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FYI: this is not a homework question. I was reading an article (http://packetlife.net/blog/2008/jun/19/ospf-network-types/) in OSPF and couldn't understand this point.

"a segment containing ten routers would require 45 adjacencies to form a mesh, but only 17 when a DR and BDR are in place."

This was specifically for the broadcast type of network in OSPF.

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8 routers form adjacencies to both the DR and BDR (8*2 = 16) plus an adjacency formed between the DR and BDR equals 17.

If a full mesh were required it would be 10 routers each with 9 connections. Counted as adjacencies this is (9*10)/2 = 45.

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