two_person_accusation: Worksheet 10 - Expert Practice two_person_accusation EXPERT

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Ravi is a truth-teller.
→ Ravi's statement 'Neha is a truth-teller' is TRUE → Neha is truth-teller.
→ Neha (truth) says 'Anita is a liar' → TRUE → Anita is liar.
→ Anita (liar) says 'Ravi is a liar' - FALSE (since Ravi is truth) → consistent.
This gives: Neha=T, Anita=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, Neha and Ravi are truth-tellers, Anita 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 Vikram is a liar.
→ Vikram's statement 'Rohan is a truth-teller' is FALSE → Rohan is a liar.
→ Sanjay says 'Vikram is a liar' - this is TRUE (since Vikram is liar).
→ If Sanjay tells truth, then Sanjay is truth-teller.
→ Rohan (liar) says 'Sanjay is a liar' - FALSE (since Sanjay is truth) → consistent.
This gives: Rohan=L, Sanjay=T, Vikram=L (two liars, one truth-teller).

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Deepa is a truth-teller.
→ Deepa'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 'Deepa is a liar' - FALSE (since Deepa is truth) → consistent.
This gives: Amit=T, Leena=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, Amit and Deepa are truth-tellers, Leena is a liar.

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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