Puzzle

[Thorwyn]

Spoiler

Switch on one of the bulbs for 2 minutes, then switch ot off again. Now switch on one of the other bulbs, leave the last one OFF and go to the other room. The burning bulb is the one you switched on. The warm bulb is the one you switched on first.

 

[elisera]

Spoiler

Switch on one of the bulbs for 2 minutes, then switch ot off again. Now switch on one of the other bulbs, leave the last one OFF and go to the other room. The burning bulb is the one you switched on. The warm bulb is the one you switched on first.

Damn they must be getting easier, will post a really hard one to get you all thinking

 

[Thorwyn]

Damn they must be getting easier

hehe... yeah, even Thorwyn can solve them...

 

[Thorondorito]

that's ok thor, but you can just switch 2 on for some time... then switch off 1 and let the other still be on.

check the burning 1, and thats the one you turned off, and the other 2 are obvious

 

[Thorwyn]

that's ok thor, but you can just switch 2 on for some time... then switch off 1 and let the other still be on.

My solution saves power.

 

[Thorondorito]

are u sure?

 

[Thorwyn]

yes... because the one that´ll stay on is turned off during the heat-up time.

 

[Thorondorito]

but i only need 10 secs to warm 1 and find the solution...

i think your solution saves more power in the case i cannot step back to the switch room and turn off the one i left

anyway... i wont start a study so i accept it thor mother earth will appreciate it

 

[tris-]

http://www.ebaumsworld.com/games/box-puzzle.html

 

[elisera]

Ok last one from me.

Gertie just came from the office of her dear departed aunt's lawyer. She was told that her aunt left her a certain amount of money in US Dollars. The lawyer explained that according to the terms of her aunt's Last Will and Testament, Gertie will get fifty times the original amount bequeathed if she could correctly guess the amount left her by midnight tomorrow. "God, that would be thousands of dollars if you succeed," the lawyer said as he handed her a note from her aunt. It read:

RAIN RIDDLE: OLD ASTRONOMY HOST ALLOWS ABLE LASS ENTRY IN OWN LAND ESTATE. Love Aunt Alley.

Question: How many thousand dollars did her millionaire aunt leave Gertie?

 

[Krait]

Spoiler

$16,000 ?

 

[adoNix]

no idea!

 

[elisera]

Spoiler

$16,000 ?

Very good, how did you get it? Or did you google it

 

[Krait]

Seen something similar before.

 

[Thorwyn]

I´ve posted this before I think, but since it´s a nice one, I might as well post it again. Here goes...

You´re participating in a game show. The host offers you two envelopes. Each one contains a certain ammount of money (in cheque form, i.e. you can´t see any difference between the envelopes) and tells you that one of the envelopes contains exactly twice the ammount of the other envelope. You may now pick one of the envelopes.
Now, after a short commercial, the host offers you to swap the envelopes. Lets take a look at the probabilities here. The probability for the ammount of money is

(0,5 * x/2) + (0,5 * 2x) = 5/4x

subtract x and you´ll have an expected win of 1/4x. Great! That´s better than any lottery in the world will offer you.

So pretty obviously, it makes sense to swap because - simply put - you gain more when you win than you lose when you lose.

Now, after a short commercial, the host asks again. And again. And again. Each time it´s mathmatically better to swap, although the envelopes are still the same.

Where´s the mistake?

(Note: there is no mistake in the probability calculation or some dodgy semantic trick... it´s a serious mathematical "problem".)

 

[Lamp]

*dribbles on desk* hussawaa?

LMAO

 

[elisera]

I´ve posted this before I think, but since it´s a nice one, I might as well post it again. Here goes...

