Pandora's Predicament: A Logic Puzzle

Key Points

• Initial Situation: Pandora accidentally opens a box releasing various imps and demons, including a crucial character, Hope, disguised as an imp.

• Demon Dialogue:

  • A greater demon reveals Hope is disguised and provides cryptic clues.
  • Abaddon knows the type of imp Hope is, but not her identity.
  • Beelzebub learns Hope's eye count, allowing eventual identification.

• Problem Framework:

  • Originally inspired by Cheryl’s birthday problem from 2015.
  • Requires analyzing the dialogue from multiple perspectives (Pandora, Abaddon, and Beelzebub).

Logical Analysis

1. Abaddon's Insight:

   • Abaddon states to Beelzebub, "I know you don’t know which one she is."
   • Abaddon knows the type but not the identity since multiple imps exist per type.
   • The implication: If Hope were of a type with distinct eye counts (like greed or wrath), Beelzebub could identify her.

2. Eliminating Possibilities:

   • Eliminate entire rows of imps with unique eye counts that would allow Beelzebub to identify Hope.
   • After considering Abaddon’s knowledge, greed and wrath types are eliminated.

3. Beelzebub's Perspective:

   • Beelzebub, now aware of eliminated types, can identify Hope by the eye count.
   • Thus, eliminate imps with non-unique eye counts among remaining types (removing both one-eyed imps).

4. Final Insight:

   • Back to Abaddon: With a refined analysis, there’s only one option for Hope.
   • Hope is identified as the six-eyed sloth imp.

Conclusion

• Pandora successfully captures Hope with newfound clarity, restoring some semblance of order amidst chaos.