One more thing, in this 'riddle' it does not matter if you pick door x first and door y later, or door y and then y, or door z and then x, or ...
It's only the result that counts.

You face two doors, one is right, one is wrong. What is the chance of picking the right one?


That's not to say you are right about there being several ways to reach the same effect. The chances of doing it in a particualr way are less than 50, less than 33%. But that's not the issue ;)


Before I forget, the other riddle's answer was an onion ;)

That logic doesn't work Legolas as there aren't two doors there are three. Remember that when the quizmaster opens one he doesn't open one at random - he opens one without a prize. That is very significant as if you haven't picked the right one (i.e. 66% of the time) then he only has one door he can open. The fact that when he asks you if you want to change there are only two doors is completely irrelevant.

But we are going round in circles on this one. The maths community of the world is actually on my side. So there!!! :D

No-ones answered my puzzle yet, and no, there was no third person involved (or 4th etc), and they didn't kill each other, they din't die from being hit by anything or hitting anything, they didn't die from natural causes.
What did cause them to die?

They were repeatedly confronted by a really hard riddle that they couldn't solve. As such their brains stopped working out of protest.

Seriously? I have no idea I am afraid.

Right, I'm just gonna repost this, but modified so everyone can try it.

<blockquote>quote:</font><hr>Originally posted by Talthyr Malkaviel:
I've got one. (It's lateral thinking)

Anthony and Cleopatra are lying dead on the floor.
Near them is a table, which has been skewed slightly, a bowl lies smashed on the floor, and there is a puddle of water on the floor.
They did not drown and they did not kill each other, they didn't die of natural causes (e.g old age), there was no third person to kill them, and they didn't die from the actions of any other person, including themselves, or for example being hit by something, or hitting themselves with something.
What caused them to die?<hr></blockquote>

D**n, and I was just getting over the headache Legolas, and 250 gave me the other night. I knew I shouldn't have stopped in here. :(

<font color= "blue">on the doors one..
The results are muttually exclusive, meaning that the door you pick in the first instance does NOT affect the second choice.
And we know that the quiz master picks a losing door- this is significant. if u have the right door to start with the choice is random. if u have a wrong dor the other wrong /*door opens. so no matter what happens ur left with a right door and a wrong door. This means the results are mutually exclusive. You therefore have a 50% chance of picking the right door. </font>

<font color= "red"> Lets assume the door which opens is Random...
</font><font color="white">
3 doors- D1 D2 D3
D1 has the prize. You choose D2.
Now if the choice was random we must assume in turn that each door opens.
If D1 opens- You know which door did have the prize, but you didnt pick it. 0% Chance.
If D2 Opens- You must choose between D1 and d3- You know one has a prize and the other doesnt. 50% chance.
If D3 Opens- Same as D2.
NOw lets assume You Pick D1.
D1 Opens-You got it Right!!! Screw Probability!!
D2 or D3 Opens- See above.
</font> <font color= "plum"> NOte that the white writing assumes the opened door is random, the blue in my previous post assumes it is not. </font>

Talthyr, I don't think anyone here'll ever figure it out.

The difference, you silly folk, is in whether or not you get to see what's behind a door before making another choice. If you make all the choices before opening any of the doors, the spread is equal. Once a door is opened, it's variable is known and the spread is now distributed over the remaining doors.

Why has Barry asked this question???
This is mental torture [img]smile.gif[/img]
Is there a mathsteacher on this forum,PLEASE????

<blockquote>quote:</font><hr>Originally posted by Campino:
Why has Barry asked this question???
This is mental torture [img]smile.gif[/img]
Is there a mathsteacher on this forum,PLEASE????<hr></blockquote>

Once you discover what a variable is, it's no longer a variable and you must re-write the problem to take that into account.

Yeah, Sir Kenyth is right, it can't be 33% each on the last remaining doors because you know one of them, it is no longer taken into account, if you know for sure it's definitely not behind that one door, it's got to be an even spread between the 2 which are left.

<blockquote>quote:</font><hr>Originally posted by Campino:
Why has Barry asked this question???
This is mental torture [img]smile.gif[/img]
Is there a mathsteacher on this forum,PLEASE????<hr></blockquote>

<font color= "blue"> Well... im not a maths teacher, but i am thinking of becoming one... and i have read many many books on stats, it is my main area of concern. So i know what im talking abut when i say things like mutually exclusive. </font>

<blockquote>quote:</font><hr>Originally posted by Campino:
Why has Barry asked this question???
This is mental torture [img]smile.gif[/img]
Is there a mathsteacher on this forum,PLEASE????<hr></blockquote>

Bwhahahahahahaha!!!!!! You shall all fall before my incomprehensible maths problems!!!

