hypothetical_count_change: Worksheet 10 - Expert Practice hypothetical_count_change EXPERT

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

Now, hypothetically assume Rahul is liar instead of truth-teller.
Then we need to re-solve:
- Rahul liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Rahul truth - contradicts Rahul liar.
- If 2 liars, then Manoj and Kiran are liars. Then Manoj liar says 'Rahul and Kiran same type' - Rahul liar, Kiran liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Manoj liar says 'Rahul and Kiran same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Rahul is liar.
Thus, if we hypothetically assume Rahul 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 Anita same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Pooja=T, Sanjay=T, Anita=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 Sanjay and Anita are liars. Then Sanjay liar says 'Pooja and Anita same type' - Pooja liar, Anita liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Pooja and Anita 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 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, Amit=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 Amit and Leena are liars. Then Amit 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 Amit 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 Rohan is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Rohan and Priya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Rohan=T, Ravi=T, Priya=L

Now, hypothetically assume Rohan is liar instead of truth-teller.
Then we need to re-solve:
- Rohan liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Rohan truth - contradicts Rohan liar.
- If 2 liars, then Ravi and Priya are liars. Then Ravi liar says 'Rohan and Priya same type' - Rohan liar, Priya liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Ravi liar says 'Rohan and Priya same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Rohan is liar.
Thus, if we hypothetically assume Rohan 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 Vikram same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Farhan=T, Manoj=T, Vikram=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 Manoj and Vikram are liars. Then Manoj liar says 'Farhan and Vikram same type' - Farhan liar, Vikram liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Manoj liar says 'Farhan and Vikram 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 Rohan same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Neha=T, Priya=T, Rohan=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 Priya and Rohan are liars. Then Priya liar says 'Neha and Rohan same type' - Neha liar, Rohan liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Priya liar says 'Neha and Rohan 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 Sanjay is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Sanjay and Meera same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Sanjay=T, Vikram=T, Meera=L

Now, hypothetically assume Sanjay is liar instead of truth-teller.
Then we need to re-solve:
- Sanjay liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Sanjay truth - contradicts Sanjay liar.
- If 2 liars, then Vikram and Meera are liars. Then Vikram liar says 'Sanjay and Meera same type' - Sanjay liar, Meera liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Vikram liar says 'Sanjay and Meera same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Sanjay is liar.
Thus, if we hypothetically assume Sanjay 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 Priya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Divya=T, Meera=T, Priya=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 Meera and Priya are liars. Then Meera liar says 'Divya and Priya same type' - Divya liar, Priya liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Meera liar says 'Divya and Priya 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 Farhan is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Farhan and Neha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Farhan=T, Gaurav=T, Neha=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 Gaurav and Neha are liars. Then Gaurav liar says 'Farhan and Neha same type' - Farhan liar, Neha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Gaurav liar says 'Farhan and Neha 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 Pooja is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Pooja and Priya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Pooja=T, Sunil=T, Priya=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 Sunil and Priya are liars. Then Sunil liar says 'Pooja and Priya same type' - Pooja liar, Priya liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sunil liar says 'Pooja and Priya 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 Harsha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Harsha and Farhan same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Harsha=T, Priya=T, Farhan=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 Priya and Farhan are liars. Then Priya liar says 'Harsha and Farhan same type' - Harsha liar, Farhan liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Priya liar says 'Harsha and Farhan 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 Priya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Priya and Rahul same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Sanjay=T, Rahul=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 Rahul are liars. Then Sanjay liar says 'Priya and Rahul same type' - Priya liar, Rahul liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Priya and Rahul 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 Rahul same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Neha=T, Rahul=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 Neha and Rahul are liars. Then Neha liar says 'Priya and Rahul same type' - Priya liar, Rahul liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Neha liar says 'Priya and Rahul 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 Leena is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Leena and Harsha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Leena=T, Divya=T, Harsha=L

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

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

Now, hypothetically assume Ravi is liar instead of truth-teller.
Then we need to re-solve:
- Ravi liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Ravi truth - contradicts Ravi liar.
- If 2 liars, then Pooja and Sanjay are liars. Then Pooja liar says 'Ravi and Sanjay same type' - Ravi liar, Sanjay liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Pooja liar says 'Ravi and Sanjay same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Ravi is liar.
Thus, if we hypothetically assume Ravi 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 Anita same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Neha=T, Anita=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 Neha and Anita are liars. Then Neha liar says 'Priya and Anita same type' - Priya liar, Anita liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Neha liar says 'Priya and Anita 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 Pooja same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Amit=T, Pooja=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 Amit and Pooja are liars. Then Amit liar says 'Priya and Pooja same type' - Priya liar, Pooja liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Amit liar says 'Priya and Pooja 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 Sanjay is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Sanjay and Harsha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Sanjay=T, Divya=T, Harsha=L

Now, hypothetically assume Sanjay is liar instead of truth-teller.
Then we need to re-solve:
- Sanjay liar -> statement 1 false -> number of liars is NOT exactly one -> 0, 2, or 3 liars.
- If 0 liars, all truth-tellers. Then Sanjay truth - contradicts Sanjay liar.
- If 2 liars, then Divya and Harsha are liars. Then Divya liar says 'Sanjay and Harsha same type' - Sanjay liar, Harsha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Divya liar says 'Sanjay and Harsha same type' - both liars -> same -> true statement - contradiction.
- Therefore, no consistent assignment exists when Sanjay is liar.
Thus, if we hypothetically assume Sanjay 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 Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Priya=T, Meera=T, Deepa=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 Meera and Deepa are liars. Then Meera liar says 'Priya and Deepa same type' - Priya liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Meera liar says 'Priya and Deepa 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 Rahul same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Pooja=T, Vikram=T, Rahul=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 Vikram and Rahul are liars. Then Vikram liar says 'Pooja and Rahul same type' - Pooja liar, Rahul liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Vikram liar says 'Pooja and Rahul 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.