minimum_liars_count: Worksheet 2 - Beginner Practice minimum_liars_count BEGINNER

Let L = number of liars.

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

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