minimum_liars_count - Absolute-Beginner Level: core concept mastery minimum_liars_count ABSOLUTE BEGINNER

Let L = number of liars.

Statement constraints:
1. Divya: L ≥ 2
2. Gaurav: L ≤ 3
3. Amit: L = 2
4. Meera: Leena is truth-teller
5. Leena: Divya 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 Divya is liar - if true, then Divya is liar.
Statement 4 says Leena is truth-teller - can be true.
This configuration is possible with L=2.

Can L=1? Statement 1 would be false, so Divya would be liar.
Then statement 5 (Leena says 'Divya is liar') would be TRUE.
So Leena would be truth-teller. Then statement 4 (Meera says 'Leena is truth-teller') would be TRUE.
So Meera would be truth-teller. That gives at least 2 truth-tellers (Leena, 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. Deepa: L ≥ 2
2. Gaurav: L ≤ 3
3. Sunil: L = 2
4. Amit: Pooja is truth-teller
5. Pooja: 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 Pooja 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 (Pooja says 'Deepa is liar') would be TRUE.
So Pooja would be truth-teller. Then statement 4 (Amit says 'Pooja is truth-teller') would be TRUE.
So Amit would be truth-teller. That gives at least 2 truth-tellers (Pooja, Amit) 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. Ravi: L ≤ 3
3. Amit: L = 2
4. Divya: Pooja is truth-teller
5. Pooja: 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 Pooja 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 (Pooja says 'Deepa is liar') would be TRUE.
So Pooja would be truth-teller. Then statement 4 (Divya says 'Pooja is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Pooja, 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. Priya: L ≥ 2
2. Anita: L ≤ 3
3. Meera: L = 2
4. Divya: Vikram is truth-teller
5. Vikram: 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 Vikram 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 (Vikram says 'Priya is liar') would be TRUE.
So Vikram would be truth-teller. Then statement 4 (Divya says 'Vikram is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Vikram, 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. Neha: L ≥ 2
2. Anita: L ≤ 3
3. Divya: L = 2
4. Sanjay: Rahul is truth-teller
5. Rahul: 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 Rahul 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 (Rahul says 'Neha is liar') would be TRUE.
So Rahul would be truth-teller. Then statement 4 (Sanjay says 'Rahul is truth-teller') would be TRUE.
So Sanjay would be truth-teller. That gives at least 2 truth-tellers (Rahul, 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. Ravi: L ≤ 3
3. Vikram: L = 2
4. Divya: Pooja is truth-teller
5. Pooja: 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 Pooja 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 (Pooja says 'Farhan is liar') would be TRUE.
So Pooja would be truth-teller. Then statement 4 (Divya says 'Pooja is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Pooja, 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. Sanjay: L ≥ 2
2. Vikram: L ≤ 3
3. Sunil: L = 2
4. Pooja: Anita is truth-teller
5. Anita: Sanjay 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 Sanjay is liar - if true, then Sanjay 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 Sanjay would be liar.
Then statement 5 (Anita says 'Sanjay is liar') would be TRUE.
So Anita would be truth-teller. Then statement 4 (Pooja says 'Anita is truth-teller') would be TRUE.
So Pooja would be truth-teller. That gives at least 2 truth-tellers (Anita, 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. Sunil: L ≤ 3
3. Gaurav: L = 2
4. Divya: Rohan is truth-teller
5. Rohan: 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 Rohan 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 (Rohan says 'Priya is liar') would be TRUE.
So Rohan would be truth-teller. Then statement 4 (Divya says 'Rohan is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Rohan, 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. Amit: L ≤ 3
3. Harsha: L = 2
4. Neha: Sanjay is truth-teller
5. Sanjay: 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 Sanjay 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 (Sanjay says 'Meera is liar') would be TRUE.
So Sanjay would be truth-teller. Then statement 4 (Neha says 'Sanjay is truth-teller') would be TRUE.
So Neha would be truth-teller. That gives at least 2 truth-tellers (Sanjay, 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. Priya: L ≥ 2
2. Divya: L ≤ 3
3. Farhan: L = 2
4. Sunil: Manoj is truth-teller
5. Manoj: 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 Manoj 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 (Manoj says 'Priya is liar') would be TRUE.
So Manoj would be truth-teller. Then statement 4 (Sunil says 'Manoj is truth-teller') would be TRUE.
So Sunil would be truth-teller. That gives at least 2 truth-tellers (Manoj, Sunil) 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. Gaurav: L ≤ 3
3. Rohan: L = 2
4. Farhan: Deepa is truth-teller
5. Deepa: 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 Deepa 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 (Deepa says 'Priya is liar') would be TRUE.
So Deepa would be truth-teller. Then statement 4 (Farhan says 'Deepa is truth-teller') would be TRUE.
So Farhan would be truth-teller. That gives at least 2 truth-tellers (Deepa, 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. Meera: L ≥ 2
2. Divya: L ≤ 3
3. Farhan: L = 2
4. Sanjay: Leena is truth-teller
5. Leena: 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 Leena 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 (Leena says 'Meera is liar') would be TRUE.
So Leena would be truth-teller. Then statement 4 (Sanjay says 'Leena is truth-teller') would be TRUE.
So Sanjay would be truth-teller. That gives at least 2 truth-tellers (Leena, 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. Vikram: L ≤ 3
3. Priya: L = 2
4. Divya: Leena is truth-teller
5. Leena: 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 Leena 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 (Leena says 'Farhan is liar') would be TRUE.
So Leena would be truth-teller. Then statement 4 (Divya says 'Leena is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Leena, 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. Deepa: L ≤ 3
3. Anita: L = 2
4. Sunil: Farhan is truth-teller
5. Farhan: 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 Farhan 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 (Farhan says 'Meera is liar') would be TRUE.
So Farhan would be truth-teller. Then statement 4 (Sunil says 'Farhan is truth-teller') would be TRUE.
So Sunil would be truth-teller. That gives at least 2 truth-tellers (Farhan, Sunil) plus possibly others, contradicting L=1.

