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Question
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.
