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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

Step 1: Assume Rahul is a liar.
→ Rahul's statement 'Harsha is a truth-teller' is FALSE → Harsha is a liar.
→ Rohan says 'Rahul is a liar' - this is TRUE (since Rahul 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, Rahul=L (two liars, one truth-teller).

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

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

Let's solve step by step:

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

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