two_person_accusation Beginner-Intermediate Worksheet: Focus on common variations practice two_person_accusation BEGINNER INTERMEDIATE

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Divya is a truth-teller.
→ Divya's statement 'Priya is a truth-teller' is TRUE → Priya is truth-teller.
→ Priya (truth) says 'Sanjay is a liar' → TRUE → Sanjay is liar.
→ Sanjay (liar) says 'Divya is a liar' - FALSE (since Divya is truth) → consistent.
This gives: Priya=T, Sanjay=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, Priya and Divya 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.
→ Rahul says 'Gaurav is a liar' - this is TRUE (since Gaurav is liar).
→ If Rahul tells truth, then Rahul is truth-teller.
→ Ravi (liar) says 'Rahul is a liar' - FALSE (since Rahul is truth) → consistent.
This gives: Ravi=L, Rahul=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 'Rahul is a liar' → TRUE → Rahul is liar.
→ Rahul (liar) says 'Gaurav is a liar' - FALSE (since Gaurav is truth) → consistent.
This gives: Ravi=T, Rahul=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, Rahul is a liar.

Let's solve step by step:

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

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

Let's solve step by step:

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

Step 2: Assume Meera is a truth-teller.
→ Meera'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 'Meera is a liar' - FALSE (since Meera is truth) → consistent.
This gives: Sanjay=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, Sanjay and Meera are truth-tellers, Ravi 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.
→ Amit says 'Vikram is a liar' - this is TRUE (since Vikram is liar).
→ If Amit tells truth, then Amit is truth-teller.
→ Kiran (liar) says 'Amit is a liar' - FALSE (since Amit is truth) → consistent.
This gives: Kiran=L, Amit=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 'Amit is a liar' → TRUE → Amit is liar.
→ Amit (liar) says 'Vikram is a liar' - FALSE (since Vikram is truth) → consistent.
This gives: Kiran=T, Amit=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, Amit is a liar.

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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

Let's solve step by step:

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

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