minimum_liars_count - Intermediate Level: tricky scenarios handling minimum_liars_count INTERMEDIATE

Let L = number of liars.

Statement constraints:
1. Leena: L ≥ 2
2. Deepa: L ≤ 3
3. Meera: L = 2
4. Kiran: Amit is truth-teller
5. Amit: Leena is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Leena is liar - if true, then Leena is liar.
Statement 4 says Amit is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Leena would be liar.
Then statement 5 (Amit says 'Leena is liar') would be TRUE.
So Amit would be truth-teller. Then statement 4 (Kiran says 'Amit is truth-teller') would be TRUE.
So Kiran would be truth-teller. That gives at least 2 truth-tellers (Amit, Kiran) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Vikram: L ≥ 2
2. Sunil: L ≤ 3
3. Rohan: L = 2
4. Divya: Manoj is truth-teller
5. Manoj: Vikram is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Vikram is liar - if true, then Vikram is liar.
Statement 4 says Manoj is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Vikram would be liar.
Then statement 5 (Manoj says 'Vikram is liar') would be TRUE.
So Manoj would be truth-teller. Then statement 4 (Divya says 'Manoj is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Manoj, Divya) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Meera: L ≥ 2
2. Pooja: L ≤ 3
3. Deepa: L = 2
4. Sanjay: Anita is truth-teller
5. Anita: Meera is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Meera is liar - if true, then Meera is liar.
Statement 4 says Anita is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Meera would be liar.
Then statement 5 (Anita says 'Meera is liar') would be TRUE.
So Anita would be truth-teller. Then statement 4 (Sanjay says 'Anita is truth-teller') would be TRUE.
So Sanjay would be truth-teller. That gives at least 2 truth-tellers (Anita, Sanjay) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Pooja: L ≥ 2
2. Sanjay: L ≤ 3
3. Vikram: L = 2
4. Rahul: Sunil is truth-teller
5. Sunil: Pooja is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Pooja is liar - if true, then Pooja is liar.
Statement 4 says Sunil is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Pooja would be liar.
Then statement 5 (Sunil says 'Pooja is liar') would be TRUE.
So Sunil would be truth-teller. Then statement 4 (Rahul says 'Sunil is truth-teller') would be TRUE.
So Rahul would be truth-teller. That gives at least 2 truth-tellers (Sunil, Rahul) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Amit: L ≥ 2
2. Sunil: L ≤ 3
3. Sanjay: L = 2
4. Rahul: Meera is truth-teller
5. Meera: Amit is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Amit is liar - if true, then Amit is liar.
Statement 4 says Meera is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Amit would be liar.
Then statement 5 (Meera says 'Amit is liar') would be TRUE.
So Meera would be truth-teller. Then statement 4 (Rahul says 'Meera is truth-teller') would be TRUE.
So Rahul would be truth-teller. That gives at least 2 truth-tellers (Meera, Rahul) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Manoj: L ≥ 2
2. Gaurav: L ≤ 3
3. Ravi: L = 2
4. Vikram: Priya is truth-teller
5. Priya: Manoj is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Manoj is liar - if true, then Manoj is liar.
Statement 4 says Priya is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Manoj would be liar.
Then statement 5 (Priya says 'Manoj is liar') would be TRUE.
So Priya would be truth-teller. Then statement 4 (Vikram says 'Priya is truth-teller') would be TRUE.
So Vikram would be truth-teller. That gives at least 2 truth-tellers (Priya, Vikram) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Deepa: L ≥ 2
2. Harsha: L ≤ 3
3. Ravi: L = 2
4. Pooja: Gaurav is truth-teller
5. Gaurav: Deepa is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Deepa is liar - if true, then Deepa is liar.
Statement 4 says Gaurav is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Deepa would be liar.
Then statement 5 (Gaurav says 'Deepa is liar') would be TRUE.
