minimum_liars_count: Worksheet 10 - Expert Practice minimum_liars_count EXPERT

Let L = number of liars.

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