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Delivery men with a false lead

Numerical territoryLevel 4 · Advanced · ●●●●○

Four distributors—Ana, Beto, Cora and Diego—came in positions from 1 to 4, without ties.
Exactly one of these notes is known to be false:

  • Ana: “I was first.”
  • Beto: “Ana arrived immediately before me.”
  • Cora: “Ana arrived before Diego.”
  • Diego: “Beto arrived before Cora.”

Determine the order of arrival.

Hints

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  1. There is no other permutation that meets that exact quota of falsehood.
  2. There is exactly one false one (Beto's), as the statement requires.
  3. Direct verification: Cora: “Ana arrived before Diego.” $1<2 \Rightarrow$ true.

Solution

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Answer:

$$ \text{Ana},\ \text{Diego},\ \text{Beto},\ \text{Cora}. $$

Direct check:

  • Ana: “I was first.” $\Rightarrow$ true.
  • Beto: “Ana arrived immediately before me.”

Beto is 3rd and Ana is 1st $\Rightarrow$ false.

  • Cora: “Ana arrived before Diego.”

$1<2$ $\Rightarrow$ true.

  • Diego: “Beto arrived before Cora.”

$3<4$ $\Rightarrow$ true.
There is exactly one false one (Beto's), as the statement requires.
There is no other permutation that meets that exact quota of falsehood.


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