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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?

  1. $5$
  2. $10$
  3. $9$
  4. $15$
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Let Englishmen be E1, E2 and E3 and Frenchmen be F1, F2 and F3. Presuming E3 knows French, so 5 calls are required so that E3 knows everybody’s secret and everybody knows E3’s secret. One call would from E1 to E2. Besides this, 3 calls i.e. F1 to F2, F2 to F3 and F1 to F3.

Hence total number of calls = 5 + 1 + 3 = 9. So answer is 3rd option.
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