guilty_or_location_deduction: Worksheet 6 - Intermediate-Advanced Practice guilty_or_location_deduction INTERMEDIATE ADVANCED

Step 1: If Anita is truth-teller, then:
- Kiran took the emerald (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).
- Harsha says 'Anita is truth-teller' - TRUE, so Harsha is truth-teller.
This gives: Anita=T, Kiran=L, Harsha=T with Kiran as thief.

Step 2: If Anita 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.
- Harsha says 'Anita is truth-teller' - FALSE, so Harsha is liar.
- Kiran says 'I did not take it' - TRUE, so Kiran is truth-teller.
- This gives Anita=L, Kiran=T, Harsha=L with no thief identified - INCONSISTENT.

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

Step 1: If Anita is truth-teller, then:
- Meera took the emerald (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).
- Pooja says 'Anita is truth-teller' - TRUE, so Pooja is truth-teller.
This gives: Anita=T, Meera=L, Pooja=T with Meera as thief.

Step 2: If Anita 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.
- Pooja says 'Anita is truth-teller' - FALSE, so Pooja is liar.
- Meera says 'I did not take it' - TRUE, so Meera is truth-teller.
- This gives Anita=L, Meera=T, Pooja=L with no thief identified - INCONSISTENT.

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

Step 1: If Priya is truth-teller, then:
- Kiran took the pearl (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).
- Gaurav says 'Priya is truth-teller' - TRUE, so Gaurav is truth-teller.
This gives: Priya=T, Kiran=L, Gaurav=T with Kiran as thief.

Step 2: If Priya 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.
- Gaurav says 'Priya is truth-teller' - FALSE, so Gaurav is liar.
- Kiran says 'I did not take it' - TRUE, so Kiran is truth-teller.
- This gives Priya=L, Kiran=T, Gaurav=L with no thief identified - INCONSISTENT.

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

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

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

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

Step 1: If Neha is truth-teller, then:
- Deepa took the silver ring (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).
- Meera says 'Neha is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Neha=T, Deepa=L, Meera=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.
- Meera says 'Neha is truth-teller' - FALSE, so Meera is liar.
- Deepa says 'I did not take it' - TRUE, so Deepa is truth-teller.
- This gives Neha=L, Deepa=T, Meera=L with no thief identified - INCONSISTENT.

Therefore, the only consistent solution is Deepa took the silver ring.

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

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

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

Step 1: If Sanjay is truth-teller, then:
- Deepa took the pearl (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).
- Neha says 'Sanjay is truth-teller' - TRUE, so Neha is truth-teller.
This gives: Sanjay=T, Deepa=L, Neha=T with Deepa as thief.

Step 2: If Sanjay 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.
- Neha says 'Sanjay is truth-teller' - FALSE, so Neha is liar.
- Deepa says 'I did not take it' - TRUE, so Deepa is truth-teller.
- This gives Sanjay=L, Deepa=T, Neha=L with no thief identified - INCONSISTENT.

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

Step 1: If Rahul is truth-teller, then:
- Priya took the pearl (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).
- Meera says 'Rahul is truth-teller' - TRUE, so Meera is truth-teller.
This gives: Rahul=T, Priya=L, Meera=T with Priya as thief.

Step 2: If Rahul 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.
- Meera says 'Rahul is truth-teller' - FALSE, so Meera is liar.
- Priya says 'I did not take it' - TRUE, so Priya is truth-teller.
- This gives Rahul=L, Priya=T, Meera=L with no thief identified - INCONSISTENT.

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

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

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

Therefore, the only consistent solution is Rahul took the silver ring.

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

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

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

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

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

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

Step 1: If Pooja is truth-teller, then:
- Rohan took the pearl (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).
- Manoj says 'Pooja is truth-teller' - TRUE, so Manoj is truth-teller.
This gives: Pooja=T, Rohan=L, Manoj=T with Rohan as thief.

Step 2: If Pooja 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.
- Manoj says 'Pooja is truth-teller' - FALSE, so Manoj is liar.
- Rohan says 'I did not take it' - TRUE, so Rohan is truth-teller.
- This gives Pooja=L, Rohan=T, Manoj=L with no thief identified - INCONSISTENT.

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

Step 1: If Manoj is truth-teller, then:
- Rohan took the gold coin (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).
- Rahul says 'Manoj is truth-teller' - TRUE, so Rahul is truth-teller.
This gives: Manoj=T, Rohan=L, Rahul=T with Rohan as thief.

Step 2: If Manoj 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.
- Rahul says 'Manoj is truth-teller' - FALSE, so Rahul is liar.
- Rohan says 'I did not take it' - TRUE, so Rohan is truth-teller.
- This gives Manoj=L, Rohan=T, Rahul=L with no thief identified - INCONSISTENT.

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

Step 1: If Pooja is truth-teller, then:
- Anita took the diamond (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).
- Rohan says 'Pooja is truth-teller' - TRUE, so Rohan is truth-teller.
This gives: Pooja=T, Anita=L, Rohan=T with Anita as thief.

Step 2: If Pooja 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.
- Rohan says 'Pooja is truth-teller' - FALSE, so Rohan is liar.
- Anita says 'I did not take it' - TRUE, so Anita is truth-teller.
- This gives Pooja=L, Anita=T, Rohan=L with no thief identified - INCONSISTENT.

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

Step 1: If Sunil is truth-teller, then:
- Deepa took the crystal (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).
- Gaurav says 'Sunil is truth-teller' - TRUE, so Gaurav is truth-teller.
This gives: Sunil=T, Deepa=L, Gaurav=T with Deepa as thief.

Step 2: If Sunil 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.
- Gaurav says 'Sunil is truth-teller' - FALSE, so Gaurav is liar.
- Deepa says 'I did not take it' - TRUE, so Deepa is truth-teller.
- This gives Sunil=L, Deepa=T, Gaurav=L with no thief identified - INCONSISTENT.

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

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

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

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

Step 1: If Rohan 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).
- Manoj says 'Rohan is truth-teller' - TRUE, so Manoj is truth-teller.
This gives: Rohan=T, Deepa=L, Manoj=T with Deepa as thief.

Step 2: If Rohan 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.
- Manoj says 'Rohan is truth-teller' - FALSE, so Manoj is liar.
- Deepa says 'I did not take it' - TRUE, so Deepa is truth-teller.
- This gives Rohan=L, Deepa=T, Manoj=L with no thief identified - INCONSISTENT.

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

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

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

Therefore, the only consistent solution is Harsha took the sapphire.

Step 1: If Meera 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).
- Pooja says 'Meera is truth-teller' - TRUE, so Pooja is truth-teller.
This gives: Meera=T, Anita=L, Pooja=T with Anita as thief.

Step 2: If Meera 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.
- Pooja says 'Meera is truth-teller' - FALSE, so Pooja is liar.
- Anita says 'I did not take it' - TRUE, so Anita is truth-teller.
- This gives Meera=L, Anita=T, Pooja=L with no thief identified - INCONSISTENT.

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

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

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

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