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

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: Kiran says 'I came second' - unknown.
Statement 4: Priya says 'Kiran 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 Kiran came second, statement 3 is true → Kiran is truth-teller.
Then statement 4 says 'Kiran is lying' - false → Priya is liar.
This gives 2 truth-tellers (Sunil, Kiran) and 2 liars, consistent.

Therefore, the only consistent assignment is Sunil 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: Leena says 'I came second' - unknown.
Statement 4: Priya says 'Leena 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 Leena came second, statement 3 is true → Leena is truth-teller.
Then statement 4 says 'Leena is lying' - false → Priya is liar.
This gives 2 truth-tellers (Divya, Leena) and 2 liars, consistent.

Therefore, the only consistent assignment is Divya came first.

Let's solve by cases:

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

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

Therefore, the only consistent assignment is Deepa came first.

Let's solve by cases:

Case 1: Sunil 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: Ravi says 'Farhan is lying'.
This leads to multiple possibilities.

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

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

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

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

Therefore, the only consistent assignment is Farhan came first.

Let's solve by cases:

Case 1: Sunil 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: Deepa says 'Vikram is lying'.
This leads to multiple possibilities.

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

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

Therefore, the only consistent assignment is Ravi 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: Divya says 'I came second' - unknown.
Statement 4: Deepa says 'Divya 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 Divya came second, statement 3 is true → Divya is truth-teller.
Then statement 4 says 'Divya is lying' - false → Deepa is liar.
This gives 2 truth-tellers (Sanjay, Divya) 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 Rohan is liar.
Statement 3: Pooja says 'I came second' - unknown.
Statement 4: Harsha says 'Pooja is lying'.
This leads to multiple possibilities.

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

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

Case 2: Manoj came first.
Then statement 1 is false → Ravi is liar.
Statement 2 is true → Manoj is truth-teller.
If Rohan came second, statement 3 is true → Rohan is truth-teller.
Then statement 4 says 'Rohan is lying' - false → Kiran is liar.
This gives 2 truth-tellers (Manoj, Rohan) 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 Kiran is liar.
Statement 3: Farhan says 'I came second' - unknown.
Statement 4: Divya says 'Farhan is lying'.
This leads to multiple possibilities.

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

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

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

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

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

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

Therefore, the only consistent assignment is Deepa 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: Divya says 'I came second' - unknown.
Statement 4: Anita says 'Divya 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 Divya came second, statement 3 is true → Divya is truth-teller.
Then statement 4 says 'Divya is lying' - false → Anita is liar.
This gives 2 truth-tellers (Amit, Divya) 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 Pooja is liar.
Statement 3: Rohan says 'I came second' - unknown.
Statement 4: Anita says 'Rohan is lying'.
This leads to multiple possibilities.

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

Therefore, the only consistent assignment is Pooja 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: Vikram says 'I came second' - unknown.
Statement 4: Meera says 'Vikram 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 Vikram came second, statement 3 is true → Vikram is truth-teller.
Then statement 4 says 'Vikram is lying' - false → Meera is liar.
This gives 2 truth-tellers (Rahul, Vikram) and 2 liars, consistent.

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

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

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

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

Therefore, the only consistent assignment is Anita came first.