Seriosly guys. This discussion took place via newspaper letter pages between extremely good academic mathematicians. They argued for ages but the 33% 66% view is now widely held. It is not 50/50 trust me!

<blockquote>quote:</font><hr>Originally posted by Barry the Sprout:
Applause for Legolas I feel. Nice one mate!

OK, heres a probability one for you. You are playing a game show and the host asks you to pick your prize. There are three doors you can pick and one of them has a prize behind it. The other two have chickens (which, I admit, would be a prize to some people but not to most).

He asks you to guess so you pick one. He then opens one of the other doors to reveal a chicken.

He asks you if you are still sure.

On the basis of pure probability should you stick or change?<hr></blockquote>

joint little late, but this is actually something I studied in Calc III

the answer is should change, because it doubles the chances of getting a prize

pick randomly is: 1/3
switch is: 2/3

so always switch

When all else fails, run a simulator.

So I did. My little Pascal program puts a washer/dryer behind one random door, and a goat and a pair of socks behind the other 2 doors. It then picks a random door, and kicks out one of the 2 losing doors.

Out of 1000 trials where the computer stayed put with its first choice, it won the prize 351 times.

Out of 1000 trials where it decided to switch to the remaining, unopened door, it got the washer/dryer 657 times.

The results are counter-intuitive, I know. That's what makes it a PUZZLE! It does make sense, though, when you look at it right: Let's say you pick Door A. Now, there's a 33% chance the prize is behind Door A, and a 66% chance it's behind (Door B OR Door C). These numbers will NOT change. When the gameshow host opens Door C to reveal a broken Rubik's Cube, the chance of Door B OR Door C being the winner is STILL 66%.....except that Door C has been eliminated, leaving that 66% sitting behind Door B.

<font color="red"> The results WILL change- because no matter what happens ur left with a right door and a wrong door.
At the first Choice- 1/3 Chance of Getting It right, 2/3 Getting it wrong.
Second Choice- U MUST BE LEFT WITH A RIGHT AND A WRONG DOOR. The argument for u changing is that once u have made a choice the probablility of it staying right remains the same EVEN IF THE CONIDTIONS ARE CHANGED. You do not have any more chance with one than u do With the Other. IF THE CHANCES WERE TH SAME BETWEEN CHOICES, THE CONIDITIONS WOULD HAVE TO CHANGE ASWELL. I will explain this in more statistical ways in a little while when i can think of how to word it.</font>

<blockquote>quote:</font><hr>The results are counter-intuitive, I know. That's what makes it a PUZZLE! It does make sense, though, when you look at it right: Let's say you pick Door A. Now, there's a 33% chance the prize is behind Door A, and a 66% chance it's behind (Door B OR Door C). These numbers will NOT change. When the gameshow host opens Door C to reveal a broken Rubik's Cube, the chance of Door B OR Door C being the winner is STILL 66%.....except that Door C has been eliminated, leaving that 66% sitting behind Door B.<hr></blockquote>

The way I see it is that there is more than one math problem here.
In the first problem you have three doors meaning that you have a 33.3..% chance of choosing correctly. If you fail to do so you are wrong. So the new the problem is that you have two doors to choose from which means that you have a 50% chance of choosing correctly.

The results say you have a 66.6% chance of winning the prize if you switch your guess. End of story.

<font color="red"> Simulator-er.... rubish.
This is the mathematical way of figuring it out:
Useful Choices : Possible Choices.
IN the first problem, there are 3 doors, 1 is useful. So the chances of getting the useful option are 1:3 or 33.33...%.
Then One useless choice is removed, thus affecting the entire problem. NO matter what we said before we now have a right and a wrong door. 2 choices, one is useful. therefore the chances of getting the right one are 1:2, or 50%. Therefore it doesnt matter what happens, we have equal chances of being right or wrong.
When all else fails, use maths, its pretty!! </font>

<font color="gold"> Ok..
Ive sent an email out to everyone who i know, they are going to run it as a survey. This contains the puzzle and the 2 possible answers. Ill have their results back in a few days, well say that the majority of people win, ok?? (as ib the same set up as an election).
This will include people at the forum, so cast ur vote soon if u havent already done so!
BTW- The results from the emails will be fair, and unaltered. I will give the exact figures from the email, so ill say something like CHANGE: 5 50-50:5. I think that this should end this battle once and for all. </font>

Being not so very good with pascal myself I am still trying to create a simulator myself. We'll talk later [img]smile.gif[/img]

But seriously, from what I see of the way your simulation works, you let it pick a certain door every time, and check to see if the prize is behind one of the other two doors. Did you think about removing one completely, or are the possible answers
Door 1, Door 1, not (2 or 3)
Door 2, Door (2 or 3), not 1
Door 3, Door (2 or 3), not 1

Obviously, if that is the case you count door 2 and 3 double.
Then there's the random number generator, which sometimes does not go from 1-6 but from 0-5, or the other way around, and could be used wrong, and so on. There's a good chance it contains a flaw. On the other hand, there's a good chance it's right as well ;)

Back to my own...

