Tribal Problems

[Mark]

A group of scientists were doing research into an ancient tribe that was believed to have a vision defect meaning that they saw things elongated. On discovering a cave full of painted diagrams of elongated animals and trees they instantly knew they were fake, how?

In another tribe a father is twice as old as his son and when they both age a year, the sons age will contain the digits of the father's age reversed. How old are they?

[Quailman]

1:The animals were stretched horizontally; the trees vertically.

[Bicho the Inhaler]

How about: Their "elongated" = our "normal." This includes drawings. Think about it. The "elongated" things they paint should still look normal to us. I'm not explaining this very well, but I think you get the picture, so to speak.

[Rollercoaster]

1. Since they would see their own paintings elongated (in the same manner as the objects they were depicting), the drawings should look perfectly normal to those of us with "normal" vision.

EDIT: Oops, you beat me to it, Bicho

[This message has been edited by Rollercoaster (edited 04-02-2002 03:12 PM).]

[Bicho the Inhaler]

#2: (36, 72)

[mikegoo]

1 (Hopefully I am explaining this correctly: The paintings of someone with that vision problem should look normal. Let's say instead that the tribe sees things upside down: if they see an M then it looks like a W to them, now when they paint that W it will look like an M to us. Seeing something as elongated and then rendering it so it looks correct to them cancels each other out. Does this make sense?

EDIT: I'm slow too.

[This message has been edited by mikegoo (edited 04-02-2002 03:15 PM).]

[test78]

I am sure Bicho is right for #2 but what about

(396, 792) or (3996, 7992) or (39996, 79992) etc

Actually I am only posting this because i was too slow to give the right answer first

[This message has been edited by test78 (edited 04-02-2002 04:04 PM).]

[Bicho the Inhaler]

test, that man not only lives to see 793, but fathers a child when he is almost 400 years old

edit: grammar

[This message has been edited by Bicho the Inhaler (edited 04-02-2002 04:04 PM).]

[test78]

what about the new ones I added?
these really are miracles of nature

[Coyote]

Okay, I'd say the 'Class #2' answers have been pretty well covered. As for Question #1:

1a: The paintings were done with acrylic paints, clearly not possible till sometime last century.

1b: There was a written message at the bottom of the paintings saying 'These are fake!'

1c: There was another written message at the bottom of the paintings saying 'No, really! They're FAKE!! Stop wasting time on all the stupid archeological stuff!! Fake, I tell you, FAKE!!'

1d: The paintings turn out to be stylized representations of various Pokemon.

[Mark]

OK everything has been pretty well covered, Bicho's first two posts were correct, so I have others.

Leader A and his son, leader B led the tribe for a total of 99 years. 4/5's of leader A's reign was equal to 2/3's of leader B's reign. How long did leader A lead the tribe.

One of the scientists is a heavy smoker, he buys eight packets of twenty cigarettes per week. He found that to save money he could produce one new cigarette from the tobacco in four of his used stubbs. So including these how many does he actually smoke per week?

[cubestudent]

Leader A ruled for 45 years.

the Scientist smokes 213 cigarettes a week.


[edited for typo-fix]



[This message has been edited by cubestudent (edited 04-03-2002 05:57 AM).]

[Cadmium]

Here goes...
A and B are:

2/3 B = 4/5 A -> 20/30 B = 24/30 A
30/30 B = 36/30 A -> B = 6/5 A
B + A = 99 -> 11/5 A = 99 -> A = 45
B = 99 - 45 -> B = 54


[edit]I switched A & B, and I was too late [/edit]

[This message has been edited by Cadmium (edited 04-03-2002 06:07 AM).]

[ctrlaltdel]

hmmm, doesnt he smoke 212.5 cigarettes?

[Cadmium]

I don't know for sure how many he smokes, but it's not 213.

code:

---

8   * 20 = 160 cigarettes


160 /  4 =  40 cigarettes extra


40  /  4 =  10 cigarettes extra


10  /  4 =   2 cigarettes extra + 2 stubbs left


          ---+


          212

---

So, it's either 212 cigarettes or 212 and a half cigerettes if he can make a half one with the two stubbs left.

