Directions: Chatia, Matia and Toni participated in a race and one of them won…

2025

Directions:

Chatia, Matia and Toni participated in a race and one of them won the race. They belong to three different communities — Sororian, Nororian and Cororian. Sororians always speak the truth, Nororians always lie, and Cororians speak the truth and lie alternately. (Each of Chatia, Matia and Toni belongs to a different one of these three communities.)

After the race, they gave these statements.

Chatia:

  1. I would have won the race if Toni had not obstructed me at the last moment.

  2. Toni always speaks the truth.

  3. Toni is the winner.

Matia:

  1. Chatia won the race.

  2. Toni is not a Nororian.

Toni:

  1. I hadn’t obstructed Chatia at the last moment.

  2. Matia won the race.

Who won the race?

  1. A.

    Matia

  2. B.

    Toni

  3. C.

    Sororian

  4. D.

    Chatia

Attempted by 3 students.

Show answer & explanation

Correct answer: D

Concept:

In a truth-teller / liar / alternator puzzle, each person is assigned exactly one of three fixed behaviours: a truth-teller's every statement is true, a liar's every statement is false, and an alternator's statements switch between true and false in the order given. Since every person here belongs to a different community, the puzzle is solved by testing which single assignment of these three behaviours makes every statement, checked in sequence, consistent with no contradictions.

Application:

  1. Assume Chatia is the truth-teller. Then Chatia's second statement, “Toni always speaks the truth,” would have to be true — but that would make Toni a truth-teller too, and two people cannot share the same community. This assignment is rejected.

  2. Assume Chatia is the alternator. Testing both possible true-false sequences across Chatia's three statements forces either (a) Toni to be the winner while Matia's truthful statement says Chatia won — a direct clash — or (b) Toni to be a truth-teller who says Matia won, while Matia (then the liar) would have to falsely deny that Toni is a liar, contradicting Toni's own truth-teller status. Both sequences break down, so this assignment is also rejected.

  3. So Chatia must be the liar. All three of Chatia's statements are then false: Toni did not obstruct Chatia at the last moment, Toni does not always speak the truth, and Toni is not the winner.

  4. Since Toni is not a truth-teller (from the previous step) and Chatia is the liar, Toni must be the alternator, leaving Matia as the truth-teller.

  5. As the truth-teller, Matia's statements must both be true: Chatia won the race, and Toni is not a liar — both consistent with Toni being the alternator.

  6. Check Toni's two statements against the alternator pattern: “I hadn’t obstructed Chatia” matches the true state of affairs (true), and “Matia won the race” is false (since Chatia actually won) — a true-then-false sequence, exactly the alternating pattern required.

Cross-check:

Every statement from all three people is now consistent with its assigned behaviour, and this is the only one of the three possible assignments for Chatia that avoids a contradiction, so the solution is unique.

Result:

Chatia won the race.

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