So Gaurav would be truth-teller. Then statement 4 (Pooja says 'Gaurav is truth-teller') would be TRUE.
So Pooja would be truth-teller. That gives at least 2 truth-tellers (Gaurav, Pooja) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Priya: L ≥ 2
2. Manoj: L ≤ 3
3. Vikram: L = 2
4. Ravi: Meera is truth-teller
5. Meera: Priya is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Priya is liar - if true, then Priya is liar.
Statement 4 says Meera is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Priya would be liar.
Then statement 5 (Meera says 'Priya is liar') would be TRUE.
So Meera would be truth-teller. Then statement 4 (Ravi says 'Meera is truth-teller') would be TRUE.
So Ravi would be truth-teller. That gives at least 2 truth-tellers (Meera, Ravi) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Amit: L ≥ 2
2. Priya: L ≤ 3
3. Vikram: L = 2
4. Anita: Deepa is truth-teller
5. Deepa: Amit is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Amit is liar - if true, then Amit is liar.
Statement 4 says Deepa is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Amit would be liar.
Then statement 5 (Deepa says 'Amit is liar') would be TRUE.
So Deepa would be truth-teller. Then statement 4 (Anita says 'Deepa is truth-teller') would be TRUE.
So Anita would be truth-teller. That gives at least 2 truth-tellers (Deepa, Anita) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Rohan: L ≥ 2
2. Manoj: L ≤ 3
3. Sunil: L = 2
4. Priya: Amit is truth-teller
5. Amit: Rohan is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Rohan is liar - if true, then Rohan is liar.
Statement 4 says Amit is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Rohan would be liar.
Then statement 5 (Amit says 'Rohan is liar') would be TRUE.
So Amit would be truth-teller. Then statement 4 (Priya says 'Amit is truth-teller') would be TRUE.
So Priya would be truth-teller. That gives at least 2 truth-tellers (Amit, Priya) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Rahul: L ≥ 2
2. Rohan: L ≤ 3
3. Sunil: L = 2
4. Manoj: Ravi is truth-teller
5. Ravi: Rahul is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Rahul is liar - if true, then Rahul is liar.
Statement 4 says Ravi is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Rahul would be liar.
Then statement 5 (Ravi says 'Rahul is liar') would be TRUE.
So Ravi would be truth-teller. Then statement 4 (Manoj says 'Ravi is truth-teller') would be TRUE.
So Manoj would be truth-teller. That gives at least 2 truth-tellers (Ravi, Manoj) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Farhan: L ≥ 2
2. Meera: L ≤ 3
3. Manoj: L = 2
4. Priya: Kiran is truth-teller
5. Kiran: Farhan is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Farhan is liar - if true, then Farhan is liar.
Statement 4 says Kiran is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Farhan would be liar.
Then statement 5 (Kiran says 'Farhan is liar') would be TRUE.
So Kiran would be truth-teller. Then statement 4 (Priya says 'Kiran is truth-teller') would be TRUE.
So Priya would be truth-teller. That gives at least 2 truth-tellers (Kiran, Priya) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Manoj: L ≥ 2
2. Amit: L ≤ 3
3. Vikram: L = 2
4. Gaurav: Priya is truth-teller
5. Priya: Manoj is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Manoj is liar - if true, then Manoj is liar.
Statement 4 says Priya is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Manoj would be liar.
Then statement 5 (Priya says 'Manoj is liar') would be TRUE.
So Priya would be truth-teller. Then statement 4 (Gaurav says 'Priya is truth-teller') would be TRUE.
So Gaurav would be truth-teller. That gives at least 2 truth-tellers (Priya, Gaurav) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Rohan: L ≥ 2
2. Rahul: L ≤ 3
3. Amit: L = 2
4. Farhan: Harsha is truth-teller
5. Harsha: Rohan is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Rohan is liar - if true, then Rohan is liar.
Statement 4 says Harsha is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Rohan would be liar.
Then statement 5 (Harsha says 'Rohan is liar') would be TRUE.
