two_person_accusation: Worksheet 2 - Beginner Practice two_person_accusation BEGINNER

Let's solve step by step:

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

Step 2: Assume Sunil is a truth-teller.
→ Sunil's statement 'Sanjay is a truth-teller' is TRUE → Sanjay is truth-teller.
→ Sanjay (truth) says 'Manoj is a liar' → TRUE → Manoj is liar.
→ Manoj (liar) says 'Sunil is a liar' - FALSE (since Sunil is truth) → consistent.
This gives: Sanjay=T, Manoj=L, Sunil=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:
Sunil also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Sanjay is a truth-teller.
→ Sanjay's statement 'Priya is a truth-teller' is TRUE → Priya is truth-teller.
→ Priya (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Sanjay is a liar' - FALSE (since Sanjay is truth) → consistent.
This gives: Priya=T, Divya=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, Priya and Sanjay are truth-tellers, Divya is a liar.

Let's solve step by step:

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

Step 2: Assume Rohan is a truth-teller.
→ Rohan's statement 'Priya is a truth-teller' is TRUE → Priya is truth-teller.
→ Priya (truth) says 'Vikram is a liar' → TRUE → Vikram is liar.
→ Vikram (liar) says 'Rohan is a liar' - FALSE (since Rohan is truth) → consistent.
This gives: Priya=T, Vikram=L, Rohan=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:
Rohan also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Ravi is a truth-teller.
→ Ravi's statement 'Manoj is a truth-teller' is TRUE → Manoj is truth-teller.
→ Manoj (truth) says 'Vikram is a liar' → TRUE → Vikram is liar.
→ Vikram (liar) says 'Ravi is a liar' - FALSE (since Ravi is truth) → consistent.
This gives: Manoj=T, Vikram=L, Ravi=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:
Ravi also says: 'Exactly one of us is a liar'

With this constraint, only Step 2 works (two truth-tellers, one liar).
Therefore, Manoj and Ravi are truth-tellers, Vikram 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.
→ Neha says 'Farhan is a liar' - this is TRUE (since Farhan 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, 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 'Neha is a liar' → TRUE → Neha is liar.
→ Neha (liar) says 'Farhan is a liar' - FALSE (since Farhan is truth) → consistent.
This gives: Sanjay=T, Neha=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, Neha is a liar.

Let's solve step by step:

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

Step 2: Assume Leena is a truth-teller.
→ Leena'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 'Leena is a liar' - FALSE (since Leena is truth) → consistent.
This gives: Ravi=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, Ravi and Leena are truth-tellers, Divya is a liar.

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Divya is a truth-teller.
→ Divya's statement 'Harsha is a truth-teller' is TRUE → Harsha is truth-teller.
→ Harsha (truth) says 'Rohan is a liar' → TRUE → Rohan is liar.
→ Rohan (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Harsha=T, Rohan=L, Divya=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:
Divya also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Farhan is a truth-teller.
→ Farhan's statement 'Gaurav is a truth-teller' is TRUE → Gaurav is truth-teller.
→ Gaurav (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: Gaurav=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, Gaurav and Farhan are truth-tellers, Ravi is a liar.

Let's solve step by step:

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

Step 2: Assume Sanjay is a truth-teller.
→ Sanjay's statement 'Manoj is a truth-teller' is TRUE → Manoj is truth-teller.
→ Manoj (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: Manoj=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, Manoj and Sanjay are truth-tellers, Rahul is a liar.

Let's solve step by step:

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

Step 2: Assume Harsha is a truth-teller.
→ Harsha's statement 'Ravi is a truth-teller' is TRUE → Ravi is truth-teller.
→ Ravi (truth) says 'Pooja is a liar' → TRUE → Pooja is liar.
→ Pooja (liar) says 'Harsha is a liar' - FALSE (since Harsha is truth) → consistent.
This gives: Ravi=T, Pooja=L, Harsha=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:
Harsha also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Pooja is a truth-teller.
→ Pooja's statement 'Sunil is a truth-teller' is TRUE → Sunil is truth-teller.
→ Sunil (truth) says 'Harsha is a liar' → TRUE → Harsha is liar.
→ Harsha (liar) says 'Pooja is a liar' - FALSE (since Pooja is truth) → consistent.
This gives: Sunil=T, Harsha=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, Sunil and Pooja are truth-tellers, Harsha 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.
→ Rohan says 'Neha is a liar' - this is TRUE (since Neha is liar).
→ If Rohan tells truth, then Rohan is truth-teller.
→ Harsha (liar) says 'Rohan is a liar' - FALSE (since Rohan is truth) → consistent.
This gives: Harsha=L, Rohan=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 'Rohan is a liar' → TRUE → Rohan is liar.
→ Rohan (liar) says 'Neha is a liar' - FALSE (since Neha is truth) → consistent.
This gives: Harsha=T, Rohan=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, Rohan is a liar.

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Rohan is a truth-teller.
→ Rohan's statement 'Amit is a truth-teller' is TRUE → Amit is truth-teller.
→ Amit (truth) says 'Leena is a liar' → TRUE → Leena is liar.
→ Leena (liar) says 'Rohan is a liar' - FALSE (since Rohan is truth) → consistent.
This gives: Amit=T, Leena=L, Rohan=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:
Rohan also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Rohan is a truth-teller.
→ Rohan's statement 'Anita is a truth-teller' is TRUE → Anita is truth-teller.
→ Anita (truth) says 'Neha is a liar' → TRUE → Neha is liar.
→ Neha (liar) says 'Rohan is a liar' - FALSE (since Rohan is truth) → consistent.
This gives: Anita=T, Neha=L, Rohan=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:
Rohan also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Harsha is a truth-teller.
→ Harsha's statement 'Vikram is a truth-teller' is TRUE → Vikram is truth-teller.
→ Vikram (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Harsha is a liar' - FALSE (since Harsha is truth) → consistent.
This gives: Vikram=T, Divya=L, Harsha=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:
Harsha also says: 'Exactly one of us is a liar'

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

Let's solve step by step:

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

Step 2: Assume Deepa is a truth-teller.
→ Deepa's statement 'Gaurav is a truth-teller' is TRUE → Gaurav is truth-teller.
→ Gaurav (truth) says 'Divya is a liar' → TRUE → Divya is liar.
→ Divya (liar) says 'Deepa is a liar' - FALSE (since Deepa is truth) → consistent.
This gives: Gaurav=T, Divya=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, Gaurav and Deepa are truth-tellers, Divya 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.
→ Gaurav says 'Farhan is a liar' - this is TRUE (since Farhan is liar).
→ If Gaurav tells truth, then Gaurav is truth-teller.
→ Sunil (liar) says 'Gaurav is a liar' - FALSE (since Gaurav is truth) → consistent.
This gives: Sunil=L, Gaurav=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 'Gaurav is a liar' → TRUE → Gaurav is liar.
→ Gaurav (liar) says 'Farhan is a liar' - FALSE (since Farhan is truth) → consistent.
This gives: Sunil=T, Gaurav=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, Gaurav is a liar.