<blockquote>quote:</font><hr>Originally posted by SookmaCook:
<font color="gold"> Ok..
Ive sent an email out to everyone who i know, they are going to run it as a survey. This contains the puzzle and the 2 possible answers. Ill have their results back in a few days, well say that the majority of people win, ok?? (as ib the same set up as an election).
This will include people at the forum, so cast ur vote soon if u havent already done so!
BTW- The results from the emails will be fair, and unaltered. I will give the exact figures from the email, so ill say something like CHANGE: 5 50-50:5. I think that this should end this battle once and for all. </font><hr></blockquote>

Um, you are joking right? You can't solve a maths puzzle by majority rules [img]graemlins/uhoh1.gif[/img] What if the majority of people are wrong? What about when Gallileo (?) said the sun was the centre of the universe? Were the people who had him killed right because they were in the majority? :rolleyes:

<blockquote>quote:</font><hr>Originally posted by Aelia Jusa:


Um, you are joking right? You can't solve a maths puzzle by majority rules [img]graemlins/uhoh1.gif[/img] What if the majority of people are wrong? What about when Gallileo (?) said the sun was the centre of the universe? Were the people who had him killed right because they were in the majority? :rolleyes: <hr></blockquote>

<font color="red"> Yes, ofcourse im joking- I know im right, so id tamper with the results to reflect that. In the mean time, im trying to figure out how to word the correct answre correctly.</font>

<font color="plum"> OK. Ill repeat the puzzle here for clarity...
U are at a game show. U choosec one door- possibly the one of the 3 that has a prize behind. Then 1 wrong door is eliminated. U can now switch doors. Should u, and y?

The correct answer is it doesnt matter. NO matter what happens you are left to choose between what must be a right door and a wrong door. This means u have 2 choices- right or wrong. 1 of these is useful, one is not. Therefore refering to every good probablility book i know of- Probabliity= Useful Choices/ Possible Choices.
this ends up being 1/2, or 50%.</font>

Maths and statistics are sooooo annoying sometimes arent they ? ;) Look at it this way:

Lets say you pick the right door the first time (33% chance of doing so). Then, after you change your opinion, you ALWAYS fail, so you have 33% chance of failing when you change.
The other choice is to pick a wrong door the first time (66% chance of doing so). Then, after you change your pick, you ALWAYS win, as the other wrong door has been opened by the quiz master, so you win the 66% of the time when you change.

Clear enough ?

BTW this has been the first time i think that i read 6 pages of a post. Riddles are sooo cool [img]smile.gif[/img] .

About the Cleopatra riddle, i think it lacks info, as you can suggest LOTS of causes that would have made them die (each of them sillier than the others [img]smile.gif[/img] ), all of them more or less correct, but youll say NO till you hear the one you wanna hear [img]smile.gif[/img] .

<font color="silver"> NO matter what happens, ur left with 2 doors- one right, one wrong. FLip a coin- Heads or Tails?? its 50-50, same situation different wording. The chances will have to change in the second choice because the situation that ur in will change.
I belive that the mistake Ertai is making is the same one that was made by whoever made this up. They try to recreate it, but dont try to prove what their saying with another example.
Heres What Will Happen:
Say u pick the right door. ur chances are 1 in 3.
When the quiz master eliminates one door, and u change or stay-u have 2 choices so ur chances are 50-50.
If you pick a wrong door, the other wrong door is eliminated so again you may stay or change. 2 choices- 50-50</font>

Simulators, mathematicians, and smart people in general agree that the odds of winning are 66.6666% if you change from your original guess.

Let's say there were a million doors. The odds of your picking the right one on the first try are one in a million. Then, the host opens all the other doors but one, and you are left with a choice: Do you want to stick with the door that has a 0.0001% chance of holding the prize, or do you want to change to the ONE door that, for SOME reason, was left closed out of all the 999,999 others?

I'll run a simulator with those odds, too, if you want.

