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zakruti.com » Knowledge, science, education » TED-Ed
The dungeon master's riddle - Alex Rosenthal

The dungeon master's riddle - Alex Rosenthal

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Rating: 4.0; Vote: 1
A group of adventurers has broken into your lair. Can you figure out who the cleric is before they start casting spells -- Yet another party of adventurers has broken into your lair to slay your minions and steal your treasures. Judging by the trail of destruction, you’re up against a fighter, a rogue, and a cleric. The first two won’t be a problem for a powerful necromancer like you but the clerics' spells are trouble. Can you figure out which adventurer is the cleric before it’s too late Alex Rosenthal shows how.
Date: 2024-10-23

Comments and reviews: 20


I started by going off of Agan's statement, since the and seemed more restrictive. What I got seems to be (to me) a simpler solution. Here is my write-up:
Statements for reference:
Agan: _Beorn is not both a lying-potion drinker and a cleric. _
Beorn: _Either Agan drank a lying-potion or I am not a cleric. _
Cedar: _The cleric drank a lying-potion. _
The solution:
1. Assume Agan drank a lying-potion:
Agan Beorn Cedar
Lying Y
Cleric
2. By Agan's (lying) statement, Beorn is both a lying-potion drinker and a cleric.
Agan Beorn Cedar
Lying Y Y
Cleric Y
3. However, Beorn's (lying) statement is true, as Agan drank a lying-potion. So, (by contradiction) Agan must have drunk a truth-potion.
Agan Beorn Cedar
Lying X
Cleric
4. Assume Beorn drank a lying-potion. By Agan's (truthful) statement, Beorn is then not a cleric.
Agan Beorn Cedar
Lying X Y
Cleric X
5. However, Beorn's (lying) statement is true, as Beorn is not a cleric. So, (by contradiction) Beorn must have drunk a truth-potion.
Agan Beorn Cedar
Lying X X
Cleric
6. By Beorn's (truthful) statement, Beorn is not a cleric.
Agan Beorn Cedar
Lying X X
Cleric X
7. If Cedar is telling the truth, there is no cleric because everyone drank a truth-potion. So, Cedar must be lying, making Agan the cleric.
Agan Beorn Cedar
Lying X X Y
Cleric Y X X
Interestingly, Beorn's statement of exclusivity was not a factor in determining this solution, which is nice because I wasn't sure how to interpret it when solving this puzzle. However, I assume part of the idea behind this puzzle is to expose people to exclusive-or operations.

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There's a simpler way of solving this:
Step 1: Assume Cedar is the cleric.
Then his statement is equivalent to 'I am lying', which is self-contradictory.
Thus, Cedar is not the cleric.
Step 2: Assume Agan is lying.
Then Beorn must be both a liar and the cleric. But then, 'Agan drank a lying potion' is true and 'I am not a cleric' is false, making Beorn's either-or statement correct, which contradicts him being a liar.
Thus Agan must be telling the truth.
Step 3: Assume Beorn is lying.
Then, per Agan's statement, which from step 1 we know to be true, he cannot also be the cleric. But then, 'Agan drank a lying potion' is false and 'I am not a cleric' is true, making Beorn's either-or statement correct, which contradicts him being a liar.
Thus Beorn must be telling the truth.
Step 4: We know from step 3 that Beorn is telling the truth, and we know from step 2 that Agan didn't drink the lying potion, so the 'I am not a cleric' part of the either-or statement must be the true part. Thus, one of the other two must be the cleric. And per step 1, we know it isn't Cedar, so that leaves Agan as the Cleric by process of elimination.
The truthfulness of Cedar's statement is irrelevant to the solution, so ignoring it leads to simpler logic. Just thinking about the problem for a bit makes this obvious: none of the other statements refer to Cedar at all, so we can't determine its truthfulness from them. And in order to determine its truthfulness from the statement itself, we'd need to know who the cleric is, and if we know that, we've already solved the problem.

