hypothetical_count_change: Worksheet 2 - Beginner Practice hypothetical_count_change BEGINNER

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 Vikram same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Manoj=T, Deepa=T, Vikram=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 Deepa and Vikram are liars. Then Deepa liar says 'Manoj and Vikram same type' - Manoj liar, Vikram liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Deepa liar says 'Manoj and Vikram 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 Sunil is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Sunil and Neha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Sunil=T, Ravi=T, Neha=L

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

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

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

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

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

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