Monty Hall, we have a PROBLEM

[XYZ]

Re: Monty Hall, we have a PROBLEM

Lynah has the right answer. First time I heard that one was some years ago and it took me a little while to figure out, but the trick is to figure out a question where both the angel and devil will give the same answer.

[owslachief]

Lynah has the right answer. First time I heard that one was some years ago and it took me a little while to figure out, but the trick is to figure out a question where both the angel and devil will give the same answer.

Not to quibble, but two correct answers were given.

[LynahFan]

Re: Monty Hall, we have a PROBLEM

Not to quibble, but two correct answers were given.

I agree. Owslachiefs answer is also "correct" in that it will give you the information you seek in this particular problem. The problem statement gives you 3 key pieces of information:

1) there is a truth teller
2) there is a liar
3) the truth teller is in front of the heaven door (so the liar is in front of the other).

Given those 3 pieces of info, owslachef's answer works perfectly. I've seen a similar problem statement that omitted item #3 above: the guardians are just standing together, off to the side, and not associated with either door. In that case, owslachef's answer doesn't work - his question will tell you which is the liar and which is the truth teller, but then you would need to ask a second question to find out which door to choose, as that information is not "linked" to which guardian is which. The answer I gave works whether the guardians are associated with the doors or not.

Interestingly, if the guardians are not assigned to particular doors and you ask the question I gave, you would be able to choose the correct door, but you would still *not* be able to identify which guardian was the liar.

[Twitch Boy]

Re: Monty Hall, we have a PROBLEM

You're in an auction with one other person. Up for bids is a crisp $100 bill. There's a catch, however: the losing bidder must pay his bid as well and gets nothing.

Bidding starts at $1.

What is the optimal bid?

$99. (Or $100, if the opponent is spiteful.)

Someone bids $1, and is in line to make $99 profit. Someone else bids $2, putting him in line to make $98 profit. The original bidder can either lose his $1 or up his bid to $3, making $97 profit. The other guy can lose his $2 or up his bid to $4, making $96 profit.

Rinse and repeat until someone bids $99. The other bidder can lose his $98 or bid $100 and break even. The other guy can now lose $99 or bid $101, losing $1. The other guy can lose $100 or bid $102, losing $2. Repeat ad infinitum.

The only "winning" move is to immediately bid $99 and make $1. However, if spite is taken into consideration your opponent can bid $100, break even, and screw you over...

[joecct]

Re: Monty Hall, we have a PROBLEM

I agree. Owslachiefs answer is also "correct" in that it will give you the information you seek in this particular problem. The problem statement gives you 3 key pieces of information:

1) there is a truth teller
2) there is a liar
3) the truth teller is in front of the heaven door (so the liar is in front of the other).

Given those 3 pieces of info, owslachef's answer works perfectly. I've seen a similar problem statement that omitted item #3 above: the guardians are just standing together, off to the side, and not associated with either door. In that case, owslachef's answer doesn't work - his question will tell you which is the liar and which is the truth teller, but then you would need to ask a second question to find out which door to choose, as that information is not "linked" to which guardian is which. The answer I gave works whether the guardians are associated with the doors or not.

Interestingly, if the guardians are not assigned to particular doors and you ask the question I gave, you would be able to choose the correct door, but you would still *not* be able to identify which guardian was the liar.

Isn't there a scenario where you ask a liar if he/she is telling the truth and if they say No, it's the truth, but they can't tell the truth so they end up in an infinite loop?

[owslachief]

Isn't there a scenario where you ask a liar if he/she is telling the truth and if they say No, it's the truth, but they can't tell the truth so they end up in an infinite loop?

Yes and Norman self-destructs just working it out .

[Twitch Boy]

Re: Monty Hall, we have a PROBLEM

Isn't there a scenario where you ask a liar if he/she is telling the truth and if they say No, it's the truth, but they can't tell the truth so they end up in an infinite loop?

You're arrested, thrown in jail, and given the death penalty.

The executioner, however, allows you to make one final statement in your last words. If it is a true statement, you'll be hanged. If it is false, you'll be beheaded.

Your statement should be "You're going to behead me." He would have to behead you to make it true, which means he should have hanged you instead. If he hangs you, then it was a false statement and he should have beheaded you instead.

[owslachief]

Isn't there a scenario where you ask a liar if he/she is telling the truth and if they say No, it's the truth, but they can't tell the truth so they end up in an infinite loop?

Yes and Norman self-deconstructs just working it out .

[Jimjamesak]

Re: Monty Hall, we have a PROBLEM

You're arrested, thrown in jail, and given the death penalty.

The executioner, however, allows you to make one final statement in your last words. If it is a true statement, you'll be hanged. If it is false, you'll be beheaded.

Your statement should be "You're going to behead me." He would have to behead you to make it true, which means he should have hanged you instead. If he hangs you, then it was a false statement and he should have beheaded you instead.

Very similar to Pinocchio saying "My nose will grow now!"

[LynahFan]

Re: Monty Hall, we have a PROBLEM

I have some reservations about Twitch Boy's auction, in white, in case anyone hasn't read his explanation:

In the abscence of spite, the key is that you only bid $99 if you're the *first* bidder. Even if the other guy has only bid $1 before your $99 bid, it would still be in his best interest to go ahead and bid $100 to improve his net position by $1 (form $1 lost to breaking even). In the real world, I wouldn't bid $99 even on the first bid with a 10-foot pole. Even if there's only a 0.0001% chance that there's a spiteful bidder in the room, throwing your hat into the ring at all exposes you to a huge potential loss, because as soon as the second bidder goes to $100, the infinite loop begins where bidding higher is not spiteful but is actually in both of your own self interests. Even if there's only that 0.0001% chance of a truly spiteful bidder, I guarantee there's at least a 10% chance of a moronic bidder who would bid $100 not out of spite but because he didn't know any better. Therefore, the optimal bid is not to bid at all.

[Priceless]

Re: Monty Hall, we have a PROBLEM

The only winning move is not to play.

[FreshFish]

Re: Monty Hall, we have a PROBLEM

I have some reservations about Twitch Boy's auction

Reminds me of that childhood game, "let's have a contest to see who can hit each other the softest. You go first."


When I hear / read about stuff parents of young children worry about today, I'm amazed that any of my peers and me made it to adulthood!

[FreshFish]

Re: Monty Hall, we have a PROBLEM

you ask a liar if he/she is telling the truth and if they say "no"...

ah but they'd never answer "no" in the first place, would they? They'd more likely respond with "I always tell the truth" or some other such non-truthful evasion.

I'll skip all the obvious political jokes too.

[XYZ]

I agree. Owslachiefs answer is also "correct" in that it will give you the information you seek in this particular problem. The problem statement gives you 3 key pieces of information:

1) there is a truth teller
2) there is a liar
3) the truth teller is in front of the heaven door (so the liar is in front of the other).

Given those 3 pieces of info, owslachef's answer works perfectly. I've seen a similar problem statement that omitted item #3 above: the guardians are just standing together, off to the side, and not associated with either door. In that case, owslachef's answer doesn't work - his question will tell you which is the liar and which is the truth teller, but then you would need to ask a second question to find out which door to choose, as that information is not "linked" to which guardian is which. The answer I gave works whether the guardians are associated with the doors or not.

Interestingly, if the guardians are not assigned to particular doors and you ask the question I gave, you would be able to choose the correct door, but you would still *not* be able to identify which guardian was the liar.

My bad on that. Didn't really read it as I assumed it was the version I had seen before in which #3 was not a given.

[Twitch Boy]

Re: Monty Hall, we have a PROBLEM

Very similar to Pinocchio saying "My nose will grow now!"

The following statement is true.

The previous statement is false.