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

Let's solve step by step:

Step 1: Assume Anita is a liar.
→ Anita's statement 'Ravi is a truth-teller' is FALSE → Ravi is a liar.
→ Divya says 'Anita is a liar' - this is TRUE (since Anita is liar).
→ If Divya tells truth, then Divya is truth-teller.
→ Ravi (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Ravi=L, Divya=T, Anita=L (two liars, one truth-teller).

Step 2: Assume Anita is a truth-teller.
→ Anita's statement 'Ravi is a truth-teller' is TRUE → Ravi is truth-teller.
→ Ravi (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Anita is a liar' - FALSE (since Anita is truth) → consistent.
This gives: Ravi=T, Divya=L, Anita=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Anita also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Ravi and Anita are truth-tellers, Divya is a liar.

Let's solve step by step:

Step 1: Assume Rahul is a liar.
→ Rahul's statement 'Sunil is a truth-teller' is FALSE → Sunil is a liar.
→ Priya says 'Rahul is a liar' - this is TRUE (since Rahul is liar).
→ If Priya tells truth, then Priya is truth-teller.
→ Sunil (liar) says 'Priya is a liar' - FALSE (since Priya is truth) → consistent.
This gives: Sunil=L, Priya=T, Rahul=L (two liars, one truth-teller).

Step 2: Assume Rahul is a truth-teller.
→ Rahul's statement 'Sunil is a truth-teller' is TRUE → Sunil is truth-teller.
→ Sunil (truth) says 'Priya is a liar' → TRUE → Priya is liar.
→ Priya (liar) says 'Rahul is a liar' - FALSE (since Rahul is truth) → consistent.
This gives: Sunil=T, Priya=L, Rahul=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Rahul also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sunil and Rahul are truth-tellers, Priya is a liar.

Let's solve step by step:

Step 1: Assume Pooja is a liar.
→ Pooja's statement 'Leena is a truth-teller' is FALSE → Leena is a liar.
→ Farhan says 'Pooja is a liar' - this is TRUE (since Pooja is liar).
→ If Farhan tells truth, then Farhan is truth-teller.
→ Leena (liar) says 'Farhan is a liar' - FALSE (since Farhan is truth) → consistent.
This gives: Leena=L, Farhan=T, Pooja=L (two liars, one truth-teller).

Step 2: Assume Pooja is a truth-teller.
→ Pooja's statement 'Leena is a truth-teller' is TRUE → Leena is truth-teller.
→ Leena (truth) says 'Farhan is a liar' → TRUE → Farhan is liar.
→ Farhan (liar) says 'Pooja is a liar' - FALSE (since Pooja is truth) → consistent.
This gives: Leena=T, Farhan=L, Pooja=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Pooja also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Leena and Pooja are truth-tellers, Farhan is a liar.

Let's solve step by step:

Step 1: Assume Leena is a liar.
→ Leena's statement 'Harsha is a truth-teller' is FALSE → Harsha is a liar.
→ Ravi says 'Leena is a liar' - this is TRUE (since Leena is liar).
→ If Ravi tells truth, then Ravi is truth-teller.
→ Harsha (liar) says 'Ravi is a liar' - FALSE (since Ravi is truth) → consistent.
This gives: Harsha=L, Ravi=T, Leena=L (two liars, one truth-teller).

Step 2: Assume Leena is a truth-teller.
→ Leena's statement 'Harsha is a truth-teller' is TRUE → Harsha is truth-teller.
→ Harsha (truth) says 'Ravi is a liar' → TRUE → Ravi is liar.
→ Ravi (liar) says 'Leena is a liar' - FALSE (since Leena is truth) → consistent.
This gives: Harsha=T, Ravi=L, Leena=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Leena also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Harsha and Leena are truth-tellers, Ravi is a liar.

Let's solve step by step:

Step 1: Assume Leena is a liar.
→ Leena's statement 'Anita is a truth-teller' is FALSE → Anita is a liar.
→ Divya says 'Leena is a liar' - this is TRUE (since Leena is liar).
→ If Divya tells truth, then Divya is truth-teller.
→ Anita (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Anita=L, Divya=T, Leena=L (two liars, one truth-teller).

Step 2: Assume Leena is a truth-teller.
→ Leena's statement 'Anita is a truth-teller' is TRUE → Anita is truth-teller.
→ Anita (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Leena is a liar' - FALSE (since Leena is truth) → consistent.
This gives: Anita=T, Divya=L, Leena=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Leena also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Anita and Leena are truth-tellers, Divya is a liar.

Let's solve step by step:

Step 1: Assume Meera is a liar.
→ Meera's statement 'Farhan is a truth-teller' is FALSE → Farhan is a liar.
→ Amit says 'Meera is a liar' - this is TRUE (since Meera is liar).
→ If Amit tells truth, then Amit is truth-teller.
→ Farhan (liar) says 'Amit is a liar' - FALSE (since Amit is truth) → consistent.
This gives: Farhan=L, Amit=T, Meera=L (two liars, one truth-teller).