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You can do the entire problem without any trial error using boolean algebra.
Step 0) Same reasoning as the video. Cedar is not the cleric based off his own statement. However, we're going to completely ignore Cedars' statement from now on.
Step 1) Formalizing as logical statements
A = Agans' statement is true
B = Beorns' statment is true
Z = Beorn is cleric
By definition:
Agan drank the lying potion =! A
Beorn drank the lying potion =! B
Converting Agans' and Beorns' statements:
A =! B & Z)
B =! A XOR! Z
Subsituting for A in B:
B =! B & Z) XOR! Z =! B & Z) XOR! Z
Step 2) Solving B =! B & Z) XOR! Z
B =! B & Z) & Z) |! B & Z) &! Z) // by definition of XOR
=! B & Z & Z) |! B & Z) &! Z) // & associativity
=! B & Z) |! B & Z) &! Z) // idempotence
=! B & Z) | (B |! Z) &! Z) // demorgans
=! B & Z) |! Z // absorption
=! B |! Z // absorption
B | B = B |! B |! Z) // equality
B = B |! B |! Z) // idemptoence
B = (B |! B) |! Z // | associativity
B = T |! Z // complement
B =! Z // identity
Substituting B for! Z
B =! Z |! Z
B = Z |! Z
B = T // complement
Z = F
Step 3) Elimination
Since Cedar nor Beorn are the cleric it must be Agan.
side note: The necromancer only GUESSES that there is a cleric among the three based off the trail of destruction. Additionally the problem statement at 1: 40 never states there must be a cleric either. So technically it is possible there is no cleric, and that would satisfy all the statements.

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1. If A is False, then B is False and B is cleric. But when B is false, A is true and B is cleric or A is false and B is not cleric must be true
1. 1 So A is True
1. 2 B is true or B is not cleric
2. When C is true, A and C cannot be cleric (cleric -> false, So B is cleric and B is false. This contradicts with 1. 2
2. 1 So C is False
2. 2 A is cleric or (B is True and B is cleric)
2. 3 C is not cleric (else A and B are both not cleric, 2. 2 is false)
3. from 2. 2, if A is not cleric, B is True and B is cleric. But when B is true, A is true and B is not cleric or A is false and B is cleric must be true. 1. 1 contradicts this
3. 1 A is cleric, so B and C is not cleric
3. 2 from 1. 2, B is true
Ans: A true, B true, C false, A is cleric
Edit:
I got it right!
I don't really like this kind of logic puzzles in english though, too many possible interpretations. I solve it through propositional logic, but it is a fuss to formalize it properly
Example:
Agan's word can be formalized as (B and Cleric_B, or (B and Cleric_B)
Beorn's words can be formalized as (A or Cleric_B, or [ (A and Cleric_B) or (A and Cleric_B)]
Cedar's words can be formalized as (Cleric_x -> x(x=A, B, C, or (Cleric_x x(x=A, B, C)
I chose the right ones, but it could be misleading for other people

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I figured this out by leaving cedars statement to the end: if agan is a liar, that means beorn has to be both a liar and a cleric, which turns down your options a lot. then you check beorns possibilities, since hes a liar, either agan is a liar and beorn isnt a cleric, or agan is telling the truth and beorn is a cleric. however, agan is a liar, so the first option has to be correct. but we already called beorn a cleric, so agan cant be lying. this means agan must be telling the truth. Since beorn cant be both a liar and a cleric, we can assume either he is a liar, a cleric, or neither. if hetells the truth, then by his own statement he must not be the cleric. if he lies, then that shows agan is telling the truth and beorn is the cleric. this doesnt work with agans statement (beorn cant be both a liar and a cleric. beorn must be telling the truth, and that leaves cedar as the only liar. the cleric has to be telling the truth then, and since beorn is telling the truth and agan isnt a liar, beorn has to not be a cleric. this leaves only agan as the cleric: )
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I found an easier way of thinking about this one involving checking each possible person to be the cleric. Also, Agan's statement can be reworded more clearly; NOT (A AND B) is the same as (NOT A) OR (NOT B, so Agan's statement can be recast as Either Beorn is T or Beorn is not a cleric.
If Cedar is the cleric, his statement is basically I am lying, which is a contradiction, so he can't be the cleric.
If Beorn is the cleric, both his and Agan's statements have an or Beorn is not the cleric clause that can be dropped (since A OR false is the same as A. So Beorn says Agan is lying while Agan says Beorn is telling the truth, which is also a contradiction.
If Agan is the cleric, everything works. Agan and Beorn are both telling the truth since Beorn isn't the cleric, and Cedar is lying about Agan. So this is the only one that works, and Agan must be the cleric.
Edit: I interpreted either/or as being OR rather than XOR (both can be true in OR, but it didn't matter.

