Can you solve the riddle of Pandora’s box? - Alex Rosenthal

Key Concepts:

• Logic puzzle involving deduction and multiple perspectives.
• Modeling knowledge and reasoning of different characters (Pandora, Abaddon, Beelzebub).
• Importance of statement order in logic problems.
• Elimination based on what others don't know.

Problem Setup:

• Pandora accidentally released evils from a box.
• 10 minor imps (wrath, greed, gluttony, sloth) and 3 greater demons remain.
• The goal is to identify which imp is Hope.
• Abaddon (A) knows the imp type.
• Beelzebub (B) knows the number of eyes.

Step-by-Step Solution:

1. Initial State: A table representing all possible imps and their attributes (type and number of eyes) is constructed.

2. Statement 1: "I know you don’t know which one she is."

   • A (Abaddon) knows the imp type, but not the specific imp.
   • A reasons that if Hope had a unique number of eyes (3 or 5), B (Beelzebub) would immediately know which imp she is.
   • Therefore, A knows that Hope doesn't have a unique number of eyes.
   • Crucial Deduction: This eliminates entire rows (imp types) containing imps with 3 or 5 eyes, not just the individual imps with those eye numbers. This is because if A knew the imp was of a type that could have 3 or 5 eyes, he couldn't be sure B wouldn't know the answer.
   • This eliminates the wrath and greed imp types.

3. Statement 2: "Well, I didn’t before, but now I know."

   • B (Beelzebub) now knows which imp is Hope.
   • B is an expert logician and has already deduced that wrath and greed are impossible.
   • For B to know the answer, there must be only one possible imp with that number of eyes remaining.
   • This eliminates any imps in columns (eye numbers) where there are multiple possibilities.
   • This eliminates the one-eyed imps.

4. Statement 3: "Then I also know which one she is."

   • A (Abaddon) now knows which imp is Hope.
   • For A to know the answer, there must be only one possible imp of that type remaining.
   • This means only one imp is left in that row.
   • Therefore, Hope must be the six-eyed sloth imp.

Conclusion:

• By carefully considering the knowledge and reasoning of both Abaddon and Beelzebub, and the order of their statements, Pandora can deduce that Hope is the six-eyed sloth imp.
• The puzzle highlights the importance of understanding not just what information is available, but also what others don't know and how that affects their reasoning.
• The solution requires a multi-layered approach, modeling the perspectives of different characters and updating their knowledge based on the dialogue.