So Harsha would be truth-teller. Then statement 4 (Farhan says 'Harsha is truth-teller') would be TRUE.
So Farhan would be truth-teller. That gives at least 2 truth-tellers (Harsha, Farhan) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Amit: L ≥ 2
2. Leena: L ≤ 3
3. Rahul: L = 2
4. Sanjay: Priya is truth-teller
5. Priya: Amit is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Amit is liar - if true, then Amit is liar.
Statement 4 says Priya is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Amit would be liar.
Then statement 5 (Priya says 'Amit is liar') would be TRUE.
So Priya would be truth-teller. Then statement 4 (Sanjay says 'Priya is truth-teller') would be TRUE.
So Sanjay would be truth-teller. That gives at least 2 truth-tellers (Priya, Sanjay) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Farhan: L ≥ 2
2. Harsha: L ≤ 3
3. Rahul: L = 2
4. Rohan: Sunil is truth-teller
5. Sunil: Farhan is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Farhan is liar - if true, then Farhan is liar.
Statement 4 says Sunil is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Farhan would be liar.
Then statement 5 (Sunil says 'Farhan is liar') would be TRUE.
So Sunil would be truth-teller. Then statement 4 (Rohan says 'Sunil is truth-teller') would be TRUE.
So Rohan would be truth-teller. That gives at least 2 truth-tellers (Sunil, Rohan) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Priya: L ≥ 2
2. Harsha: L ≤ 3
3. Divya: L = 2
4. Neha: Amit is truth-teller
5. Amit: Priya is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Priya is liar - if true, then Priya is liar.
Statement 4 says Amit is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Priya would be liar.
Then statement 5 (Amit says 'Priya is liar') would be TRUE.
So Amit would be truth-teller. Then statement 4 (Neha says 'Amit is truth-teller') would be TRUE.
So Neha would be truth-teller. That gives at least 2 truth-tellers (Amit, Neha) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Neha: L ≥ 2
2. Kiran: L ≤ 3
3. Ravi: L = 2
4. Rohan: Pooja is truth-teller
5. Pooja: Neha is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Neha is liar - if true, then Neha is liar.
Statement 4 says Pooja is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Neha would be liar.
Then statement 5 (Pooja says 'Neha is liar') would be TRUE.
So Pooja would be truth-teller. Then statement 4 (Rohan says 'Pooja is truth-teller') would be TRUE.
So Rohan would be truth-teller. That gives at least 2 truth-tellers (Pooja, Rohan) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Deepa: L ≥ 2
2. Leena: L ≤ 3
3. Rahul: L = 2
4. Meera: Kiran is truth-teller
5. Kiran: Deepa is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Deepa is liar - if true, then Deepa is liar.
Statement 4 says Kiran is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Deepa would be liar.
Then statement 5 (Kiran says 'Deepa is liar') would be TRUE.
So Kiran would be truth-teller. Then statement 4 (Meera says 'Kiran is truth-teller') would be TRUE.
So Meera would be truth-teller. That gives at least 2 truth-tellers (Kiran, Meera) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.

Let L = number of liars.

Statement constraints:
1. Rahul: L ≥ 2
2. Gaurav: L ≤ 3
3. Priya: L = 2
4. Deepa: Divya is truth-teller
5. Divya: Rahul is liar

From statement 3, L must be exactly 2 for that statement to be true.
But statements 1 and 2 are consistent with L=2 as well.
Now check statements 4 and 5:
If L=2, then 3 truth-tellers exist.
Statement 5 says Rahul is liar - if true, then Rahul is liar.
Statement 4 says Divya is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Rahul would be liar.
Then statement 5 (Divya says 'Rahul is liar') would be TRUE.
So Divya would be truth-teller. Then statement 4 (Deepa says 'Divya is truth-teller') would be TRUE.
So Deepa would be truth-teller. That gives at least 2 truth-tellers (Divya, Deepa) plus possibly others, contradicting L=1.

Therefore L cannot be 1.
The minimum L is 2.