Master competition_setting_claims - Intermediate-Advanced Level Problems competition_setting_claims INTERMEDIATE ADVANCED

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Manoj 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 Kiran is liar.
Statement 3: Manoj says 'I came second' - unknown.
Statement 4: Rahul says 'Manoj is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Kiran 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 Pooja is liar.
Statement 3: Vikram says 'I came second' - unknown.
Statement 4: Ravi says 'Vikram is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Pooja 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 Harsha is liar.
Statement 3: Rohan says 'I came second' - unknown.
Statement 4: Divya says 'Rohan is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Harsha came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Deepa came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Anita 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 Rohan is liar.
Statement 3: Amit says 'I came second' - unknown.
Statement 4: Rahul says 'Amit is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Rohan 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 Neha is liar.
Statement 3: Harsha says 'I came second' - unknown.
Statement 4: Sanjay says 'Harsha is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Neha 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 Neha is liar.
Statement 3: Amit says 'I came second' - unknown.
Statement 4: Leena says 'Amit is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Neha 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 Gaurav is liar.
Statement 3: Farhan says 'I came second' - unknown.
Statement 4: Anita says 'Farhan is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Gaurav 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 Divya is liar.
Statement 3: Farhan says 'I came second' - unknown.
Statement 4: Neha says 'Farhan is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Divya came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Vikram 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: Neha says 'I came second' - unknown.
Statement 4: Rahul says 'Neha 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 Neha came second, statement 3 is true → Neha is truth-teller.
Then statement 4 says 'Neha is lying' - false → Rahul 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: Harsha came first.
Then statement 1 is true, statement 2 is false.
If statement 2 is false, then Pooja is liar.
Statement 3: Neha says 'I came second' - unknown.
Statement 4: Rahul says 'Neha is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Pooja 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 Sunil is liar.
Statement 3: Deepa says 'I came second' - unknown.
Statement 4: Anita says 'Deepa is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Sunil 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 Manoj is liar.
Statement 3: Farhan says 'I came second' - unknown.
Statement 4: Deepa says 'Farhan is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Manoj came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Priya 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 Amit is liar.
Statement 3: Sanjay says 'I came second' - unknown.
Statement 4: Leena says 'Sanjay is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Amit 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 Kiran is liar.
Statement 3: Harsha says 'I came second' - unknown.
Statement 4: Rohan says 'Harsha is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Kiran came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Rahul came first.