Thats it, SixOfSpades. The reason why its 66 % and not 50 is that you know that that door has been left closed BECAUSE the quiz master didnt want to show the gift. The example of the 1000 doors is so clear. After discarding 998 doors, you have door A (first choice) and door B (the one that the quiz master left closed). Id bet that door B has the prize because the quiz master decided to leave it closed, because he CHOSE that door between 999 doors. You dont have to think that maybe he chose that door randomly because you already had pciked the right one, thinking that wouldnt be clever i think because the chances of you picking the right one the first time are 1/1000, so 999 times out of 1000 the quiz master would have POINTED you the right door.

The odds would be 50/50 if, after the quiz master discarded the doors, a NEW person appeared and had to choose between the 2 doors, without knowing which one is the one that the master decided to keep closed.

I think its clear now, but if you want me to reason it further, just ask ;) . Im gonna sleep now, see ya

Ummmmmmm..... I feel silly. I didn't read the entire thread before spouting my opinion. I didn't realize the Game Host HAD to open an empty prize door. This throws a monkey wrench into the works as HIS choice isn't random either. Exactly how much this affects the natural 50/50 probability of the remaining two doors is a matter for statisticians to debate. Since he KNOWS which door the prize is behind, the door he DIDN'T pick has a higher probability of being the one with a prize in comparison to your COMPLETELY RANDOM guess. Think of it as him having an inside tip that you don't have.

And last, look at this example: you have 1000 doors, the prize is on door #1000 ok ?

Now imagine that you are given 1000 chances:
first time, you choose door 1, and after the master opens all except number 1000, you switch your choice, and you WIN.
same for number 2, number 3.... till number 999.
last time, you choose number 1000. after the master opening all of the rest except a random one, you switch your choice and you LOSE.

You would have won 999 times out of 1000. I think its transparent as water now :D

<blockquote>quote:</font><hr>Originally posted by Sir Kenyth:
Ummmmmmm..... I feel silly. I didn't read the entire thread before spouting my opinion. I didn't realize the Game Host HAD to open an empty prize door. This throws a monkey wrench into the works as HIS choice isn't random either. Exactly how much this affects the natural 50/50 probability of the remaining two doors is a matter for statisticians to debate. Since he KNOWS which door the prize is behind, the door he DIDN'T pick has a higher probability of being the one with a prize in comparison to your COMPLETELY RANDOM guess. Think of it as him having an inside tip that you don't have.<hr></blockquote>

Exactly Sir Kenyth! That is what I have been trying to say for quite some time now! I posted the riddle yet no one seems to want to beleive me about the answer. Well they can disagree with me, as long as they don't mind disagreeing with the majority of the mathematics community.

Also, just a quick one Six. IT DOESNT MATTER HOW MANY DOORS YOU HAVE NOW (not shouting - just emphasis). What matters is which door you chose and which door the quiz master chose. Ertai explained it much better than me, read his posts. But basically it makes more sense if you talk about 100 hundred doors, and so on.

<font color="red"> If there are 100 doors, and 1 is right- first choice- 1 useful option, 100 posible options. Chnaces o fu getting it right- 1/100. Then the quiz master gets rid of all but 2, the pne uv got and another one. ONE OF THESE IS RIGHT. there are 2 possible choices and 1 useful options. 50% chance of getting it right.
Yes, logically it sounds like it shouldnt change, and that logic works, but this must be the correct answer because it is mathematicaly justified- IN a maths problem, u must use maths all the way through.
So basically- we were all wrong. There are possible answers. If presented as a math problem its 50-50, if presented as a logic problem u should change because of what ertai said...
so can we have a puzzle that everyone will agree on?? \/\/3|_3 |\|3|/3|2 63+ 4|\| 46|233|\/|3|\|+ 0|\| +|-|][5!!

Yay.....we seem to have reached something at least resembling an agreement. Here's hoping we're done....

And hey! That means it's time for......ANOTHER RIDDLE! Don't worry, though, this one's just trivia.

Without looking up the answer, how many of you (us) can name all 13 Dwarves who accompanied Bilbo Baggins in The Hobbit? Just off the top of your head.
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This blank space is to remind you to hit the 'Reply' button now, before looking at other peoples' answers.
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Thorin, Bifur, Bombur, Oin, Gloin, Balin, Dwalin, Fili, Kili, Bofur

uhhhh

EDIT: Dori, Nori, Ori.. I knew about these 3 but I wasnt sure if they were correct..

<font color="gold"> Havent read lord of the rings yet... or the hobit for that matter... So could u post a riddle that we can solve from the information given?? Trivia is kind of hard to get if u have never been exposed to anything which would help u answer it... not that u could have known before this. </font>