Master minimum_liars_count - Beginner Level Problems minimum_liars_count BEGINNER

Let L = number of liars.

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

Let L = number of liars.

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

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