competition_setting_claims: Worksheet 2 - Beginner Practice competition_setting_claims BEGINNER

Let's solve by cases:

Case 1: Deepa came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Priya is liar.
Statement 3: Leena says 'I came second' - unknown.
Statement 4: Ravi says 'Leena is lying'.
This leads to multiple possibilities.

Case 2: Priya came first.
Then statement 1 is false → Deepa is liar.
Statement 2 is true → Priya is truth-teller.
If Leena came second, statement 3 is true → Leena is truth-teller.
Then statement 4 says 'Leena is lying' - false → Ravi is liar.
This gives 2 truth-tellers (Priya, Leena) and 2 liars, consistent.

Therefore, the only consistent assignment is Priya came first.

Let's solve by cases:

Case 1: Sanjay came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Sunil is liar.
Statement 3: Manoj says 'I came second' - unknown.
Statement 4: Kiran says 'Manoj is lying'.
This leads to multiple possibilities.

Case 2: Sunil came first.
Then statement 1 is false → Sanjay is liar.
Statement 2 is true → Sunil is truth-teller.
If Manoj came second, statement 3 is true → Manoj is truth-teller.
Then statement 4 says 'Manoj is lying' - false → Kiran is liar.
This gives 2 truth-tellers (Sunil, Manoj) and 2 liars, consistent.

Therefore, the only consistent assignment is Sunil came first.

Let's solve by cases:

Case 1: Amit came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Meera is liar.
Statement 3: Divya says 'I came second' - unknown.
Statement 4: Kiran says 'Divya is lying'.
This leads to multiple possibilities.

Case 2: Meera came first.
Then statement 1 is false → Amit is liar.
Statement 2 is true → Meera is truth-teller.
If Divya came second, statement 3 is true → Divya is truth-teller.
Then statement 4 says 'Divya is lying' - false → Kiran is liar.
This gives 2 truth-tellers (Meera, Divya) and 2 liars, consistent.

Therefore, the only consistent assignment is Meera came first.

Let's solve by cases:

Case 1: Priya came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Pooja is liar.
Statement 3: Anita says 'I came second' - unknown.
Statement 4: Kiran says 'Anita is lying'.
This leads to multiple possibilities.

Case 2: Pooja came first.
Then statement 1 is false → Priya is liar.
Statement 2 is true → Pooja is truth-teller.
If Anita came second, statement 3 is true → Anita is truth-teller.
Then statement 4 says 'Anita is lying' - false → Kiran is liar.
This gives 2 truth-tellers (Pooja, Anita) and 2 liars, consistent.

Therefore, the only consistent assignment is Pooja came first.

Let's solve by cases:

Case 1: Harsha came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Farhan is liar.
Statement 3: Deepa says 'I came second' - unknown.
Statement 4: Gaurav says 'Deepa is lying'.
This leads to multiple possibilities.

Case 2: Farhan came first.
Then statement 1 is false → Harsha is liar.
Statement 2 is true → Farhan is truth-teller.
If Deepa came second, statement 3 is true → Deepa is truth-teller.
Then statement 4 says 'Deepa is lying' - false → Gaurav is liar.
This gives 2 truth-tellers (Farhan, Deepa) and 2 liars, consistent.

Therefore, the only consistent assignment is Farhan came first.

Let's solve by cases:

Case 1: Ravi came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Rahul is liar.
Statement 3: Divya says 'I came second' - unknown.
Statement 4: Manoj says 'Divya is lying'.
This leads to multiple possibilities.

Case 2: Rahul came first.
Then statement 1 is false → Ravi is liar.
Statement 2 is true → Rahul is truth-teller.
If Divya came second, statement 3 is true → Divya is truth-teller.
Then statement 4 says 'Divya is lying' - false → Manoj is liar.
This gives 2 truth-tellers (Rahul, Divya) and 2 liars, consistent.

Therefore, the only consistent assignment is Rahul came first.

Let's solve by cases:

Case 1: Deepa came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Ravi is liar.
Statement 3: Kiran says 'I came second' - unknown.
Statement 4: Vikram says 'Kiran is lying'.
This leads to multiple possibilities.

