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

First, solve the original puzzle:
- If Deepa is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Deepa and Leena same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Deepa=T, Anita=T, Leena=L

Now, hypothetically assume Deepa is liar instead of truth-teller.
Then we need to re-solve:
- Deepa liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Deepa truth - contradicts Deepa liar.
- If 2 liars, then Anita and Leena are liars. Then Anita liar says 'Deepa and Leena same type' - Deepa liar, Leena liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Anita liar says 'Deepa and Leena same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Deepa is liar.
Thus, if we hypothetically assume Deepa is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Manoj is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Manoj and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Manoj=T, Sunil=T, Deepa=L

Now, hypothetically assume Manoj is liar instead of truth-teller.
Then we need to re-solve:
- Manoj liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Manoj truth - contradicts Manoj liar.
- If 2 liars, then Sunil and Deepa are liars. Then Sunil liar says 'Manoj and Deepa same type' - Manoj liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sunil liar says 'Manoj and Deepa same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Manoj is liar.
Thus, if we hypothetically assume Manoj is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Priya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Priya and Harsha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Sanjay=T, Harsha=L

Now, hypothetically assume Priya is liar instead of truth-teller.
Then we need to re-solve:
- Priya liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Priya truth - contradicts Priya liar.
- If 2 liars, then Sanjay and Harsha are liars. Then Sanjay liar says 'Priya and Harsha same type' - Priya liar, Harsha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Priya and Harsha same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Priya is liar.
Thus, if we hypothetically assume Priya is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Priya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Priya and Amit same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Rahul=T, Amit=L

Now, hypothetically assume Priya is liar instead of truth-teller.
Then we need to re-solve:
- Priya liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Priya truth - contradicts Priya liar.
- If 2 liars, then Rahul and Amit are liars. Then Rahul liar says 'Priya and Amit same type' - Priya liar, Amit liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Rahul liar says 'Priya and Amit same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Priya is liar.
Thus, if we hypothetically assume Priya is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Pooja is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Pooja and Meera same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Pooja=T, Rohan=T, Meera=L

Now, hypothetically assume Pooja is liar instead of truth-teller.
Then we need to re-solve:
- Pooja liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Pooja truth - contradicts Pooja liar.
- If 2 liars, then Rohan and Meera are liars. Then Rohan liar says 'Pooja and Meera same type' - Pooja liar, Meera liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Rohan liar says 'Pooja and Meera same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Pooja is liar.
Thus, if we hypothetically assume Pooja is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Neha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Neha and Vikram same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Neha=T, Deepa=T, Vikram=L

Now, hypothetically assume Neha is liar instead of truth-teller.
Then we need to re-solve:
- Neha liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Neha truth - contradicts Neha liar.
- If 2 liars, then Deepa and Vikram are liars. Then Deepa liar says 'Neha and Vikram same type' - Neha liar, Vikram liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Deepa liar says 'Neha and Vikram same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Neha is liar.
Thus, if we hypothetically assume Neha is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Ravi same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Harsha=T, Ravi=L

Now, hypothetically assume Kiran is liar instead of truth-teller.
Then we need to re-solve:
- Kiran liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Kiran truth - contradicts Kiran liar.
- If 2 liars, then Harsha and Ravi are liars. Then Harsha liar says 'Kiran and Ravi same type' - Kiran liar, Ravi liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Harsha liar says 'Kiran and Ravi same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Kiran is liar.
Thus, if we hypothetically assume Kiran is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Vikram is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Vikram and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Vikram=T, Neha=T, Deepa=L

Now, hypothetically assume Vikram is liar instead of truth-teller.
Then we need to re-solve:
- Vikram liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Vikram truth - contradicts Vikram liar.
- If 2 liars, then Neha and Deepa are liars. Then Neha liar says 'Vikram and Deepa same type' - Vikram liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Neha liar says 'Vikram and Deepa same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Vikram is liar.
Thus, if we hypothetically assume Vikram is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Divya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Divya and Leena same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Divya=T, Farhan=T, Leena=L

Now, hypothetically assume Divya is liar instead of truth-teller.
Then we need to re-solve:
- Divya liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Divya truth - contradicts Divya liar.
- If 2 liars, then Farhan and Leena are liars. Then Farhan liar says 'Divya and Leena same type' - Divya liar, Leena liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Farhan liar says 'Divya and Leena same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Divya is liar.
Thus, if we hypothetically assume Divya is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Harsha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Harsha and Neha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Harsha=T, Sanjay=T, Neha=L

Now, hypothetically assume Harsha is liar instead of truth-teller.
Then we need to re-solve:
- Harsha liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Harsha truth - contradicts Harsha liar.
- If 2 liars, then Sanjay and Neha are liars. Then Sanjay liar says 'Harsha and Neha same type' - Harsha liar, Neha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Harsha and Neha same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Harsha is liar.
Thus, if we hypothetically assume Harsha is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Gaurav is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Gaurav and Harsha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Gaurav=T, Priya=T, Harsha=L