Step 2: Assume Meera is a truth-teller.
→ Meera's statement 'Farhan is a truth-teller' is TRUE → Farhan is truth-teller.
→ Farhan (truth) says 'Amit is a liar' → TRUE → Amit is liar.
→ Amit (liar) says 'Meera is a liar' - FALSE (since Meera is truth) → consistent.
This gives: Farhan=T, Amit=L, Meera=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Meera also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Farhan and Meera are truth-tellers, Amit is a liar.

Let's solve step by step:

Step 1: Assume Meera is a liar.
→ Meera's statement 'Farhan is a truth-teller' is FALSE → Farhan is a liar.
→ Ravi says 'Meera is a liar' - this is TRUE (since Meera is liar).
→ If Ravi tells truth, then Ravi is truth-teller.
→ Farhan (liar) says 'Ravi is a liar' - FALSE (since Ravi is truth) → consistent.
This gives: Farhan=L, Ravi=T, Meera=L (two liars, one truth-teller).

Step 2: Assume Meera is a truth-teller.
→ Meera's statement 'Farhan is a truth-teller' is TRUE → Farhan is truth-teller.
→ Farhan (truth) says 'Ravi is a liar' → TRUE → Ravi is liar.
→ Ravi (liar) says 'Meera is a liar' - FALSE (since Meera is truth) → consistent.
This gives: Farhan=T, Ravi=L, Meera=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Meera also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Farhan and Meera are truth-tellers, Ravi is a liar.

Let's solve step by step:

Step 1: Assume Deepa is a liar.
→ Deepa's statement 'Sanjay is a truth-teller' is FALSE → Sanjay is a liar.
→ Neha says 'Deepa is a liar' - this is TRUE (since Deepa is liar).
→ If Neha tells truth, then Neha is truth-teller.
→ Sanjay (liar) says 'Neha is a liar' - FALSE (since Neha is truth) → consistent.
This gives: Sanjay=L, Neha=T, Deepa=L (two liars, one truth-teller).

Step 2: Assume Deepa is a truth-teller.
→ Deepa's statement 'Sanjay is a truth-teller' is TRUE → Sanjay is truth-teller.
→ Sanjay (truth) says 'Neha is a liar' → TRUE → Neha is liar.
→ Neha (liar) says 'Deepa is a liar' - FALSE (since Deepa is truth) → consistent.
This gives: Sanjay=T, Neha=L, Deepa=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Deepa also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sanjay and Deepa are truth-tellers, Neha is a liar.

Let's solve step by step:

Step 1: Assume Farhan is a liar.
→ Farhan's statement 'Sunil is a truth-teller' is FALSE → Sunil is a liar.
→ Divya says 'Farhan is a liar' - this is TRUE (since Farhan is liar).
→ If Divya tells truth, then Divya is truth-teller.
→ Sunil (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Sunil=L, Divya=T, Farhan=L (two liars, one truth-teller).

Step 2: Assume Farhan is a truth-teller.
→ Farhan's statement 'Sunil is a truth-teller' is TRUE → Sunil is truth-teller.
→ Sunil (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Farhan is a liar' - FALSE (since Farhan is truth) → consistent.
This gives: Sunil=T, Divya=L, Farhan=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Farhan also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sunil and Farhan are truth-tellers, Divya is a liar.

Let's solve step by step:

Step 1: Assume Manoj is a liar.
→ Manoj's statement 'Sanjay is a truth-teller' is FALSE → Sanjay is a liar.
→ Meera says 'Manoj is a liar' - this is TRUE (since Manoj is liar).
→ If Meera tells truth, then Meera is truth-teller.
→ Sanjay (liar) says 'Meera is a liar' - FALSE (since Meera is truth) → consistent.
This gives: Sanjay=L, Meera=T, Manoj=L (two liars, one truth-teller).

Step 2: Assume Manoj is a truth-teller.
→ Manoj's statement 'Sanjay is a truth-teller' is TRUE → Sanjay is truth-teller.
→ Sanjay (truth) says 'Meera is a liar' → TRUE → Meera is liar.
→ Meera (liar) says 'Manoj is a liar' - FALSE (since Manoj is truth) → consistent.
This gives: Sanjay=T, Meera=L, Manoj=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Manoj also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sanjay and Manoj are truth-tellers, Meera is a liar.

Let's solve step by step:

Step 1: Assume Farhan is a liar.
→ Farhan's statement 'Sanjay is a truth-teller' is FALSE → Sanjay is a liar.
→ Ravi says 'Farhan is a liar' - this is TRUE (since Farhan is liar).
→ If Ravi tells truth, then Ravi is truth-teller.
→ Sanjay (liar) says 'Ravi is a liar' - FALSE (since Ravi is truth) → consistent.
This gives: Sanjay=L, Ravi=T, Farhan=L (two liars, one truth-teller).

