minimum_liars_count Beginner-Intermediate Worksheet: Focus on common variations practice minimum_liars_count BEGINNER INTERMEDIATE

Let L = number of liars.

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