A little riddle

[SinbadEV]

I don't believe in gambling or statistics.

[manored]

And a hard one:
3 men will pass through this test: one disk will be attached to the back of each, and then they must discover what color is the disk is in their back, and provide logical explanaition (guess not allowed). They know that there are 3 white disks and 2 black disks. The first man could see the disks in the other 2 before answering, but failed. the second could only see the one from the last man and know that the first had missed, but also failed. the third could not see anybodys disk but knew both had missed, and concluded his disk was white through logical deduction. Explain his line of tough.

If the first had seen two black ones he would have said white and been correct, as he hasn't answered that at least one of the two remaining must have a white disc. The second could have said white and be correct had the last a black disc (as that would leave only the second for having a white disc). As the second didn't say that the third must have a white disc.

Correct! And only 9 minutes after I posted it :) How about the easy one tough?

[bibim]

What is it broken, then its name is spoken?

the silence ?

Concerning my initial riddle, indeed, you should change. The wikipedia link explains it very well, I had planned to give it when enough ppl have given their opinion but Dragon45 was faster . KDR_11k's explanation is very good too.

Here is a slightly different version of this riddle I had planned to ask after the first one (Actually KDR_11K already answered it but I give it anyway for the others ). This time no one knows where is the money, but there is another player who tries to find the money.
Here are the rules of this new game:

There are 3 closed doors. There is money behind one of these doors, but there is nothing behind the others. If you open the door with the money, you win it.
First, you choose one door without opening it.
Then, someone who doesn't know where is the money comes and opens one of the 2 other doors. It so happens that there is nothing behind his door.
Lastly, you are offered to open the door you had chosen previously, or change and open the last door.

What would you do ?

1) keep the door initially selected
2) change
3) It doesn't matter

[manored]

3

Yes, its silence.

[det]

This is a really cool problem. I totally thought it would be 1/3 chance either way. I wrote a program to simulate it and it made it more clear to me why it is 1/3 probability without change and 2/3 probability with the change. The program runs 10 million games and I ran it several times. The simulation results agreed with 1/3, 2/3, within 0.01%, every time I ran it.

Example results:

Code: Select all

chris@chris-desktop:~/projects$ ocamlopt.opt -o riddle  riddle.ml 
chris@chris-desktop:~/projects$ ./riddle 
Running change door simulation...
Wins: 6664387, Losses: 3335613, Ratio: 0.666439
Running keep door simulation...
Wins: 3334216, Losses: 6665784, Ratio: 0.333422

Source code is here.

[det]

Riddle #2: I don't see how this is any different than Riddle #1.

[SwiftSpear]

Riddle 2 isn't different, because fundamentally it doesn't matter if the other player knows the results or not, if he fails 100% of the time he's always performing exactly the same function as the player who does know where the results are. If he succeeds 1/3rd of the time, the game ends every time he succeeds, but every time he fails the change over gives the player a 2/3rds chance of success.

[rattle]

I don't quite get it... one empty door will be taken out, so you basically have a 50% chance from the start which makes the first pick meaningless. "Random" computer simulations don't count.

[KDR_11k]

Um, silence doesn't make sense. When silence is broken SOMETHING is said (or maybe a noise is made) but not necessarily the word "silence".

[rattle]

It's silence, because the riddle goes What is broken every time it's spoken? Though, english might be right as well.

[KDR_11k]

I'm sure if he meant to say that he'd have said it .

[lurker]

I don't quite get it... one empty door will be taken out, so you basically have a 50% chance from the start which makes the first pick meaningless. "Random" computer simulations don't count.

You have two possibilites, but they are not equal, so it's not 50%. The best way to truly understand this is to use a slightly altered version where switching both follows the math and is highly intuitive:
There are 100 doors, and behind one is the prize. You pick a door. Now 98 unchosen doors with nothing behind them are opened. It's clear here that 99% of the time that last unchosen door will have the prize, because you only had a 1% chance of picking the right door at the start.

The thing that's not being taken into account with the base intuitive answer is the specific way in which the door opening is nonrandom, which throws off the 1/2 average expected. Because the opening of doors is only performed amongst the unchosen, the prize probability of each door that is opened is effectively dumped into the remaining unchosen doors.

[Sleksa]

Here are the rules of the game:

There are 3 closed doors. There is money behind one of these doors, but there is nothing behind the others. If you open the door with the money, you win it.
First, you choose one door without opening it.
Then, someone who knows where is the money comes and opens one of the 2 other doors to show you there is nothing behind it.
Lastly, you are offered to open the door you had chosen previously, or change and open the last door.

What would you do ?

1) keep the door initially selected
2) change
3) It doesn't matter

If you change you get a 66% chance to win

[tombom]

Um, silence doesn't make sense. When silence is broken SOMETHING is said (or maybe a noise is made) but not necessarily the word "silence".

It never said that silence wasn't broken when other words were said.

rattle: The Wikipedia article for this is actually pretty good and offers a lot of different explanations for it.

SinbadEV: You don't believe in statistics? What on earth?

[koshi]

maybe sinbad meant: i don't believe in statistics i haven't forged myself

[SinbadEV]

There is either a 100% chance that something is or isn't... at any given moment. While in the context of the riddle and within statistics you have a better chance of switching doors in reality if there's no money behind the other door theres no money behind the other door. Statistics are good for trending events in order to make informed decisions but I've played too many games of chance where 6, 7 and 8 get rolled fewer times than 12 or 2 on a pair of dice to believe that just because I haven't rolled 6, 7 or 8 yet today means I have a better chance of rolling it now... that's just stupid.

[koshi]

... believe that just because I haven't rolled 6, 7 or 8 yet today means I have a better chance of rolling it now... that's just stupid.

yes it is. It is also very, very wrong, but no one here has proposed that as far as i read. Dice rolls are independent events, but in the "riddle" we have conditional choices. that's where Bayes comes in and why intuition fails.

btw it's stochastics we're concerned here with, not statistics

[manored]

Um, silence doesn't make sense. When silence is broken SOMETHING is said (or maybe a noise is made) but not necessarily the word "silence".

Do you know anything else that breaks then you say its name? :) Im not saying other things cannot break it.

[KDR_11k]

Um, silence doesn't make sense. When silence is broken SOMETHING is said (or maybe a noise is made) but not necessarily the word "silence".

It never said that silence wasn't broken when other words were said.

rattle: The Wikipedia article for this is actually pretty good and offers a lot of different explanations for it.

SinbadEV: You don't believe in statistics? What on earth?

He said it's broken, then its name is said.

[lurker]

I'm pretty sure he did mean 'when'. The other riddle had some issues too.