guilty_or_location_deduction Advanced Worksheet: Focus on exam-oriented approach guilty_or_location_deduction ADVANCED

Step 1: If Vikram is truth-teller, then:
- Divya took the emerald (from statement 1).
- Exactly one person took the item (from statement 4).
- Divya says 'I did not take it' - FALSE, so Divya is liar (consistent).
- Meera says 'Vikram is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Vikram=T, Divya=L, Meera=T with Divya as thief.

Step 2: If Vikram is liar, then:
- Divya did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Divya didn't take it, someone else must have.
- Meera says 'Vikram is truth-teller' - FALSE, so Meera is liar.
- Divya says 'I did not take it' - TRUE, so Divya is truth-teller.
- This gives Vikram=L, Divya=T, Meera=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Divya took the emerald.

Step 1: If Anita is truth-teller, then:
- Neha took the emerald (from statement 1).
- Exactly one person took the item (from statement 4).
- Neha says 'I did not take it' - FALSE, so Neha is liar (consistent).
- Meera says 'Anita is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Anita=T, Neha=L, Meera=T with Neha as thief.

Step 2: If Anita is liar, then:
- Neha did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Neha didn't take it, someone else must have.
- Meera says 'Anita is truth-teller' - FALSE, so Meera is liar.
- Neha says 'I did not take it' - TRUE, so Neha is truth-teller.
- This gives Anita=L, Neha=T, Meera=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Neha took the emerald.

Step 1: If Deepa is truth-teller, then:
- Leena took the emerald (from statement 1).
- Exactly one person took the item (from statement 4).
- Leena says 'I did not take it' - FALSE, so Leena is liar (consistent).
- Manoj says 'Deepa is truth-teller' - TRUE, so Manoj is truth-teller.
This gives: Deepa=T, Leena=L, Manoj=T with Leena as thief.

Step 2: If Deepa is liar, then:
- Leena did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Leena didn't take it, someone else must have.
- Manoj says 'Deepa is truth-teller' - FALSE, so Manoj is liar.
- Leena says 'I did not take it' - TRUE, so Leena is truth-teller.
- This gives Deepa=L, Leena=T, Manoj=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Leena took the emerald.

Step 1: If Divya is truth-teller, then:
- Leena took the pearl (from statement 1).
- Exactly one person took the item (from statement 4).
- Leena says 'I did not take it' - FALSE, so Leena is liar (consistent).
- Gaurav says 'Divya is truth-teller' - TRUE, so Gaurav is truth-teller.
This gives: Divya=T, Leena=L, Gaurav=T with Leena as thief.

Step 2: If Divya is liar, then:
- Leena did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Leena didn't take it, someone else must have.
- Gaurav says 'Divya is truth-teller' - FALSE, so Gaurav is liar.
- Leena says 'I did not take it' - TRUE, so Leena is truth-teller.
- This gives Divya=L, Leena=T, Gaurav=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Leena took the pearl.

Step 1: If Divya is truth-teller, then:
- Priya took the ruby (from statement 1).
- Exactly one person took the item (from statement 4).
- Priya says 'I did not take it' - FALSE, so Priya is liar (consistent).
- Harsha says 'Divya is truth-teller' - TRUE, so Harsha is truth-teller.
This gives: Divya=T, Priya=L, Harsha=T with Priya as thief.

Step 2: If Divya is liar, then:
- Priya did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Priya didn't take it, someone else must have.
- Harsha says 'Divya is truth-teller' - FALSE, so Harsha is liar.
- Priya says 'I did not take it' - TRUE, so Priya is truth-teller.
- This gives Divya=L, Priya=T, Harsha=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Priya took the ruby.

Step 1: If Sanjay is truth-teller, then:
- Kiran took the ruby (from statement 1).
- Exactly one person took the item (from statement 4).
- Kiran says 'I did not take it' - FALSE, so Kiran is liar (consistent).
- Ravi says 'Sanjay is truth-teller' - TRUE, so Ravi is truth-teller.
This gives: Sanjay=T, Kiran=L, Ravi=T with Kiran as thief.

Step 2: If Sanjay is liar, then:
- Kiran did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Kiran didn't take it, someone else must have.
- Ravi says 'Sanjay is truth-teller' - FALSE, so Ravi is liar.
- Kiran says 'I did not take it' - TRUE, so Kiran is truth-teller.
- This gives Sanjay=L, Kiran=T, Ravi=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Kiran took the ruby.

Step 1: If Amit is truth-teller, then:
- Neha took the diamond (from statement 1).
- Exactly one person took the item (from statement 4).
- Neha says 'I did not take it' - FALSE, so Neha is liar (consistent).
- Vikram says 'Amit is truth-teller' - TRUE, so Vikram is truth-teller.
This gives: Amit=T, Neha=L, Vikram=T with Neha as thief.