Step 2: Assume Farhan is a truth-teller.
→ Farhan's statement 'Sanjay is a truth-teller' is TRUE → Sanjay is truth-teller.
→ Sanjay (truth) says 'Ravi is a liar' → TRUE → Ravi is liar.
→ Ravi (liar) says 'Farhan is a liar' - FALSE (since Farhan is truth) → consistent.
This gives: Sanjay=T, Ravi=L, Farhan=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Farhan also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sanjay and Farhan are truth-tellers, Ravi is a liar.

Let's solve step by step:

Step 1: Assume Neha is a liar.
→ Neha's statement 'Harsha is a truth-teller' is FALSE → Harsha is a liar.
→ Priya says 'Neha is a liar' - this is TRUE (since Neha is liar).
→ If Priya tells truth, then Priya is truth-teller.
→ Harsha (liar) says 'Priya is a liar' - FALSE (since Priya is truth) → consistent.
This gives: Harsha=L, Priya=T, Neha=L (two liars, one truth-teller).

Step 2: Assume Neha is a truth-teller.
→ Neha's statement 'Harsha is a truth-teller' is TRUE → Harsha is truth-teller.
→ Harsha (truth) says 'Priya is a liar' → TRUE → Priya is liar.
→ Priya (liar) says 'Neha is a liar' - FALSE (since Neha is truth) → consistent.
This gives: Harsha=T, Priya=L, Neha=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Neha also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Harsha and Neha are truth-tellers, Priya is a liar.

Let's solve step by step:

Step 1: Assume Sanjay is a liar.
→ Sanjay's statement 'Pooja is a truth-teller' is FALSE → Pooja is a liar.
→ Neha says 'Sanjay is a liar' - this is TRUE (since Sanjay is liar).
→ If Neha tells truth, then Neha is truth-teller.
→ Pooja (liar) says 'Neha is a liar' - FALSE (since Neha is truth) → consistent.
This gives: Pooja=L, Neha=T, Sanjay=L (two liars, one truth-teller).

Step 2: Assume Sanjay is a truth-teller.
→ Sanjay's statement 'Pooja is a truth-teller' is TRUE → Pooja is truth-teller.
→ Pooja (truth) says 'Neha is a liar' → TRUE → Neha is liar.
→ Neha (liar) says 'Sanjay is a liar' - FALSE (since Sanjay is truth) → consistent.
This gives: Pooja=T, Neha=L, Sanjay=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Sanjay also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Pooja and Sanjay are truth-tellers, Neha is a liar.

Let's solve step by step:

Step 1: Assume Sanjay is a liar.
→ Sanjay's statement 'Sunil is a truth-teller' is FALSE → Sunil is a liar.
→ Rahul says 'Sanjay is a liar' - this is TRUE (since Sanjay is liar).
→ If Rahul tells truth, then Rahul is truth-teller.
→ Sunil (liar) says 'Rahul is a liar' - FALSE (since Rahul is truth) → consistent.
This gives: Sunil=L, Rahul=T, Sanjay=L (two liars, one truth-teller).

Step 2: Assume Sanjay is a truth-teller.
→ Sanjay's statement 'Sunil is a truth-teller' is TRUE → Sunil is truth-teller.
→ Sunil (truth) says 'Rahul is a liar' → TRUE → Rahul is liar.
→ Rahul (liar) says 'Sanjay is a liar' - FALSE (since Sanjay is truth) → consistent.
This gives: Sunil=T, Rahul=L, Sanjay=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Sanjay also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Sunil and Sanjay are truth-tellers, Rahul is a liar.

Let's solve step by step:

Step 1: Assume Sanjay is a liar.
→ Sanjay's statement 'Gaurav is a truth-teller' is FALSE → Gaurav is a liar.
→ Anita says 'Sanjay is a liar' - this is TRUE (since Sanjay is liar).
→ If Anita tells truth, then Anita is truth-teller.
→ Gaurav (liar) says 'Anita is a liar' - FALSE (since Anita is truth) → consistent.
This gives: Gaurav=L, Anita=T, Sanjay=L (two liars, one truth-teller).

Step 2: Assume Sanjay is a truth-teller.
→ Sanjay's statement 'Gaurav is a truth-teller' is TRUE → Gaurav is truth-teller.
→ Gaurav (truth) says 'Anita is a liar' → TRUE → Anita is liar.
→ Anita (liar) says 'Sanjay is a liar' - FALSE (since Sanjay is truth) → consistent.
This gives: Gaurav=T, Anita=L, Sanjay=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Sanjay also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Gaurav and Sanjay are truth-tellers, Anita is a liar.

