Master minimum_liars_count - Intermediate-Advanced Level Problems minimum_liars_count INTERMEDIATE ADVANCED

Let L = number of liars.

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

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