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I went like this: Cedar could not be the cleric because either is lying and therefore the cleric tells the truth so it's not him or he's telling the truth and then he can't be the cleric that is a liar. So I just eliminated him and didn't bother further with him.
Beorn said either Agan drank a lying potion or I'm not cleric. If he's lying, it means Agand's telling the truth AND he's the cleric. But if Agan's telling the truth it contradicts Beorn, it's impossible. So Beorn is telling the truth. So either Agan is lying or Beorn's not a cleric. Well, if Agan's lying it means Beorn is lying which we established is'nt true. So Agan didn't drink a lying potion so Beorn is not a cleric (by his statement. By process of elimination Agan is then the cleric.
We didn't need to assess if Cedar is telling the truth or not, we just needed to be able to rule him out for the process of elimination. And we can determine if Agan and Beorn are lying just with their 2 statements alone.

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The premise that they would answer that way is faulty. If they wish to win the battle, they would answer in some fashion that prevents you (the necromancer) from having any logical way to figure out who the cleric is. If all three say Blue Person is the cleric, then you cannot differentiate between two possibilities: Blue Person is the cleric and they're all under true-potion, or someone else is the cleric and they're all under lie-potion. Or what if they all say I am the cleric One of them will be the cleric, and the cleric has drunk true-potion, so that person says I am the cleric. And the other two are not the cleric, and they've both drunk lie-potion, and both say I am the cleric, which is a lie. But you don't know WHICH of them is the truthing cleric and which two are the lying non-clerics. There are probably other sets of answers that leave you no way to reason-it-out. And one of those answer-trios is the answer-trio they'd deploy.
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A real Lich would form an abomination from the hewn bits of the cleric's late party members, made sure the faces were animated and suffering so the cleric has an existential crisis, and be done in time to pour another cup of tea while you eagerly anticipate the birth of your latest aliven't cleric thrall. Which will be of pristine quality and capable of containing. just oodles of dark purpose. Far more than enough to defend the lair for a few centuries against any random band of adventurers silly enough to square up.
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The potions they drank will compel each to answer one question with either the truth or a lie.
They then proceed to answer Which of you is the cleric with a series of statements that do not actually answer the question. So either the potions don't actually work, or answer with either a true or a lie means they could just say any statement at all, as long as it's either a truth or a lie. Someone who drank a lie potion could answer Apples are not fruit.

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i got the truth-tellers and liars right but then somehow got to the conclusion Beorn was the cleric. i honestly don't know how
edit: oh wait i remember i figured the way Agon phrased his statement meant that Beorn was neither, and that would make the I am not a cleric part of Beorn's statement true.
They both said the same thing thing but the different phrasing threw me off.

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Thank you for this educative puzzle/riddle, I always confuse with this type of puzzle. For opinion, in this video, in REAL DnD or any RPG games, the party supposedly wore equipment that define their CLASS, but I'm pretty sure the adventurers wore the most simple clothes in order to confuse Lich King. And lastly, Do Cleric fall in love with Lich King
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Agan: Beorn is not both a lying potion drinker and a cleric
If Agan is lying you are saying that Beron is both (lying and a cleric. But Agan would also lie if either statement is wrong.
If Beron is a lying potion drinker but not a cleric, Agan would fave spoken a lie with his statement. This was not explaind, if I'm not mistaken.

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4: 53 You're not a monster.
But.
What if I'm the monster
What if I'm in the wrong
What if I'm the problem that's been hiding all along
What if I'm the one that killed you,
Every time I caved to guilt
What if I've been too kind to foes,
But a monster to ourselves
What if I'm the monster

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What a brilliant riddle! Alex Rosenthal does an incredible job of weaving storytelling with logic. The twists in the maze really keep you on your toes! I love how these riddles challenge our problem-solving skills while making us think outside the box. Who else is trying to solve it before watching the answer
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Step 1: Tell them at least two of you have green eyes
Step 2: Being perfect logicians, they will deduce that they all have green eyes after no one leaves on the first night
Step 3: Give Agan some of your treasure as a gift when she leaves on the second night
Step 4: Repeat steps 1 and 2 every Monday

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This was a fun riddle, but I think one thing that could be made clearer is that Beorn's statement is an exclusive or (although I believe it's still solvable if it is an inclusive or. Generally, either. or. is still an inclusive or in logic, even though colloquially it's thought of as exclusive or.
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so if I had the choice to let the whole world go through global warming and everyone had to Parrish but I got what I didn't need as long as I did that or I can go without with what I don't need and i have to let a million Parish to save the rest of them what do I do
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Cedar is irrelevant in the riddle
None of the other characters mention him in their statements
Once you determine he isn't the Cleric then his statement is the Cleric is Lying which can either be true or a lie, so that information is also useless

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REALLY, putting in two different sneaky conditions that weren't in the list:
1. Putting in an x/or instead of the normal and/or.
2. Requiring that they don't drink all truth or all lying potions.
I got it right anyway, but that this is BS.

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