Let's solve step by step:

Step 1: Assume Leena is a liar.
→ Leena's statement 'Deepa is a truth-teller' is FALSE → Deepa is a liar.
→ Manoj says 'Leena is a liar' - this is TRUE (since Leena is liar).
→ If Manoj tells truth, then Manoj is truth-teller.
→ Deepa (liar) says 'Manoj is a liar' - FALSE (since Manoj is truth) → consistent.
This gives: Deepa=L, Manoj=T, Leena=L (two liars, one truth-teller).

Step 2: Assume Leena is a truth-teller.
→ Leena's statement 'Deepa is a truth-teller' is TRUE → Deepa is truth-teller.
→ Deepa (truth) says 'Manoj is a liar' → TRUE → Manoj is liar.
→ Manoj (liar) says 'Leena is a liar' - FALSE (since Leena is truth) → consistent.
This gives: Deepa=T, Manoj=L, Leena=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Leena also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Deepa and Leena are truth-tellers, Manoj is a liar.

Let's solve step by step:

Step 1: Assume Priya is a liar.
→ Priya's statement 'Amit is a truth-teller' is FALSE → Amit is a liar.
→ Sunil says 'Priya is a liar' - this is TRUE (since Priya is liar).
→ If Sunil tells truth, then Sunil is truth-teller.
→ Amit (liar) says 'Sunil is a liar' - FALSE (since Sunil is truth) → consistent.
This gives: Amit=L, Sunil=T, Priya=L (two liars, one truth-teller).

Step 2: Assume Priya is a truth-teller.
→ Priya's statement 'Amit is a truth-teller' is TRUE → Amit is truth-teller.
→ Amit (truth) says 'Sunil is a liar' → TRUE → Sunil is liar.
→ Sunil (liar) says 'Priya is a liar' - FALSE (since Priya is truth) → consistent.
This gives: Amit=T, Sunil=L, Priya=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Priya also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Amit and Priya are truth-tellers, Sunil is a liar.

Let's solve step by step:

Step 1: Assume Meera is a liar.
→ Meera's statement 'Neha is a truth-teller' is FALSE → Neha is a liar.
→ Harsha says 'Meera is a liar' - this is TRUE (since Meera is liar).
→ If Harsha tells truth, then Harsha is truth-teller.
→ Neha (liar) says 'Harsha is a liar' - FALSE (since Harsha is truth) → consistent.
This gives: Neha=L, Harsha=T, Meera=L (two liars, one truth-teller).

Step 2: Assume Meera is a truth-teller.
→ Meera's statement 'Neha is a truth-teller' is TRUE → Neha is truth-teller.
→ Neha (truth) says 'Harsha is a liar' → TRUE → Harsha is liar.
→ Harsha (liar) says 'Meera is a liar' - FALSE (since Meera is truth) → consistent.
This gives: Neha=T, Harsha=L, Meera=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Meera also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Neha and Meera are truth-tellers, Harsha is a liar.

Let's solve step by step:

Step 1: Assume Kiran is a liar.
→ Kiran's statement 'Pooja is a truth-teller' is FALSE → Pooja is a liar.
→ Divya says 'Kiran is a liar' - this is TRUE (since Kiran is liar).
→ If Divya tells truth, then Divya is truth-teller.
→ Pooja (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Pooja=L, Divya=T, Kiran=L (two liars, one truth-teller).

Step 2: Assume Kiran is a truth-teller.
→ Kiran's statement 'Pooja is a truth-teller' is TRUE → Pooja is truth-teller.
→ Pooja (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Kiran is a liar' - FALSE (since Kiran is truth) → consistent.
This gives: Pooja=T, Divya=L, Kiran=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Kiran also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Pooja and Kiran are truth-tellers, Divya is a liar.

Let's solve step by step:

Step 1: Assume Anita is a liar.
→ Anita's statement 'Neha is a truth-teller' is FALSE → Neha is a liar.
→ Sunil says 'Anita is a liar' - this is TRUE (since Anita is liar).
→ If Sunil tells truth, then Sunil is truth-teller.
→ Neha (liar) says 'Sunil is a liar' - FALSE (since Sunil is truth) → consistent.
This gives: Neha=L, Sunil=T, Anita=L (two liars, one truth-teller).

Step 2: Assume Anita is a truth-teller.
→ Anita's statement 'Neha is a truth-teller' is TRUE → Neha is truth-teller.
→ Neha (truth) says 'Sunil is a liar' → TRUE → Sunil is liar.
→ Sunil (liar) says 'Anita is a liar' - FALSE (since Anita is truth) → consistent.
This gives: Neha=T, Sunil=L, Anita=T (two truth-tellers, one liar).

Both assignments are valid! This puzzle has two solutions.

To guarantee a unique solution, we add a fourth person:
Anita also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Neha and Anita are truth-tellers, Sunil is a liar.