minimum_liars_count: Worksheet 6 - Intermediate-Advanced Practice minimum_liars_count INTERMEDIATE ADVANCED

Let L = number of liars.

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

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