*the* smart question

[Aragorn1]

A bit like the orc one:

YOu are lost in the wood and there are two paths, one leads to safety and oen further into the wood. There are two twins, only one of which speaks the truth, what question should you ask in order to know which is the right path?

[Morgeruat]

Originally posted by Aragorn1: A bit like the orc one: YOu are lost in the wood and there are two paths, one leads to safety and oen further into the wood. There are two twins, only one of which speaks the truth, what question should you ask in order to know which is the right path?

which direction would the other guy tell me to go in, and then go the other direction.

[mad=dog]

Yes that is the one mine is a variation of. Rather than simply give the answer I'll give the analytical reasoning you need to apply to reach the answer. You know you will either get a lie or truth from either source. You know that each source is consistent to this end. So your only option is to guarantee that you will get both a lie and a true statement.

Another one that tricks the mind into jumping to a conclusion prematurely:

A guest in a price show is shown three closed lockets. He is informed that only one of the lockets contain the price and is asked to make a pick. After he has chosen the host opens one of the other lockets and reveals it to be empty. He then asks the guest if he wants to change his choice.
Which of the following is true
1) It is smartest to stick with his initial choice
2) It is smartest to switch his choice
3) It doesn't matter. The chance is equal

[Q'alooaith]

it is smartest for him to stick with his initial choice, because he already knows that the one the host has is empty, thus he does not want it.

[Seraph]

You want to switch your choice.
When you first pick you have a 1/3 chance of picking the correct locket. Once one of the two other lockets is opened you still have that 1/3 chance of picking the correct locket, so you know that the other locket has a 2/3 chance of containing the prize.

[Morgeruat]

Once the host opens one to reveal the empty locket the # of choices becomes 2, rather than one, each locket has the same probability of being the one with the price, in this case 50%, so it really doesn't matter whether you change or not, you've got the same odds either way.

[ 06-22-2005, 01:33 PM: Message edited by: Morgeruat ]

[Q'alooaith]

why would you want to switch?

If the one in the hosts hands has nothing and is taken out of the equation you don't have a better chance of picking the better of the two just because one has been removed, it's gone from a one in three, to a one in two, slightly better odds overall but changing does not increase the odds of getting the correct one.

[Seraph]

You are making a false assumption, namely that just because the locket is opened that is suddenly is out of the problem.
Lets say there are three lockets A, B, and C, and lets define A as the locket you pick.
There are three equally probable choices.
1) A contains the prize.
2) B contains the prize.
3) C contains the prize.
In case (1) the host will open up locket B or C and you'll lose if you you switch.
In case (2) or (3) the host will open up the other empty locket, and you'll win if you switch.

By not switching you'll win in case (1), which will happen 1/3 of the time.
By switching you'll win in case (2) or in case (3), which will happen 2/3 of the time.

[ 06-22-2005, 01:59 PM: Message edited by: Seraph ]

[Morgeruat]

If you roll a 6 sided die three times and get a 6 each time, what are the odds of getting another 6? one in six. Statistically it will not be very likely as there are 1296 possible combinations, but the straight odds of rolling a 6 on any die roll is still 1 in six. (barring a weighted die of course)

If I put 5 red stones 3 yellow stones and 1 blue stone in a bag, what would be the probability of drawing the blue stone, the answer 1 in 9, if 3 red stones and 1 yellow were removed it would not continue to keep the odds at 1 in 9 to draw the stone because the 4 stones have been removed from teh equation (just like the one locket) the new chance is instead 1 in 5 as the others have been REMOVED FROM THE EQUATION.

[Q'alooaith]

Seraph, you already know that the locket in the hosts hand is empty, so you must rule it out of the equation.

You only have a 50, 50 chance of picking the right one, not 66%

Your logic is faulty.

You have to rule out the opened locket, because picking it has a 100% chance of losing, it's not part of the game.

Of the remaining two you have an equal chance of picking the right one, so it is better to stick with what you've got, since you gain nothing by switching.