Best...Puzzle...Ever....

[MerakSpielman]

One of them is a boy. That eliminates one of the four possibilities; now we know that my kids are:
Mary Harry
Tom Harry
Tom Jane

Yes?

What are the odds that the other is a girl?
Of the three possibilities, two of them include a girl member. The odds are therefore 2/3.

Daniel

Wrong. Wrong.

Spoiler

You have 2 children. Child A and Child B

These are the possibilities:
1) Child A: Boy, Child B: Boy
2) Child A: Boy, Child B: Girl
3) Child A: Girl, Child B: Boy
4) Child A: Girl, Child B: Girl

If you know that one of the children is a boy, the question you are failing to ask is WHICH CHILD IS THE BOY? Child A or B?

If Child A is a boy, you have the remaining possilibities:

1) 1) Child A: Boy, Child B: Boy
2) Child A: Boy, Child B: Girl

And Child B has a 50-50 chance of being a boy or a girl.

If Child B is the boy, you have the remaining possibilities:

1) Child A: Boy, Child B: Boy
3) Child A: Girl, Child B: Boy

And Child A has a 50-50 chance of being a boy or a girl.

 

[Pyske]

Sorry Psyke, but you're wrong and I can prove it.

Spoiler

If the first child is a boy, you eliminate two possibilities: GB and GG cannot occur, for the sex of the child in the first position can no longer be a girl.

I might very well be wrong; I certainly apply my comment about intuitive grasp of probability to myself, as well. However, I don't think you've proved it yet, because of a semantic difference.

You're correct that

Spoiler

if the first child is a boy, we eliminate 2 possibilities. However, the problem does not specify this. It specifies that a child is a boy. This leaves both GB and BG as valid possibilities.

. . . . . . . -- Eric

 

[Piratecat]

Tuzenbach, did you post the answer to your "faces" riddle? If so, I missed it.

Richards, I was reading your latest Challenge of Champions adventure in Dungeon, and it seemed to me that the art department screwed up a crucial illustration and made one of the riddles unsolveable. Am I mistaken?

 

[Piratecat]

My all-time favorite puzzle/trap has to the tesseract (sp?) that was published in Dragon magazine back in the early 80s. It would take me too long to describe it, and I’d need a diagram, but the short explanation is, imagine a stack of 6 sided dice. Perhaps 4 or 5 stacked on top of each other in a column. Now imagine that each one is a room. Now imagine that there are doors on all the walls, floors and ceilings. Now imagine that the space is warped so that when you leave one door, you step into another on another level. The diagram showed which doors were connected to each other. Gravity was relative (IRRC). That plus some illusions and some traditional riddles made for one of the craziest games I have ever run.

I have this all worked out. Does anyone want to see it?

 

[PennStud77]

I reluctantly think Nasma is right on this. It may help to divide things into shorter sentences and analyze the probabilities after each.

I have two children. Assuming no hermaphrodites, the possibilities are:
Mary Harry
Tom Harry
Tom Jane
Mary Jane

Yes?

One of them is a boy. That eliminates one of the four possibilities; now we know that my kids are:
Mary Harry
Tom Harry
Tom Jane

Yes?

What are the odds that the other is a girl?
Of the three possibilities, two of them include a girl member. The odds are therefore 2/3.

Daniel

Your scenario only works when you have 8 people standing in a row (in pairs) holding name signs or something, and you dismiss people when that pair is no longer valid. Because you have assigned them names, it makes it harder to see that Mary Harry and Tom Jane are the same thing. If you had said "one is Tom" instead of "one is a boy" then that more closely mimicks the riddle and you can see that it goes back to 1/2 probability.

 

[Pielorinho]

Wrong. Wrong.

If you know that one of the children is a boy, the question you are failing to ask is WHICH CHILD IS THE BOY? Child A or B?

The problem is that the riddle doesn't ask this question; when you add it in, you get a very different riddle. We don't need to know which child is the boy; we don't get to know that. By adding in an extra step, you end up getting an incorrect answer.

Daniel

 

[MerakSpielman]

You're correct that

Spoiler

if the first child is a boy, we eliminate 2 possibilities. However, the problem does not specify this. It specifies that a child is a boy. This leaves both GB and BG as valid possibilities.

It doesn't matter. A single child has been revealed as a boy. This boy either has to be the first or the second child. Either way, it works out. See my most recent post on the topic above, in response to Pielorinho.

 

[MerakSpielman]

The problem is that the riddle doesn't ask this question; when you add it in, you get a very different riddle. We don't need to know which child is the boy; we don't get to know that. By adding in an extra step, you end up getting an incorrect answer.

Daniel

I'm sorry, but it doesn't matter. No matter which child is the boy, it still works out, but you have to accept the possibility that the boy can be either Child A or Child B.

Example:
You have a boy. Named Harry if you wish. There is another child behind a curtain. This child is either Eric or Sally.

Your possibilities are:

Harry-Eric (BB)
Harry-Sally (BG)

There are no other options.

 

[Pielorinho]

Your scenario only works when you have 8 people standing in a row (in pairs) holding name signs or something, and you dismiss people when that pair is no longer valid. Because you have assigned them names, it makes it harder to see that Mary Harry and Tom Jane are the same thing. If you had said "one is Tom" instead of "one is a boy" then that more closely mimicks the riddle and you can see that it goes back to 1/2 probability.

If you say one is Tom, you get a different riddle. Let me give them a different naming schema: Mom decided her firstborn son would be Harry, her second son Tom; her first daughter would be Mary, her second Jane. Then, given the first bit of information (two kids), you know that they consist of one of the following four pairs, though you don't know which pair:

Mary Harry
Harry Tom
Harry Mary
Mary Jane

Note that pairs 1 and 3 look similar, but in pair 1, Mary's the older and Harry's the younger; pair 3 is reversed. There are no other possible combinations, given the first bit of information we have.

Now you find out that one of the kids is a boy. What possible pairs are you left with?

If this is too confusing, we can come up with a more elaborate naming schema, in which mother chooses kids names based on both their order and their gender, but all that'll do is further distinguish 1 from 3. Lemme know if you need me to do that.

Daniel

 

[apsuman]

how do you black out your text responses?

I want to contribute, but I want my answers to remain hidden. I used to know how to do this.

Help?