guilty_or_location_deduction: Worksheet 2 - Beginner Practice guilty_or_location_deduction BEGINNER

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

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

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

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

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

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

Step 1: If Neha is truth-teller, then:
- Divya took the ruby (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 'Neha is truth-teller' - TRUE, so Anita is truth-teller.
This gives: Neha=T, Divya=L, Anita=T with Divya as thief.

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

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

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

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

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

Step 1: If Manoj 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).
- Sanjay says 'Manoj is truth-teller' - TRUE, so Sanjay is truth-teller.
This gives: Manoj=T, Sunil=L, Sanjay=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.
- Sanjay says 'Manoj is truth-teller' - FALSE, so Sanjay is liar.
- Sunil says 'I did not take it' - TRUE, so Sunil is truth-teller.
- This gives Manoj=L, Sunil=T, Sanjay=L with no thief identified - INCONSISTENT.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Step 1: If Harsha 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).
- Rahul says 'Harsha is truth-teller' - TRUE, so Rahul is truth-teller.
This gives: Harsha=T, Divya=L, Rahul=T with Divya as thief.

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

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

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

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

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

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

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

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

Step 1: If Manoj 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 'Manoj is truth-teller' - TRUE, so Rahul is truth-teller.
This gives: Manoj=T, Anita=L, Rahul=T with Anita as thief.

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

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

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

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

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

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

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

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

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

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