A small private club has 100 members. If everyone trusts the president of the club and all communication is routed through them, how many secret keys are needed in total?
Understand the Problem
The question is asking for the total number of secret keys needed for communication among 100 members of a club, assuming trust is established via the president. This involves understanding communication protocols within a network of members.
Answer
99
Answer for screen readers
99
Steps to Solve
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Understanding Communication Setup
In this scenario, there are 100 members but all communication goes through the president. Each member will only need a secret key shared with the president. -
Calculating the Keys Needed
Each of the 99 other members will need a secret key to communicate with the president. The total number of keys required is simply the number of members excluding the president.Calculation:
$$ \text{Total Keys} = 99 $$ -
Finalizing the Answer
Since we only need one key per member (excluding the president), the total number of keys needed is 99.
99
More Information
In this communication model, the president acts as a central hub for all communication, allowing for a reduction in the total number of keys necessary for secure communication among the members.
Tips
- Confusing the total number of secret keys with the total number of members.
- Assuming that each member needs a key for every other member; this isn’t necessary since the president facilitates all communications.
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