You´re participating in a game show. The host offers you two envelopes. Each one contains a certain ammount of money (in cheque form, i.e. you can´t see any difference between the envelopes) and tells you that one of the envelopes contains exactly twice the ammount of the other envelope. You may now pick one of the envelopes.
Now, after a short commercial, the host offers you to swap the envelopes. Lets take a look at the probabilities here. The probability for the ammount of money is

(0,5 * x/2) + (0,5 * 2x) = 5/4x

subtract x and you´ll have an expected win of 1/4x. Great! That´s better than any lottery in the world will offer you.

So pretty obviously, it makes sense to swap because - simply put - you gain more when you win than you lose when you lose.

Now, after a short commercial, the host asks again. And again. And again. Each time it´s mathmatically better to swap, although the envelopes are still the same.

Where´s the mistake?

(Note: there is no mistake in the probability calculation or some dodgy semantic trick... it´s a serious mathematical "problem".)

I might be wrong but I thought the key error was usually in the fact that you had looked at what you had in the envelope before being offered the swap. That changes the probability to a conditional probability not the usual 50:50 each way thing.

 

[Serbitar]

I would say that once you have swapped back to the envelope's original positions the probabilities are reset back to their original states

 

[Thorwyn]

I might be wrong but I thought the key error was usually in the fact that you had looked at what you had in the envelope before being offered the swap. That changes the probability to a conditional probability not the usual 50:50 each way thing.

Hm.. that´s not bad, but it´s not the full answer.

I would say that once you have swapped back to the envelope's original positions the probabilities are reset back to their original states

Nope. The expected gain probability doesn´t care about what envelope it is. It remains correct (if it is correct in the first place), so the expected gain is increasing each time.

 

[Thorondorito]

(0,5 * x/2) + (0,5 * 2x) = 5/4x

Is this correct? I mean, If 1 envelope has the double amount than the other... is the formula correct? Isnt it (0,5 * x/2) + (0,5 * x) = 3/4x ?

If you now substract x you have -1/4x so thats it

I'll take a look later at home, im not sure

 

[elisera]

(0,5 * x/2) + (0,5 * 2x) = 5/4x

Is this correct? I mean, If 1 envelope has the double amount than the other... is the formula correct? Isnt it (0,5 * x/2) + (0,5 * x) = 3/4x ?

I'll take a look later at home

That bit is the addition of the probability that the other one contains half of what you have in your envelope (x/2) and the probability that the other one contains double what you have in your envelope (2x)

 

[Thorondorito]

ok, im not good at maths

let me go on guessing hehe it was a start

 

[Thorwyn]

um.. no, because when youre swapping, you either get twice (2x) or half (x/2) the ammount, both with a probability of 0,5.
The formula is "correct".

 

[Thorondorito]

I think the problem is still in the formula (not incorrect, its now clear its valid), something about applying it correctly every time you swap.

 

[Serbitar]

i think the problem lies in the winnings. you dont win 2x or x/2, you win x or 2x

 

[elisera]

i think the problem lies in the winnings. you dont win 2x or x/2, you win x or 2x

You could just as easily say you win x or x/2 though... So the question is looking at both probabilities as you take what you have in your envelope as x.

 

[Serbitar]

yes, but in both '2x or x' and 'x and x/2' the difference is double.

with 'x/2 or 2x' the difference is quadruple

 

[Thorondorito]

You could just as easily say you win x or x/2 though... So the question is looking at both probabilities as you take what you have in your envelope as x.

And there's where the application of the formula doesnt work for me.
(0,5 * x/2) + (0,5 * 2x)

In the left term x stands for the amount of envelope1, in the right term it stands for the amount of envelope2 which we all know its not equal, so x is not a constant.

 

[elisera]

But the equation is looking at the probability that the envelope has half of your x OR the probability that it has double your x. x is still constant as the amount you have in your envelope.

The equation as it stands is Correct as Thor has said.

I am still almost certain that the problem lies in the fact that you no longer have equal chance of finding each of these so it is the 0.5 in each half of the equation I think is the error but I just don't have time in work to think about it for long!

 

[Thorondorito]

I give up