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?

• A. \(10\)
• B. \(9\)
• C. \(8\)
• D. \(7\)
• E. \(6\)

Answer 1

The Correct Option is B

Concept: This is a
gossip problem with language constraint:

• Secrets must spread within groups first
• Only one Englishman can communicate with Frenchmen

Step 1: Within English group.
3 Englishmen → minimum calls = \(3\)
Step 2: Within French group.
3 Frenchmen → minimum calls = \(3\)
Step 3: Bridge communication.
The bilingual Englishman exchanges secrets with French group efficiently: \[ 3 \text{ additional calls} \]
Step 4: Total calls.
\[ 3 + 3 + 3 = 9 \]
Step 5: Option analysis.

• (A) More than needed $\times$
• (B) Correct \checkmark
• (C) Insufficient $\times$
• (D) Insufficient $\times$
• (E) Impossible $\times$

Conclusion:
Thus, the correct answer is
Option (B).