Aspire Faculty ID #4056 · Topic: NIMCET 2019 · Just now
NIMCET 2019

John, Johny and Janardan participated in a race and each won a different medal among Gold, Silver and Bronze, not necessarily in that order. Each person among them gives two replies to any question, one of which is true and the other is false (in any order). When asked about the details of the medals obtained by them, the following were their replies:
John: I won the Gold medal.Johny won the Bronze medal.
Johny: John won the Silver medal.I won the Gold medal.
Janardan: Johny won the Silver medal.I won the Gold medal.

Which among the following is the correct order of the persons who won the Gold medal, the Silver medal and the Bronze medal respectively?

Solution

Solution (One True & One False per person)

  1. Assumption rule: From each pair of statements, exactly one is true.
  2. Check Johny’s pair:
    • S₁: “John won Silver.”
    • S₂: “I (Johny) won Gold.”
    Exactly one true ⇒ If S₂ were true (Johny = Gold), then S₁ must be false (John ≠ Silver). But that doesn’t fix others cleanly. Try the other way: make S₁ true and S₂ false ⇒ John = Silver and Johny ≠ Gold.
  3. Assign Gold: With John already Silver, Gold must be either John or Janardan. John can’t be Gold now ⇒ Janardan = Gold.
  4. Remaining Bronze: goes to Johny.
John’s statements:
  • “I won Gold.” → False
  • “Johny won Bronze.” → True
Johny’s statements:
  • “John won Silver.” → True
  • “I won Gold.” → False
Janardan’s statements:
  • “Johny won Silver.” → False
  • “I won Gold.” → True
✅ Final Order (Gold, Silver, Bronze): Janardan, John, Johny
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