competition_setting_claims: Worksheet 10 - Expert Practice competition_setting_claims EXPERT

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 Manoj is liar.
Statement 3: Priya says 'I came second' - unknown.
Statement 4: Leena says 'Priya is lying'.
This leads to multiple possibilities.

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

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

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

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

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

Therefore, the only consistent assignment is Harsha 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: Farhan says 'I came second' - unknown.
Statement 4: Kiran says 'Farhan 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 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 (Pooja, Farhan) and 2 liars, consistent.

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

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

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

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

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

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

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

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

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

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

Therefore, the only consistent assignment is Rahul came first.

Let's solve by cases:

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

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

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

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

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

Therefore, the only consistent assignment is Harsha 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: Farhan says 'I came second' - unknown.
Statement 4: Kiran says 'Farhan 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 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 (Sunil, Farhan) and 2 liars, consistent.

Therefore, the only consistent assignment is Sunil 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: Farhan says 'I came second' - unknown.
Statement 4: Kiran says 'Farhan 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 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 (Ravi, Farhan) and 2 liars, consistent.

Therefore, the only consistent assignment is Ravi came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Sanjay came first.

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 Harsha is liar.
Statement 3: Anita says 'I came second' - unknown.
Statement 4: Manoj says 'Anita is lying'.
This leads to multiple possibilities.

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

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

Case 2: Amit came first.
Then statement 1 is false → Meera is liar.
Statement 2 is true → Amit 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 (Amit, Vikram) and 2 liars, consistent.

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

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

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

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

Therefore, the only consistent assignment is Leena came first.