Now, hypothetically assume Gaurav is liar instead of truth-teller.
Then we need to re-solve:
- Gaurav liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Gaurav truth - contradicts Gaurav liar.
- If 2 liars, then Priya and Harsha are liars. Then Priya liar says 'Gaurav and Harsha same type' - Gaurav liar, Harsha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Priya liar says 'Gaurav and Harsha same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Gaurav is liar.
Thus, if we hypothetically assume Gaurav is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Farhan is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Farhan and Sunil same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Farhan=T, Kiran=T, Sunil=L

Now, hypothetically assume Farhan is liar instead of truth-teller.
Then we need to re-solve:
- Farhan liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Farhan truth - contradicts Farhan liar.
- If 2 liars, then Kiran and Sunil are liars. Then Kiran liar says 'Farhan and Sunil same type' - Farhan liar, Sunil liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Kiran liar says 'Farhan and Sunil same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Farhan is liar.
Thus, if we hypothetically assume Farhan is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Vikram is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Vikram and Meera same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Vikram=T, Leena=T, Meera=L

Now, hypothetically assume Vikram is liar instead of truth-teller.
Then we need to re-solve:
- Vikram liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Vikram truth - contradicts Vikram liar.
- If 2 liars, then Leena and Meera are liars. Then Leena liar says 'Vikram and Meera same type' - Vikram liar, Meera liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Leena liar says 'Vikram and Meera same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Vikram is liar.
Thus, if we hypothetically assume Vikram is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Priya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Priya and Sunil same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Sanjay=T, Sunil=L

Now, hypothetically assume Priya is liar instead of truth-teller.
Then we need to re-solve:
- Priya liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Priya truth - contradicts Priya liar.
- If 2 liars, then Sanjay and Sunil are liars. Then Sanjay liar says 'Priya and Sunil same type' - Priya liar, Sunil liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Priya and Sunil same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Priya is liar.
Thus, if we hypothetically assume Priya is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Anita is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Anita and Rahul same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Anita=T, Sunil=T, Rahul=L

Now, hypothetically assume Anita is liar instead of truth-teller.
Then we need to re-solve:
- Anita liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Anita truth - contradicts Anita liar.
- If 2 liars, then Sunil and Rahul are liars. Then Sunil liar says 'Anita and Rahul same type' - Anita liar, Rahul liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sunil liar says 'Anita and Rahul same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Anita is liar.
Thus, if we hypothetically assume Anita is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Farhan is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Farhan and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Farhan=T, Leena=T, Deepa=L

Now, hypothetically assume Farhan is liar instead of truth-teller.
Then we need to re-solve:
- Farhan liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Farhan truth - contradicts Farhan liar.
- If 2 liars, then Leena and Deepa are liars. Then Leena liar says 'Farhan and Deepa same type' - Farhan liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Leena liar says 'Farhan and Deepa same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Farhan is liar.
Thus, if we hypothetically assume Farhan is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Neha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Neha and Sunil same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Neha=T, Meera=T, Sunil=L

Now, hypothetically assume Neha is liar instead of truth-teller.
Then we need to re-solve:
- Neha liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Neha truth - contradicts Neha liar.
- If 2 liars, then Meera and Sunil are liars. Then Meera liar says 'Neha and Sunil same type' - Neha liar, Sunil liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Meera liar says 'Neha and Sunil same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Neha is liar.
Thus, if we hypothetically assume Neha is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Anita is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Anita and Amit same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Anita=T, Harsha=T, Amit=L

Now, hypothetically assume Anita is liar instead of truth-teller.
Then we need to re-solve:
- Anita liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Anita truth - contradicts Anita liar.
- If 2 liars, then Harsha and Amit are liars. Then Harsha liar says 'Anita and Amit same type' - Anita liar, Amit liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Harsha liar says 'Anita and Amit same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Anita is liar.
Thus, if we hypothetically assume Anita is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Ravi same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Neha=T, Ravi=L

Now, hypothetically assume Kiran is liar instead of truth-teller.
Then we need to re-solve:
- Kiran liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Kiran truth - contradicts Kiran liar.
- If 2 liars, then Neha and Ravi are liars. Then Neha liar says 'Kiran and Ravi same type' - Kiran liar, Ravi liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Neha liar says 'Kiran and Ravi same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Kiran is liar.
Thus, if we hypothetically assume Kiran is liar, there would be ZERO truth-tellers.

First, solve the original puzzle:
- If Anita is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Anita and Priya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Anita=T, Manoj=T, Priya=L

Now, hypothetically assume Anita is liar instead of truth-teller.
Then we need to re-solve:
- Anita liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Anita truth - contradicts Anita liar.
- If 2 liars, then Manoj and Priya are liars. Then Manoj liar says 'Anita and Priya same type' - Anita liar, Priya liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Manoj liar says 'Anita and Priya same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Anita is liar.
Thus, if we hypothetically assume Anita is liar, there would be ZERO truth-tellers.