is only blue-eyed person). They have to be 100% sure of their own eye color before they have to kill themselves.

okay I'm really not sure whether i explained that well, I rewrote it four times and I'm still not really happy with it, but i hope you understand what I'm trying to say...  :D

[c-square]

If a tribesperson does discover his or her own eye color, then their religion compels them to commit ritual suicide at noon the following day in the village square for all to witness.

Ahh... I missed that part.  In that case, yeah, you're right! 

Spoiler:

Day 100 is doomsday for all the blue-eyed people!  The brown eyed people will still live.  Good deduction there, Sayumi.  But, I don't like that scenario.  I'm going to pretend that they can't be sure someone isn't color blind, so they don't have to kill themselves.

(If you want a quick way to kill them all tell them there are people with red eyes. They will all kill themselves the next day  )

LOL!  Yes, that would be very cruel!