Select the correct alternative from the given choices.

Sameer, Sameep, and Sumer participated in a quiz contest and each one of them received exactly one title amongst the Winner, the First Runner-up and the Second Runner-up. When asked, "Who among you three is the winner?", the following were their replies:**Sameer:** I am the winner.

Sameep is not the 1st Runner-up.**Sameep**: I am the winner, Sameer is the 2nd runner up.**Sumer: **I am the winner.

Sameep is the 2nd runner-up.

It is also known that one among them always tells the truth, one always lies and one alternate between the truth and lie (not necessarily in that order).**Who can never be the first runner-up?**

#### Options

Sameer

Sameep

Sumer

Cannot be determined

#### Solution

(T → True; F → False)

(i) Assuming that Sameer is the Truth-teller, we get the following arrangement

Statement I |
Statement II |
|||

Sameer |
T | T | Truthteller | Winner |

Sameep |
F | F | Liar | 2nd runner-up |

Sumer |
F | T | Alt | 1st runner-up |

(ii) Assuming Sameep is the Truth-teller, we get the following arrangement

Statement I |
Statement II |
||

Sameer |
F | T | 2nd runner-up |

Sameep |
T | T | Winner |

Sumer |
F | F | 1st runner-up |

(iii) Assuming Sumer is the Truth-teller, we get the following arrangement.

Statement I |
Statement II |
|||

Sameer |
F | T | Alt | 1st runner-up |

Sameep |
F | F | Liar | 2nd runner-up |

Sumer |
T | T | Truthteller | Winner |

Hence, either Sameer or Sumer can be the 1st runner-up, but not Sameep.

So, **Sameep **is the correct option.