Step 2: If Amit is liar, then:
- Neha did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Neha didn't take it, someone else must have.
- Vikram says 'Amit is truth-teller' - FALSE, so Vikram is liar.
- Neha says 'I did not take it' - TRUE, so Neha is truth-teller.
- This gives Amit=L, Neha=T, Vikram=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Neha took the diamond.

Step 1: If Priya is truth-teller, then:
- Anita took the gold coin (from statement 1).
- Exactly one person took the item (from statement 4).
- Anita says 'I did not take it' - FALSE, so Anita is liar (consistent).
- Meera says 'Priya is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Priya=T, Anita=L, Meera=T with Anita as thief.

Step 2: If Priya is liar, then:
- Anita did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Anita didn't take it, someone else must have.
- Meera says 'Priya is truth-teller' - FALSE, so Meera is liar.
- Anita says 'I did not take it' - TRUE, so Anita is truth-teller.
- This gives Priya=L, Anita=T, Meera=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Anita took the gold coin.

Step 1: If Neha is truth-teller, then:
- Deepa took the ruby (from statement 1).
- Exactly one person took the item (from statement 4).
- Deepa says 'I did not take it' - FALSE, so Deepa is liar (consistent).
- Pooja says 'Neha is truth-teller' - TRUE, so Pooja is truth-teller.
This gives: Neha=T, Deepa=L, Pooja=T with Deepa as thief.

Step 2: If Neha is liar, then:
- Deepa did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Deepa didn't take it, someone else must have.
- Pooja says 'Neha is truth-teller' - FALSE, so Pooja is liar.
- Deepa says 'I did not take it' - TRUE, so Deepa is truth-teller.
- This gives Neha=L, Deepa=T, Pooja=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Deepa took the ruby.

Step 1: If Meera is truth-teller, then:
- Divya took the crystal (from statement 1).
- Exactly one person took the item (from statement 4).
- Divya says 'I did not take it' - FALSE, so Divya is liar (consistent).
- Amit says 'Meera is truth-teller' - TRUE, so Amit is truth-teller.
This gives: Meera=T, Divya=L, Amit=T with Divya as thief.

Step 2: If Meera is liar, then:
- Divya did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Divya didn't take it, someone else must have.
- Amit says 'Meera is truth-teller' - FALSE, so Amit is liar.
- Divya says 'I did not take it' - TRUE, so Divya is truth-teller.
- This gives Meera=L, Divya=T, Amit=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Divya took the crystal.

Step 1: If Leena is truth-teller, then:
- Meera took the bronze medal (from statement 1).
- Exactly one person took the item (from statement 4).
- Meera says 'I did not take it' - FALSE, so Meera is liar (consistent).
- Priya says 'Leena is truth-teller' - TRUE, so Priya is truth-teller.
This gives: Leena=T, Meera=L, Priya=T with Meera as thief.

Step 2: If Leena is liar, then:
- Meera did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Meera didn't take it, someone else must have.
- Priya says 'Leena is truth-teller' - FALSE, so Priya is liar.
- Meera says 'I did not take it' - TRUE, so Meera is truth-teller.
- This gives Leena=L, Meera=T, Priya=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Meera took the bronze medal.

Step 1: If Gaurav is truth-teller, then:
- Divya took the crystal (from statement 1).
- Exactly one person took the item (from statement 4).
- Divya says 'I did not take it' - FALSE, so Divya is liar (consistent).
- Anita says 'Gaurav is truth-teller' - TRUE, so Anita is truth-teller.
This gives: Gaurav=T, Divya=L, Anita=T with Divya as thief.

Step 2: If Gaurav is liar, then:
- Divya did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Divya didn't take it, someone else must have.
- Anita says 'Gaurav is truth-teller' - FALSE, so Anita is liar.
- Divya says 'I did not take it' - TRUE, so Divya is truth-teller.
- This gives Gaurav=L, Divya=T, Anita=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Divya took the crystal.

Step 1: If Deepa is truth-teller, then:
- Neha took the pearl (from statement 1).
- Exactly one person took the item (from statement 4).
- Neha says 'I did not take it' - FALSE, so Neha is liar (consistent).
- Meera says 'Deepa is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Deepa=T, Neha=L, Meera=T with Neha as thief.

Step 2: If Deepa is liar, then:
- Neha did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Neha didn't take it, someone else must have.
- Meera says 'Deepa is truth-teller' - FALSE, so Meera is liar.
- Neha says 'I did not take it' - TRUE, so Neha is truth-teller.
- This gives Deepa=L, Neha=T, Meera=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Neha took the pearl.

Step 1: If Divya is truth-teller, then:
- Sunil took the diamond (from statement 1).
- Exactly one person took the item (from statement 4).
- Sunil says 'I did not take it' - FALSE, so Sunil is liar (consistent).
- Manoj says 'Divya is truth-teller' - TRUE, so Manoj is truth-teller.
This gives: Divya=T, Sunil=L, Manoj=T with Sunil as thief.

