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Question:

Three Englishmen and three Frenchmen work for the same company. Each of them knows a secret not known to others. They need to exchange these secrets over person-to-person phone calls so that eventually each person knows all six secrets. None of the Frenchmen knows English, and only one Englishman knows French. What is the minimum number of phone calls needed for the above purpose?

Explanation:

Let E₁, E₂ and E₃ be the three Englishmen and F₁, F₂ and F₃ be the three Frenchmen.

Let E₃ be the only Englishman knowing French.

Now, Let A ↔ B denote a phone call between A and B, where they both tell each other their secrets.The following phone calls will ensure that all six persons know all the six secrets.

1. E₁ ↔ E₃
2. E₂ ↔ E₃ (Now E₃ knows all the secrets with the Englishmen)

3. F₁ ↔ F₃
4. F₂ ↔ F₃ (Now F₃ knows all the secrets with the Frenchmen)

5. F₃ ↔ E₃ (Now F₃ and E₃ know all the secrets)

6. E₃ ↔ E₂
7. E₃ ↔ E₁ (Now E₁ and E₂ know all the secrets)

8. F₃ ↔ F₂
9. F₃ ↔ F₁(Now F₁ and F₂ know all the secrets)

Thus, a minimum of 9 calls are needed to pass all the secrets to all the six persons.

Hence, option (c).

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