minimum_liars_count Advanced Worksheet: Focus on exam-oriented approach minimum_liars_count ADVANCED

Let L = number of liars.

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

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