Step 2: If Divya is liar, then:
- Sunil did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Sunil didn't take it, someone else must have.
- Manoj says 'Divya is truth-teller' - FALSE, so Manoj is liar.
- Sunil says 'I did not take it' - TRUE, so Sunil is truth-teller.
- This gives Divya=L, Sunil=T, Manoj=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Sunil took the diamond.

Step 1: If Farhan is truth-teller, then:
- Priya took the gold coin (from statement 1).
- Exactly one person took the item (from statement 4).
- Priya says 'I did not take it' - FALSE, so Priya is liar (consistent).
- Kiran says 'Farhan is truth-teller' - TRUE, so Kiran is truth-teller.
This gives: Farhan=T, Priya=L, Kiran=T with Priya as thief.

Step 2: If Farhan is liar, then:
- Priya did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Priya didn't take it, someone else must have.
- Kiran says 'Farhan is truth-teller' - FALSE, so Kiran is liar.
- Priya says 'I did not take it' - TRUE, so Priya is truth-teller.
- This gives Farhan=L, Priya=T, Kiran=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Priya took the gold coin.

Step 1: If Neha is truth-teller, then:
- Rohan took the crystal (from statement 1).
- Exactly one person took the item (from statement 4).
- Rohan says 'I did not take it' - FALSE, so Rohan is liar (consistent).
- Anita says 'Neha is truth-teller' - TRUE, so Anita is truth-teller.
This gives: Neha=T, Rohan=L, Anita=T with Rohan as thief.

Step 2: If Neha is liar, then:
- Rohan did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Rohan didn't take it, someone else must have.
- Anita says 'Neha is truth-teller' - FALSE, so Anita is liar.
- Rohan says 'I did not take it' - TRUE, so Rohan is truth-teller.
- This gives Neha=L, Rohan=T, Anita=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Rohan took the crystal.

Step 1: If Sanjay is truth-teller, then:
- Neha took the pearl (from statement 1).
- Exactly one person took the item (from statement 4).
- Neha says 'I did not take it' - FALSE, so Neha is liar (consistent).
- Deepa says 'Sanjay is truth-teller' - TRUE, so Deepa is truth-teller.
This gives: Sanjay=T, Neha=L, Deepa=T with Neha as thief.

Step 2: If Sanjay is liar, then:
- Neha did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Neha didn't take it, someone else must have.
- Deepa says 'Sanjay is truth-teller' - FALSE, so Deepa is liar.
- Neha says 'I did not take it' - TRUE, so Neha is truth-teller.
- This gives Sanjay=L, Neha=T, Deepa=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Neha took the pearl.

Step 1: If Priya is truth-teller, then:
- Anita took the artifact (from statement 1).
- Exactly one person took the item (from statement 4).
- Anita says 'I did not take it' - FALSE, so Anita is liar (consistent).
- Rahul says 'Priya is truth-teller' - TRUE, so Rahul is truth-teller.
This gives: Priya=T, Anita=L, Rahul=T with Anita as thief.

Step 2: If Priya is liar, then:
- Anita did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Anita didn't take it, someone else must have.
- Rahul says 'Priya is truth-teller' - FALSE, so Rahul is liar.
- Anita says 'I did not take it' - TRUE, so Anita is truth-teller.
- This gives Priya=L, Anita=T, Rahul=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Anita took the artifact.

Step 1: If Harsha is truth-teller, then:
- Ravi took the diamond (from statement 1).
- Exactly one person took the item (from statement 4).
- Ravi says 'I did not take it' - FALSE, so Ravi is liar (consistent).
- Priya says 'Harsha is truth-teller' - TRUE, so Priya is truth-teller.
This gives: Harsha=T, Ravi=L, Priya=T with Ravi as thief.

Step 2: If Harsha is liar, then:
- Ravi did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Ravi didn't take it, someone else must have.
- Priya says 'Harsha is truth-teller' - FALSE, so Priya is liar.
- Ravi says 'I did not take it' - TRUE, so Ravi is truth-teller.
- This gives Harsha=L, Ravi=T, Priya=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Ravi took the diamond.

Step 1: If Manoj is truth-teller, then:
- Sunil took the artifact (from statement 1).
- Exactly one person took the item (from statement 4).
- Sunil says 'I did not take it' - FALSE, so Sunil is liar (consistent).
- Deepa says 'Manoj is truth-teller' - TRUE, so Deepa is truth-teller.
This gives: Manoj=T, Sunil=L, Deepa=T with Sunil as thief.

Step 2: If Manoj is liar, then:
- Sunil did NOT take the item (statement 1 false).
- 'Exactly one person took it' is FALSE → either 0 or 2+ people took it.
- Since Sunil didn't take it, someone else must have.
- Deepa says 'Manoj is truth-teller' - FALSE, so Deepa is liar.
- Sunil says 'I did not take it' - TRUE, so Sunil is truth-teller.
- This gives Manoj=L, Sunil=T, Deepa=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Sunil took the artifact.