Case 2: Ravi came first.
Then statement 1 is false → Deepa is liar.
Statement 2 is true → Ravi is truth-teller.
If Kiran came second, statement 3 is true → Kiran is truth-teller.
Then statement 4 says 'Kiran is lying' - false → Vikram is liar.
This gives 2 truth-tellers (Ravi, Kiran) and 2 liars, consistent.

Therefore, the only consistent assignment is Ravi came first.

Let's solve by cases:

Case 1: Manoj came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Kiran is liar.
Statement 3: Farhan says 'I came second' - unknown.
Statement 4: Rohan says 'Farhan is lying'.
This leads to multiple possibilities.

Case 2: Kiran came first.
Then statement 1 is false → Manoj is liar.
Statement 2 is true → Kiran is truth-teller.
If Farhan came second, statement 3 is true → Farhan is truth-teller.
Then statement 4 says 'Farhan is lying' - false → Rohan is liar.
This gives 2 truth-tellers (Kiran, Farhan) and 2 liars, consistent.

Therefore, the only consistent assignment is Kiran came first.

Let's solve by cases:

Case 1: Anita came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Kiran is liar.
Statement 3: Neha says 'I came second' - unknown.
Statement 4: Rohan says 'Neha is lying'.
This leads to multiple possibilities.

Case 2: Kiran came first.
Then statement 1 is false → Anita is liar.
Statement 2 is true → Kiran is truth-teller.
If Neha came second, statement 3 is true → Neha is truth-teller.
Then statement 4 says 'Neha is lying' - false → Rohan is liar.
This gives 2 truth-tellers (Kiran, Neha) and 2 liars, consistent.

Therefore, the only consistent assignment is Kiran came first.

Let's solve by cases:

Case 1: Gaurav came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Manoj is liar.
Statement 3: Ravi says 'I came second' - unknown.
Statement 4: Rohan says 'Ravi is lying'.
This leads to multiple possibilities.

Case 2: Manoj came first.
Then statement 1 is false → Gaurav is liar.
Statement 2 is true → Manoj is truth-teller.
If Ravi came second, statement 3 is true → Ravi is truth-teller.
Then statement 4 says 'Ravi is lying' - false → Rohan is liar.
This gives 2 truth-tellers (Manoj, Ravi) and 2 liars, consistent.

Therefore, the only consistent assignment is Manoj came first.

Let's solve by cases:

Case 1: Meera came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Sanjay is liar.
Statement 3: Priya says 'I came second' - unknown.
Statement 4: Rohan says 'Priya is lying'.
This leads to multiple possibilities.

Case 2: Sanjay came first.
Then statement 1 is false → Meera is liar.
Statement 2 is true → Sanjay is truth-teller.
If Priya came second, statement 3 is true → Priya is truth-teller.
Then statement 4 says 'Priya is lying' - false → Rohan is liar.
This gives 2 truth-tellers (Sanjay, Priya) and 2 liars, consistent.

Therefore, the only consistent assignment is Sanjay came first.

Let's solve by cases:

Case 1: Meera came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Sunil is liar.
Statement 3: Ravi says 'I came second' - unknown.
Statement 4: Rohan says 'Ravi is lying'.
This leads to multiple possibilities.

Case 2: Sunil came first.
Then statement 1 is false → Meera is liar.
Statement 2 is true → Sunil is truth-teller.
If Ravi came second, statement 3 is true → Ravi is truth-teller.
Then statement 4 says 'Ravi is lying' - false → Rohan is liar.
This gives 2 truth-tellers (Sunil, Ravi) and 2 liars, consistent.

Therefore, the only consistent assignment is Sunil came first.

Let's solve by cases:

Case 1: Amit came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Manoj is liar.
Statement 3: Harsha says 'I came second' - unknown.
Statement 4: Farhan says 'Harsha is lying'.
This leads to multiple possibilities.

Case 2: Manoj came first.
Then statement 1 is false → Amit is liar.
Statement 2 is true → Manoj is truth-teller.
If Harsha came second, statement 3 is true → Harsha is truth-teller.
Then statement 4 says 'Harsha is lying' - false → Farhan is liar.
This gives 2 truth-tellers (Manoj, Harsha) and 2 liars, consistent.

Therefore, the only consistent assignment is Manoj came first.

Let's solve by cases:

Case 1: Rahul came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Priya is liar.
Statement 3: Vikram says 'I came second' - unknown.
Statement 4: Sunil says 'Vikram is lying'.
This leads to multiple possibilities.

