hypothetical_count_change Beginner-Intermediate Worksheet: Focus on common variations practice hypothetical_count_change BEGINNER INTERMEDIATE

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 Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Rohan=T, Sunil=T, Deepa=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 Sunil and Deepa are liars. Then Sunil liar says 'Rohan and Deepa same type' - Rohan liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sunil liar says 'Rohan and Deepa 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 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, Farhan=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 Farhan and Rahul are liars. Then Farhan 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 Farhan 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 Neha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Neha and Rahul same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Neha=T, Ravi=T, Rahul=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 Ravi and Rahul are liars. Then Ravi liar says 'Neha and Rahul same type' - Neha liar, Rahul liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Ravi liar says 'Neha and Rahul 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 Neha is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Neha and Sanjay same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Neha=T, Anita=T, Sanjay=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 Anita and Sanjay are liars. Then Anita liar says 'Neha and Sanjay same type' - Neha liar, Sanjay liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Anita liar says 'Neha and Sanjay 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 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, Anita=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 Anita and Sunil are liars. Then Anita 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 Anita 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 Rahul is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Rahul and Divya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Rahul=T, Harsha=T, Divya=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 Harsha and Divya are liars. Then Harsha liar says 'Rahul and Divya same type' - Rahul liar, Divya liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Harsha liar says 'Rahul and Divya 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 Gaurav is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Gaurav and Sunil same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Gaurav=T, Sanjay=T, Sunil=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 Sanjay and Sunil are liars. Then Sanjay liar says 'Gaurav and Sunil same type' - Gaurav liar, Sunil liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sanjay liar says 'Gaurav and Sunil 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 Pooja is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Pooja and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Pooja=T, Sunil=T, Deepa=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 Deepa are liars. Then Sunil liar says 'Pooja and Deepa same type' - Pooja liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Sunil liar says 'Pooja and Deepa 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 Neha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Meera=T, Farhan=T, Neha=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 Farhan and Neha are liars. Then Farhan liar says 'Meera and Neha same type' - Meera liar, Neha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Farhan liar says 'Meera and Neha 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 Sanjay is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Sanjay and Amit same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Sanjay=T, Vikram=T, Amit=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 Amit are liars. Then Vikram liar says 'Sanjay and Amit same type' - Sanjay liar, Amit liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Vikram liar says 'Sanjay and Amit 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 Amit is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Amit and Sunil same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Amit=T, Rohan=T, Sunil=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 Rohan and Sunil are liars. Then Rohan liar says 'Amit and Sunil same type' - Amit liar, Sunil liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Rohan liar says 'Amit and Sunil 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 Manoj is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Manoj and Harsha same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Manoj=T, Pooja=T, Harsha=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 Pooja and Harsha are liars. Then Pooja liar says 'Manoj and Harsha same type' - Manoj liar, Harsha liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Pooja liar says 'Manoj and Harsha 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 Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Anita=T, Deepa=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 Anita and Deepa are liars. Then Anita liar says 'Kiran and Deepa same type' - Kiran liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Anita liar says 'Kiran and Deepa 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 Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Anita same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Divya=T, Anita=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 Divya and Anita are liars. Then Divya liar says 'Kiran and Anita same type' - Kiran liar, Anita liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Divya liar says 'Kiran and Anita 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 Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Amit same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Harsha=T, Amit=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 Amit are liars. Then Harsha liar says 'Kiran and Amit same type' - Kiran liar, Amit liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Harsha liar says 'Kiran and Amit 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 Divya same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Vikram=T, Rahul=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 Rahul and Divya are liars. Then Rahul 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 Rahul 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 Divya is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Divya and Manoj same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Divya=T, Anita=T, Manoj=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 Anita and Manoj are liars. Then Anita liar says 'Divya and Manoj same type' - Divya liar, Manoj liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Anita liar says 'Divya and Manoj 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 Ravi is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Ravi and Deepa same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Ravi=T, Divya=T, Deepa=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 Divya and Deepa are liars. Then Divya liar says 'Ravi and Deepa same type' - Ravi liar, Deepa liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Divya liar says 'Ravi and Deepa 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 Sunil is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Sunil and Pooja same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Sunil=T, Rahul=T, Pooja=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 Rahul and Pooja are liars. Then Rahul liar says 'Sunil and Pooja same type' - Sunil liar, Pooja liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Rahul liar says 'Sunil and Pooja 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 Kiran is truth-teller -> exactly one liar -> p2 and p3 are truth-tellers.
Then p2 (truth) says 'Kiran and Anita same type' - true (both truth) - consistent.
p3 (truth) says 'at least one truth-teller' - true - consistent.
Solution: Kiran=T, Vikram=T, Anita=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 Vikram and Anita are liars. Then Vikram liar says 'Kiran and Anita same type' - Kiran liar, Anita liar -> same type -> true statement, but liar can't make true - contradiction.
- If 3 liars, all are liars. Then Vikram liar says 'Kiran and Anita 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.