[edit]
cubestudent, you're right !! The last two extra cigarettes become stubbs as well and therefor you can make the last 213th cigarette.
[/edit]



[This message has been edited by Cadmium (edited 04-03-2002 07:37 AM).]

[Mark]

After solving all of the problems the scientists discover that the entrance to the cave has been blocked off. They search around and eventually find a door with a combination lock. Now realising that they were lured there to be captured they notice 26 cards hanging on the wall each marked with a letter of the alphabet. On the reverse of each card is a number.

The only clue to which cards contain the combination could be the phrases on the opposite wall:

6th's-
ACT: RUB IN OIL
ONE IS APART
TENDER NAME
CARE IS NOTED
IT EGGS US ON
THE CLASSROOM
VOICES RANT ON
LOVE TO RUIN

Which cards contain the combination?

[One Skunk Todd]

Is it: it eggs us on?

[One Skunk Todd]

No, that doesn't work, does it?

[ralphmerridew]

Well, at least two of the phrases (TENDER NAME and LOVE TO RUIN) are rather appropriate anagrams. (I'm leaving off what they anagram to because I had seen those outside this group.)

[Quailman]

They're all appropos anagrams. I'm guessing the answer involves the letters an the back of cards LSECSSCR

[dave10000]

I disagree with the intended solution to #1, about the elongated trees. Perhaps the natives KNEW they saw things differently, and tried to paint things so that others would see them as the natives saw them. Thus, perhaps they intentionally overcompensated.

Surely at some point the natives had to communicate their "condition" to others, or else how would anyone even suspect they had this condition? Drawing trees and animals that looked elongated to "normal-sighted" folks would be a good way to do this.

The point is, if the scientists saw elongated drawings, they could not "instantly" know they were fake, as opposed to being an attempt by the tribe to represent to others they way that they really saw the world. Could they?

DEEPER QUESTION -- if everyone in the tribe really did see things elongated, is there any way that anyone would ever know this? Isn't it like the paradigm of the guy whose perceptions of red and green were exactly reversed from normal? How would he ever know -- or communicate -- that there was a difference? Is there a test that could be done that could distinguish a "normal-seer" from an "elongated-seer"? If so, what test would that be?

[Icarus]

Better yet - what if the paintings were real. The scientists theory was wrong...

[cubestudent]

to cadmium and other unbelievers :

code:

---

8   * 20 = 160               160


160 /  4 = 40                 40


40  /  4 = 10                 10


10  /  4 = 2 (and 2 butts)     2


2   /  4 = 0 (and 2 butts)     0


                             + 1 (from the four 'leftover' butts)


                           ------


                             213

---

[edit]oops! didn't notice Cadmium's edit. so this is not to cadmium.[/edit]
[edit]i suppose i should delete it. . . naahh.[/edit]




[This message has been edited by cubestudent (edited 04-03-2002 03:20 PM).]

[Rollercoaster]

dave10000 - that's a good point (the DEEPER QUESTION). I think it would be difficult to devise such a test, and I doubt the members of the tribe would ever know. That's why, if somehow you KNEW they saw elongated, you would also know the paintings were fake.

Now, how would you know they saw that way? Aside from being an evil chief who forces his tribe to wear funny glasses ALL of the time, that would be difficult too. Even in that instance, I'm sure the brain would quickly compensate to eliminate some of the nasty headaches that are sure to arise from spinning objects.



[This message has been edited by Rollercoaster (edited 04-03-2002 03:33 PM).]

[Mark]

I agree that it is unlikely that we would ever find out if they did have such a defect, but if we didn't know then thet would know no different and not paint a painting showing their defect.

[mathgrant]

I happen to know the general answer to "If a man buys c cigarettes every month and he can make s stubs into another cigarette, how many cigarettes does he smoke in one month?" Does anyone here know it? You might have fun finding it.

[Sofis]

[CrystyB]

[cs/(s-1)]?