Case 2: Priya came first.
Then statement 1 is false → Rahul is liar.
Statement 2 is true → Priya is truth-teller.
If Vikram came second, statement 3 is true → Vikram is truth-teller.
Then statement 4 says 'Vikram is lying' - false → Sunil is liar.
This gives 2 truth-tellers (Priya, Vikram) and 2 liars, consistent.

Therefore, the only consistent assignment is Priya came first.

Let's solve by cases:

Case 1: Manoj came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Meera is liar.
Statement 3: Gaurav says 'I came second' - unknown.
Statement 4: Vikram says 'Gaurav is lying'.
This leads to multiple possibilities.

Case 2: Meera came first.
Then statement 1 is false → Manoj is liar.
Statement 2 is true → Meera is truth-teller.
If Gaurav came second, statement 3 is true → Gaurav is truth-teller.
Then statement 4 says 'Gaurav is lying' - false → Vikram is liar.
This gives 2 truth-tellers (Meera, Gaurav) and 2 liars, consistent.

Therefore, the only consistent assignment is Meera came first.

Let's solve by cases:

Case 1: Gaurav came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Meera is liar.
Statement 3: Neha says 'I came second' - unknown.
Statement 4: Kiran says 'Neha is lying'.
This leads to multiple possibilities.

Case 2: Meera came first.
Then statement 1 is false → Gaurav is liar.
Statement 2 is true → Meera is truth-teller.
If Neha came second, statement 3 is true → Neha is truth-teller.
Then statement 4 says 'Neha is lying' - false → Kiran is liar.
This gives 2 truth-tellers (Meera, Neha) and 2 liars, consistent.

Therefore, the only consistent assignment is Meera came first.

Let's solve by cases:

Case 1: Pooja came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Deepa is liar.
Statement 3: Ravi says 'I came second' - unknown.
Statement 4: Meera says 'Ravi is lying'.
This leads to multiple possibilities.

Case 2: Deepa came first.
Then statement 1 is false → Pooja is liar.
Statement 2 is true → Deepa is truth-teller.
If Ravi came second, statement 3 is true → Ravi is truth-teller.
Then statement 4 says 'Ravi is lying' - false → Meera is liar.
This gives 2 truth-tellers (Deepa, Ravi) and 2 liars, consistent.

Therefore, the only consistent assignment is Deepa came first.

Let's solve by cases:

Case 1: Gaurav came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Sanjay is liar.
Statement 3: Neha says 'I came second' - unknown.
Statement 4: Sunil says 'Neha is lying'.
This leads to multiple possibilities.

Case 2: Sanjay came first.
Then statement 1 is false → Gaurav is liar.
Statement 2 is true → Sanjay is truth-teller.
If Neha came second, statement 3 is true → Neha is truth-teller.
Then statement 4 says 'Neha is lying' - false → Sunil is liar.
This gives 2 truth-tellers (Sanjay, Neha) and 2 liars, consistent.

Therefore, the only consistent assignment is Sanjay came first.

Let's solve by cases:

Case 1: Ravi came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Amit is liar.
Statement 3: Manoj says 'I came second' - unknown.
Statement 4: Farhan says 'Manoj is lying'.
This leads to multiple possibilities.

Case 2: Amit came first.
Then statement 1 is false → Ravi is liar.
Statement 2 is true → Amit is truth-teller.
If Manoj came second, statement 3 is true → Manoj is truth-teller.
Then statement 4 says 'Manoj is lying' - false → Farhan is liar.
This gives 2 truth-tellers (Amit, Manoj) and 2 liars, consistent.

Therefore, the only consistent assignment is Amit came first.

Let's solve by cases:

Case 1: Neha came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Pooja is liar.
Statement 3: Sanjay says 'I came second' - unknown.
Statement 4: Manoj says 'Sanjay is lying'.
This leads to multiple possibilities.

Case 2: Pooja came first.
Then statement 1 is false → Neha is liar.
Statement 2 is true → Pooja is truth-teller.
If Sanjay came second, statement 3 is true → Sanjay is truth-teller.
Then statement 4 says 'Sanjay is lying' - false → Manoj is liar.
This gives 2 truth-tellers (Pooja, Sanjay) and 2 liars, consistent.

Therefore, the only consistent assignment is Pooja came first.