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Corredores with a hint false

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Four runners, four statements and a single lie. The difficulty is not in testing random orders, but in seeing which statements can coexist without breaking the central condition.

Four runners—Ana, Beto, Cora and Diego—came in positions from 1 to 4, without ties. Exactly one of these statements is known to be false: - Ana: “I wasn't the first.”

  • Beto: “Ana came second.”
  • Cora: “Diego arrived immediately before me.”
  • Diego: “Beto came second.” In what order did they arrive?

Hints

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  1. It begins with Beto's statement: if it is true, it directly establishes a position.
  2. Cora's phrase not only compares two runners; forms a consecutive block.
  3. Check what happens if Diego's sentence were true. There must be exactly one lie, not one or several.

Solution

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Answer: They arrived in this order: $$
\t\t\t\t\t\t\t\t\text{Beto},\ \t\t\t\t\t\t\t\t\text{Ana},\ \t\t\t\t\t\t\t\t\text{Diego},\ \t\t\t\t\t\t\t\t\text{Cora}.
$$ We know that exactly one statement is false. Beto's phrase says that Ana came second. Let's assume it's true. So Ana occupies position 2. Cora's sentence says that Diego arrived immediately before her. If Ana is already in position 2, the only possible block for Diego and Cora is: Diego 3rd, Cora 4th. The remaining position, the first, goes to Beto. Thus we obtain: 1. Beto

  1. Anna
  2. Diego
  3. Cora Now we check the four statements: - Ana said: “I wasn't the first.” TRUE.
  • Beto said: “Ana came second.” TRUE.
  • Cora said: “Diego arrived immediately before me.” TRUE.
  • Diego said: “Beto came second.” Fake. There is exactly one false statement, as the statement requires. Therefore, the order is unique: Beto, Ana, Diego, Cora.

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