Consider that 15 machines need to be connected in a LAN using 8-port Ethernet…
2019
Consider that 15 machines need to be connected in a LAN using 8-port Ethernet switches. Assume that these switches do not have any separate uplink ports. The minimum number of switches needed is__________.
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Correct answer: 3
Key insight: each 8-port switch has 8 ports, but ports used for links between switches are not available to connect machines.
Total ports across N switches = 8N.
To connect N switches into one LAN you need at least N-1 links; each link uses 2 ports (one on each switch), so ports used for inter-switch links = 2(N-1).
Ports available for machines = 8N - 2(N-1) = 6N + 2.
Find the smallest integer N such that 6N + 2 ≥ 15.
Solve: 6N + 2 ≥ 15 ⇒ 6N ≥ 13 ⇒ N ≥ 13/6 ⇒ N ≥ 2.167, so the minimum integer N is 3.
Therefore the minimum number of 8-port switches required is 3.
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