Brain teaser thread - Page 14

Immortal Wombat · October 31, 2002, 18:09

His horse was called Monday, then he bought a new horse named Friday.

CyberGnu · October 31, 2002, 18:21

Eh, why would he walk on his first horse?

But in essence correct

Your turn.

Immortal Wombat · October 31, 2002, 18:35

oh, yeah. Different version caught me.

This is easy, but anyway:

Three busloads of students drove off on a field trip.
Fifty students rode the first bus. The ratio of boys to girls on this bus was 2:3.
The ratio of boys on the first bus to boys on the second bus was 5:6, though the ratio of girls to boys on bus 2 was 50:50.
The ratio of girls on the 3rd bus to girls on the 2nd bus was 7:8.
Boys comprised 40% of the students on the third bus.

Dauphin · October 31, 2002, 18:46

And the question is.....where were they going?

A: On a field trip.

Urban Ranger · October 31, 2002, 23:08

Yeah, so what's the question?

Immortal Wombat · November 1, 2002, 09:14

how many boys and girls are there?

Paul Hanson · November 1, 2002, 09:43

I make it to be 58 boys and 75 girls in total.

Immortal Wombat · November 1, 2002, 10:51

yes. it is.

Urban Ranger · November 1, 2002, 11:33

Okay, here is a simple one.

There is a jar with an amoeba inside. It splits every minute. In an hour the jar will be filled.

Suppose that there are two amoebae to start with, how long will it take to fill the jar?

Urban Ranger · November 1, 2002, 12:30

This is interesting.

Check out this magic trick and see if you can figure out how it works.

JohnM2433 · November 1, 2002, 12:42

If there are two amoebae to start with, it will take 59 minutes to fill the jar, as the situation at the start is the same as it was after one minute in the first instance (59 minutes remaining).

It was fairly obvious to me how that "trick" works. I checked just to make sure. With some sleight of hand, you could probably do the same thing with real cards.

JohnM2433 · November 1, 2002, 12:59

OK, this same basic problem, only in another form, was covered in another thread. But I can't think of anything better, so...

You are on a game show, and you are shown three doors. The grand prize is behind one of the doors. You are asked to select a door. Not knowing which door the prize is behind, you pick one at random. Then the host points to one of the remaining doors and tells you that the prize is not behind that door. Now he asks you to pick one of the doors again, and this time you really will get the prize if it is behind the door, and will lose it if it is not.

Assuming that the host is telling the truth, and that the same thing would have happened no matter which door you picked, which of the remaining doors is more likely to have the grand prize behind it: the one you selected or the other door that the host didn't point out?

Hurricane · November 1, 2002, 13:22

I saw that card trick earlier. You have to be pretty naive to be fooled by it.

CyberGnu · November 1, 2002, 15:38

Urban, that was way to obvious. Bob ate the card. (Because he ran out of burgers.)

John, you should take the other door, since there is a 67% chance of that being the prize winning one.

Dauphin · November 1, 2002, 16:33

Quote:

Originally posted by Urban Ranger
This is interesting.

Check out this magic trick and see if you can figure out how it works.

I picked all the cards in one go and then they all disappeared - ands were replaced by other ones. Amazing!

Dauphin · November 1, 2002, 19:04

Quote:

Originally posted by JohnM2433
Assuming that the host is telling the truth, and that the same thing would have happened no matter which door you picked, which of the remaining doors is more likely to have the grand prize behind it: the one you selected or the other door that the host didn't point out?

Even if there were a thousand other doors and you were shown one was empty, the other doors have a greater chance of holding the grand prize than the one you picked.

CyberGnu · November 1, 2002, 21:27

Forgot that I'm supposed to put a new riddle in..

What loses its head in the morning,but gains its head at night?

Urban Ranger · November 2, 2002, 23:55

*bump*

JohnM2433 · November 3, 2002, 00:16

CyberGnu gave the correct answer to my problem. Sagacious Dolphin's observation that the same principle holds for any number of doors (more than two) is also correct; the odds of the original door containing the prize will not change, and indeed cannot, since you must get the same basic information about that door (i.e., none) each time. Or to put it another way, the probability of the door you picked being the correct one when you pick it is the average of the probabilities of it being correct for each other door the host might point out, since he is equally likely to select each one. But since the cases are all symetrical, the probability for the chosen door must be the same in each case, and thus the same as it was originally. Only the odds for the doors you did not select change.

There was another thread in which someone presented the following senario: Of three prisoners, one will die and the other two will go free, but none of them knows which is which. One prisoner asks a guard to give a letter to one of the other prisoners who will go free. The guard does so, and tells him which one. How is it that the prisoner's odds of dying have now increased from 1/3 to 1/2, since they would have been the same if the other of the other two prisoners had gotten the letter?

Well, his odds of dying actually stay the same, and the odds of the other prisoner who didn't get the letter dying go up to 2/3. I posted as much. The comparison to the game show problem is obvious. But now I can't seem to locate that thread. I can't remember its name or what forum it was in, so I would appreciate if anyone could tell me which it was, as I wanted to check in on it.

I'm still trying to get the answer to CyberGnu's latest riddle...

Zero-Tau · November 5, 2002, 16:28

Time to bump this thread up again.

Now, about the doors riddle...

I agree, the other door has a bigger chance to have the prize. The important fact is that it is always one of the other doors that are opened. If the host randomly chose one of the doors without the prize, so he might open the one you chose, then your chances would be 50-50 afterwards.

The same thing applies to the prisoners. Had the prisoner asked the guard to pick one of the prisoners who was to go free at random, then his odds had increased when the letter was delivered to one of the other two.

And CyberGnu: