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Subject: The Prophecy of the Escaping Legend rss

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Vlaada Chvatil
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"Great lord: The gods have given us three new prophecies."

"Speak then, priests, and tell me what they are."

"The prophecies tell of a mighty creature that will escape the arena of Tash-Kalar."

"What creature is this that could do such a thing?"

"We do not know. But the first prophecy says its name is not Leviathan."

"Well, that is good to hear. What of the second prophecy?"

"The second prophecy says it is a mighty elemental."

"Oh, that is bad! What, then, is the third prophecy?"

"The third prophecy says ... that exactly two of the three prophecies are true."

"What? What sort of trickery is this? Do you mean to say these prophecies may be false?"

"Only some of them may be false, great lord. The gods assure us that at least one of these three prophecies is true."

"Bah! We have no time for such riddles. We have our own prophecies. You told me that good stone will be difficult to find next season. And yet, we will need much stone when it is over. Now I think that if we send some people down to the quarry ..."
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David Goldfarb
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It seems to me that there are two consistent solutions:

First, and likely intended, is that it is a mighty elemental named Leviathan. (I.e., #1 is false and #2 and #3 true.)

Second is that it is not a mighty elemental, and its name is unknown except for NOT being Leviathan. (I.e., #1 is true, and #2 is false...ironically, #3 is indeterminate here! It could be either true or false.)
 
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Joshua R
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David Goldfarb wrote:
It seems to me that there are two consistent solutions:

First, and likely intended, is that it is a mighty elemental named Leviathan. (I.e., #1 is false and #2 and #3 true.)

Second is that it is not a mighty elemental, and its name is unknown except for NOT being Leviathan. (I.e., #1 is true, and #2 is false...ironically, #3 is indeterminate here! It could be either true or false.)

I think I concur with your first conclusion. It's a bit of a bender, though.

Fun to see what a legendary game designer does with his free time on BGG, though. Happy holidays, Vlaada!
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Jonathan Harrison
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The Prophecy of the Escaping Legend
Escaped Legend Clue
Legendary Escape
Stories of Escaped Pets (and Legends)
Escaped Legend
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Shalom Craimer
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David Goldfarb wrote:
It seems to me that there are two consistent solutions:

First, and likely intended, is that it is a mighty elemental named Leviathan. (I.e., #1 is false and #2 and #3 true.)

Second is that it is not a mighty elemental, and its name is unknown except for NOT being Leviathan. (I.e., #1 is true, and #2 is false...ironically, #3 is indeterminate here! It could be either true or false.)


I disagree!

#1 => Not Leviathan
#2 => Elemental
#3 => Only 2 of #1,#2,#3 is true.

The only thing we can logically deduct is that #1 and #2 cannot both be true. Since if they are, then #3 is also correct, which means all three of them are true, which contradicts #3.

TL;DR #3 must be true. So only #1 or #2 but not both are true.

That's about as far as I can go. So basically we only have two options:

- #1 true and #2 false, which means it's neither Leviathan nor an elemental
- #1 false and #2 true, which means it's Leviathan and an elemental.

Since I don't know if Leviathan is considered an elemental in this mythology, I can't contradict the second sentence. Which leaves us guessing.
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David Goldfarb
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scraimer: You are correct that #3 (along with the later statement that at least one prophecy is true) implies that #1 and #2 must have different truth-values; they cannot be both true or both false. You are not correct that #3 must be true. If #1 and #2 have differing truth-values, then #3 can consistently be regarded as either true or false. Try it.
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This clue is quite good.
However, you can read too much into it.
 
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Ryan Graham
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Here are the six eight possibilities:

not leviathan - true
elemental - true
2 are true - true
invalid. If "2 are true" is true, then all three can't be true.

not leviathan - false
elemental - true
only 2 are true - true
invalid. can't be leviathan and an elemental.

not leviathan - false
elemental - false
only 2 are true - true
invalid. if "2 are true" is true, then one more of these would have to be true as well.

not leviathan - true
elemental - false
only 2 are true - false
invalid. if "only 2 are true" is false, this implies that all remaining prophecies are true.

not leviathan - false
elemental - false
2 are true - false
invalid. if "only 2 are true" is false, this implies that all remaining prophecies are true.

not leviathan - true
elemental - true
2 are true - false
invalid. If "only 2 are true" is false then there can't only be two that are true.

not leviathan - false
elemental - true
2 are true - false
invalid. can't be leviathan and an elemental.

not leviathan - true
elemental - false
2 are true - true

I believe this is the only valid option, and therefore the clue is that the released legend is not named Leviathan. Also, since the prophecy if it being a Mighty Elemental is false, this also means we can rule out all elementals.

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Russ Williams
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gramaw wrote:
Here are the six possibilities:

2*2*2 = 8; you left out two possibilities.

But note that this is still a live contest...
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Ryan Graham
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russ wrote:
gramaw wrote:
Here are the six possibilities:

2*2*2 = 8; you left out two possibilities.

But note that this is still a live contest...


This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

From wikipedia:
"The number of permutations of n distinct objects is "n factorial" usually written as "n!", which means the product of all positive integers less than or equal to n."

http://en.wikipedia.org/wiki/Permutation

I knew all that math in school would come in handy one day!


EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there. MATH FAIL. I've edited my original post but still come to the same conclusion
 
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Russ Williams
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gramaw wrote:
This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there.

You're confusing permutations (the number of possible orderings of a set of n elements = n!) with possible assignments of 2 values (true or false) to n elements (2 to the nth power)... See e.g. http://en.wikipedia.org/wiki/Truth_table
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Ido Abelman
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gramaw wrote:
if "only 2 are true" is false, this implies that all remaining prophecies are true.

FALSE. if "only 2 are true" is false, only one or 0 of the others can be true. I follow different reasonings about the options you "invalidated" with this statement. Your #5 (false, false, false) could be true with the prophecies themselves - it's only invalidated by the statement "The gods assure us that at least one of these three prophecies is true". Your #4 (true, false, false) is actually valid - but the outcome is identical to the last one. The truthfullness of "only 2 are true" does not directly affect the identity of the escaped legend.
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Jason Hinchliffe
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russ wrote:
gramaw wrote:
This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there.

You're confusing permutations (the number of possible orderings of a set of n elements = n!) with possible assignments of 2 values (true or false) to n elements (2 to the nth power)... See e.g. http://en.wikipedia.org/wiki/Truth_table


Yeah, this is n choose x. Number of ways you can get 2 results out of 3 possibilities. There are only 3 possible permutations.

 
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clockwerk76 wrote:
russ wrote:
gramaw wrote:
This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there.

You're confusing permutations (the number of possible orderings of a set of n elements = n!) with possible assignments of 2 values (true or false) to n elements (2 to the nth power)... See e.g. http://en.wikipedia.org/wiki/Truth_table


Yeah, this is n choose x. Number of ways you can get 2 results out of 3 possibilities. There are only 3 possible permutations.

Hmm? I'm not sure what you mean. N choose x is "combinations", not "permutations". I agree that (3 choose 2) = 3, but that's not really relevant here, since you don't actually know at the start whether exactly 2 out of the 3 statements are true. (One of the statements asserts that this is so, but it could be wrong!) You're trying to find which statements are true, but you don't know how many are true.

gramaw was (reasonably) enumerating all possible truth value assignments to the 3 statements, which is simply 2*2*2 = 8 possibilities, and then check which of the 8 possibilities are contradictory and can be eliminated as impossible.
 
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David Goldfarb
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Yes, although he got some of them wrong -- for instance, "true-false-false" is valid when he said it was invalid, because "one true" does mean that "exactly two are true" is false.
 
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Kelly Beyer
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gramaw wrote:

not leviathan - false
elemental - false
2 are true - false
invalid. if "only 2 are true" is false, this implies that all remaining prophecies are true.


All three prophecies can be false - I'm not sure how the 3rd being false somehow implies that the remaining ones are true.

If all three are false then:

1) The escapee's name is Leviathan.
2) The escape is not an elemental.
3) The statement "Exactly two of the prophecies are true" is not correct. This doesn't imply anything about the other two.

 
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Zak Jarvis
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rowe33 wrote:
All three prophecies can be false - I'm not sure how the 3rd being false somehow implies that the remaining ones are true.


It doesn't but the gods assure you that at least one is true. Presumably the gods telling you is a way of indicating that you can definitely believe this fact.

All of the things can't be true due to prophecy three. All of the prophecies can't be false 'cos the gods told you. So one and only one out of the first two must be true. The number of true prophecies is undefined (two or one true are both valid, due to the nature of prophecy three).

So either the Leviathan, the escapee, is a mighty elemental or the escapee, who isn't a mighty elemental, equally isn't called Leviathan.
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David Goldfarb
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popeye09 wrote:
So either the Leviathan, the escapee, is a mighty elemental or the escapee, who isn't a mighty elemental, equally isn't called Leviathan.

All of which I worked out back in the second post to the thread.

Which of these is true is not decidable on just the information we have in this thread, but in the context of the contest it becomes clear.
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russ wrote:
clockwerk76 wrote:
russ wrote:
gramaw wrote:
This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there.

You're confusing permutations (the number of possible orderings of a set of n elements = n!) with possible assignments of 2 values (true or false) to n elements (2 to the nth power)... See e.g. http://en.wikipedia.org/wiki/Truth_table


Yeah, this is n choose x. Number of ways you can get 2 results out of 3 possibilities. There are only 3 possible permutations.

Hmm? I'm not sure what you mean. N choose x is "combinations", not "permutations". I agree that (3 choose 2) = 3, but that's not really relevant here, since you don't actually know at the start whether exactly 2 out of the 3 statements are true. (One of the statements asserts that this is so, but it could be wrong!) You're trying to find which statements are true, but you don't know how many are true.

gramaw was (reasonably) enumerating all possible truth value assignments to the 3 statements, which is simply 2*2*2 = 8 possibilities, and then check which of the 8 possibilities are contradictory and can be eliminated as impossible.


Yes you do. You know statement 3 is true. The puzzle isn't that tricky. The catch is in the phrasing, not he truth value.

Yes, combination is correct. Oops.
 
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clockwerk76 wrote:
russ wrote:
clockwerk76 wrote:
russ wrote:
gramaw wrote:
This is not the correct way to calculate the number of permuatations. There are three different elements in the set, therefore the number of permutations is 3 * 2 * 1 or 3!.

EDIT: It would appear that there were some missing possibilities (thanks Russ!) so I'm not sure where I went wrong with the math there.

You're confusing permutations (the number of possible orderings of a set of n elements = n!) with possible assignments of 2 values (true or false) to n elements (2 to the nth power)... See e.g. http://en.wikipedia.org/wiki/Truth_table


Yeah, this is n choose x. Number of ways you can get 2 results out of 3 possibilities. There are only 3 possible permutations.

Hmm? I'm not sure what you mean. N choose x is "combinations", not "permutations". I agree that (3 choose 2) = 3, but that's not really relevant here, since you don't actually know at the start whether exactly 2 out of the 3 statements are true. (One of the statements asserts that this is so, but it could be wrong!) You're trying to find which statements are true, but you don't know how many are true.

gramaw was (reasonably) enumerating all possible truth value assignments to the 3 statements, which is simply 2*2*2 = 8 possibilities, and then check which of the 8 possibilities are contradictory and can be eliminated as impossible.


Yes you do. You know statement 3 is true. The puzzle isn't that tricky. The catch is in the phrasing, not he truth value.

Yes, combination is correct. Oops.


Well, I'm not sure whether my logic was correct or not but I do know that I have maximum entries in the contest so I must've been onto something
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clockwerk76 wrote:
You know statement 3 is true.

Really? How? (BTW, to be clear: this is my polite way of saying "you are wrong".)

gramaw wrote:
Well, I'm not sure whether my logic was correct or not

Rest assured that it was not correct. Guess you lucked out. (you went wrong here: 'if "only 2 are true" is false, this implies that all remaining prophecies are true.'. Suppose that exactly one statement is true. What would be the truth value of "exactly two are true"?)
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Evil Brother wrote:
clockwerk76 wrote:
You know statement 3 is true.

Really? How? (BTW, to be clear: this is my polite way of saying "you are wrong".)

gramaw wrote:
Well, I'm not sure whether my logic was correct or not

Rest assured that it was not correct. Guess you lucked out. (you went wrong here: 'if "only 2 are true" is false, this implies that all remaining prophecies are true.'. Suppose that exactly one statement is true. What would be the truth value of "exactly two are true"?)


Because you create a paradox if it isn't because prophecy 3 is circular logic. I'm quite correct I assure you. By the way, that was really sparky and immature and completely unnecessary. You can always ask someone to probe their point politely.

In fact, if we go one step further, we can see there is in fact only one possible combination that satisfies the conditions of the problem.

If a is false and b is true you also get a paradoxical result.

If both are true, c must be true but can't be. Paradox.

Hence c must be true.
 
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clockwerk76 wrote:
russ wrote:

gramaw was (reasonably) enumerating all possible truth value assignments to the 3 statements, which is simply 2*2*2 = 8 possibilities, and then check which of the 8 possibilities are contradictory and can be eliminated as impossible.


Yes you do. You know statement 3 is true.

To clarify: I meant that at the beginning you don't know whether statement 3 is true, any more than you know whether statement 1 or 2 is true. After analyzing and solving the puzzle, of course you know more.

But at the start, we're simply told (by the gods, according to a priest) that at least one of the statements is true, but not which one(s), so we don't know whether statement 3 is true without doing further reasoning.


(Of course one might wonder "Why should we believe the gods... or the priest who says what the gods said...?")
 
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clockwerk76 wrote:
Because you create a paradox if it isn't because prophecy 3 is circular logic. I'm quite correct I assure you.

You can assure me all you like, but that doesn't change the fact that you are wrong. Whether prophecy 3 is true or false is not relevant in 'the' correct answer. In other words: Inverting the truth value of the third prophecy in 'the' correct solution gives you an equally correct solution. Therefore your assertion that prophecy 3 must be true is false.

Also, I do not think "circular logic" means what you think it means. The same goes for the word "paradox".
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russ wrote:
clockwerk76 wrote:
russ wrote:

gramaw was (reasonably) enumerating all possible truth value assignments to the 3 statements, which is simply 2*2*2 = 8 possibilities, and then check which of the 8 possibilities are contradictory and can be eliminated as impossible.


Yes you do. You know statement 3 is true.

To clarify: I meant that at the beginning you don't know whether statement 3 is true, any more than you know whether statement 1 or 2 is true. After analyzing and solving the puzzle, of course you know more.

But at the start, we're simply told (by the gods, according to a priest) that at least one of the statements is true, but not which one(s), so we don't know whether statement 3 is true without doing further reasoning.


(Of course one might wonder "Why should we believe the gods... or the priest who says what the gods said...?")


C should be self evidently true the moment you read it. It is the first conclusion you reach because it can not be false because it is self referencing. If it is false, the whole riddle is gibberish.
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