GATE 2019 CS – Question 59
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
Explanation
Connecting $k$ switches in a tree uses $2(k-1)$ ports for the links, leaving $8k-2(k-1)=6k+2$ ports for machines. We need $6k+2\ge15$, so $k\ge\frac{13}{6}$ and $k=3$.