[Sumudu2]

just to explain the cigarette problem:
A cigarette consists of 's' stubs, and smoking a cigarette leaves a stub. Therefore, we can view the problem as having a pool of stubs and removing (s-1) at a time. The initial number of stubs is (c*s), therefore you can smoke (cs/(s-1)) cigarettes before having less than 's' stubs left. Since this is not always an integer (only if c is a multiple of (s-1)), we must use the "Floor" function, denoted here by [x], which returns the greatest integer less than or equal to x. therefore the answer is [cs/(s-1)] as CrystyB said.

[mathgrant]

Not 4235r1ly correct. . .

The numbers 12345 in the sentence above spell a Pokemon in that order. Which one?

------------------
Sometimes life gives you a deck without any aces. Deal with it.

[eruonna]

In response to Sofis's response to the DEEPER QUESTION:

The problem with comparing circles is how to communicate what a circle is, in terms of visual sensation. If we show them a circle and say, "This is a circle," they will "see" an oval. (I put "see" in quotation marks because this is the sensation they receive; it is not the same as their perception.) If they then try to draw a circle, they will draw what they "see" as and oval, which we see as a circle. We cannot tell them how we see a circle. It is still the red/green thing.
Even the changes in perception caused by changes in orientation would not give any information. They have seen things behaving this way all their lives; they will not realize on their own that anything is wrong with it. They would most likely not perceive the changes. If we showed them two sticks of the same length with different orientations, they would say that the sticks were the same length. Everything in their experience tells them that the sensation of a stick seems to change length as the stick is rotated, and they automatically correct for it. Similarly, if we show them sticks of different lengths, oriented so that the tribe's sensation of the sticks seems the same length, they would still perceive the sticks as having different lengths.
The only difference we might actually find is that their field of vision is squashed along the direction of the stretching. This might not even apply, depending on how exactly the stretching takes place.

[oxford student]

In answer to the DEEPER QUESTION

Wouldnt you discover their affliction by asking them to describe what happens when they look at a circle ( what we call a circle) and tilt their head onto one side?

[Chuck]

What if one of them had a horrible, disfiguring accident which left one eye turned 90°? If that happened to me and I was looking at a circle I'd expect to still see a circle since a 90° rotation leaves it unchanged. What would it look like to one of them?

[Rollercoaster]

This definitely points out the difference between what your eyes see and how your brain percieves these images. If you had a funny eyeball that saw things elongated, there would be some very conflicting sensations if you HELD a circle and rotated it (along the lines of Chuck's argument). Over time, one of two things would happen - 1) you would have to live with this conflicting information (my earlier 'headache' comment) or 2) your brain would just "build" a different image of the circle to be consistent with your other senses. I suspect that all of us don't have perfect eyeballs that transmit perfect images to the brain, but we ALL see a geometrically defined circle as a circle. Over time, probably from the day we were born, our brain has been compensating for the imperfections.

I think something along the lines of dave10000's red/green argument is a little different, mainly because there isn't another sense, other than sight, that would provide conflicting information. Perhaps in that case, we really DO see colors differently because this never causes conflicting information.

[Sofis]

[Icarus]

Why not just hold up a ruler, or any other device with marks that are equally spaced apart. Ask each person if the marks appear to be equally spaced. If your vision is elongated, would you see an equal spacing of marks ?

[dave10000]

[Sumudu2]

Mathgrant: Entei, of course

are you sure it's not correct? can you give me values for c and s as a counterexample?

[Sofis]

dave10000:

That's true, I suppose. Still, that would be yet another way for them to figure out that something is wrong with their vision: they know that all points on the circle are equally far away from the midpoint (because they drew it with a compass) but it clearly doesn't look like all points on the circle are equally far away from the midpoint (or any point).

[This message has been edited by Sofis (edited 04-04-2002 04:44 PM).]

[dave10000]

Sofis:

I think that to them it might. From birth, they know how a 12" ruler looks when looked at horizontally, and how it looks when looked at vertically. When they look at a circle, they'll think "Hmmmm . . . it's as wide as a horizontal ruler, and as tall as a vertical ruler -- thus, the width and height are the same."