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

Let L = number of liars.

Statement constraints:
1. Sanjay: L ≥ 2
2. Anita: L ≤ 3
3. Ravi: L = 2
4. Sunil: Divya is truth-teller
5. Divya: Sanjay 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 Sanjay is liar - if true, then Sanjay 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 Sanjay would be liar.
Then statement 5 (Divya says 'Sanjay is liar') would be TRUE.
So Divya would be truth-teller. Then statement 4 (Sunil says 'Divya is truth-teller') would be TRUE.
So Sunil would be truth-teller. That gives at least 2 truth-tellers (Divya, Sunil) 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. Sunil: L ≤ 3
3. Vikram: L = 2
4. Anita: Ravi is truth-teller
5. Ravi: 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 Ravi 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 (Ravi says 'Pooja is liar') would be TRUE.
So Ravi would be truth-teller. Then statement 4 (Anita says 'Ravi is truth-teller') would be TRUE.
So Anita would be truth-teller. That gives at least 2 truth-tellers (Ravi, 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. Farhan: L ≥ 2
2. Gaurav: L ≤ 3
3. Deepa: L = 2
4. Rohan: Leena is truth-teller
5. Leena: 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 Leena 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 (Leena says 'Farhan is liar') would be TRUE.
So Leena would be truth-teller. Then statement 4 (Rohan says 'Leena is truth-teller') would be TRUE.
So Rohan would be truth-teller. That gives at least 2 truth-tellers (Leena, 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. Sunil: L ≤ 3
3. Anita: L = 2
4. Divya: Kiran is truth-teller
5. Kiran: 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 Kiran 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 (Kiran says 'Priya is liar') would be TRUE.
So Kiran would be truth-teller. Then statement 4 (Divya says 'Kiran is truth-teller') would be TRUE.
So Divya would be truth-teller. That gives at least 2 truth-tellers (Kiran, 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. Gaurav: L ≥ 2
2. Amit: L ≤ 3
3. Rahul: L = 2
4. Leena: Priya is truth-teller
5. Priya: Gaurav 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 Gaurav is liar - if true, then Gaurav 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 Gaurav would be liar.
Then statement 5 (Priya says 'Gaurav is liar') would be TRUE.
So Priya would be truth-teller. Then statement 4 (Leena says 'Priya is truth-teller') would be TRUE.
So Leena would be truth-teller. That gives at least 2 truth-tellers (Priya, Leena) 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. Divya: L ≤ 3
3. Neha: L = 2
4. Meera: Sanjay is truth-teller
5. Sanjay: 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 Sanjay 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 (Sanjay says 'Deepa is liar') would be TRUE.
So Sanjay would be truth-teller. Then statement 4 (Meera says 'Sanjay is truth-teller') would be TRUE.
So Meera would be truth-teller. That gives at least 2 truth-tellers (Sanjay, Meera) plus possibly others, contradicting L=1.

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