How many point-to-point WANs are needed to connect n LANs if each LAN should be able to directly communicate with any other LAN?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To connect n<\/strong> LANs with point-to-point WANs<\/strong> such that each LAN can directly communicate with every other LAN<\/strong>, we need to create a fully connected (mesh) network<\/strong>.<\/p>\n\n\n\n n(n\u22121)2\\frac{n(n – 1)}{2}<\/p>\n\n\n\n In a fully connected<\/strong> network using point-to-point Wide Area Networks (WANs)<\/strong>, each LAN must have a direct connection<\/strong> to every other LAN<\/strong>. A point-to-point connection<\/strong> means that there is a dedicated line<\/strong> (or link) between exactly two nodes<\/strong>\u2014in this case, between two LANs.<\/p>\n\n\n\n To find out how many such connections are needed, we use a fundamental concept from combinatorics:<\/p>\n\n\n\n The number of unique pairs that can be formed from n<\/strong> elements is given by:(n2)=n(n\u22121)2\\binom{n}{2} = \\frac{n(n – 1)}{2}<\/p>\n<\/blockquote>\n\n\n\n Each pair of LANs represents one required point-to-point WAN<\/strong> connection.<\/p>\n\n\n\n Suppose you have 4 LANs: LAN1, LAN2, LAN3, and LAN4.<\/p>\n\n\n\n Using the formula: 4(4\u22121)2=4\u00d732=6\\frac{4(4 – 1)}{2} = \\frac{4 \\times 3}{2} = 6<\/p>\n\n\n\n So you need 6 point-to-point WANs<\/strong> to ensure direct communication<\/strong> between all LANs.<\/p>\n\n\n\n Using fewer WAN connections<\/strong> would mean some LANs have to communicate indirectly<\/strong> (via another LAN), which violates<\/strong> the condition that each LAN must communicate directly<\/strong> with every other.<\/p>\n\n\n\n This setup is expensive and complex in large networks, which is why technologies like switches<\/strong>, routers<\/strong>, or central hubs<\/strong> (like in star topology) are used to simplify connections.<\/p>\n\n\n\n For n LANs<\/strong>, the number of point-to-point WANs<\/strong> needed for full direct communication is: n(n\u22121)2\\boxed{\\frac{n(n – 1)}{2}}<\/p>\n","protected":false},"excerpt":{"rendered":" How many point-to-point WANs are needed to connect n LANs if each LAN should be able to directly communicate with any other LAN? The correct answer and explanation is: To connect n LANs with point-to-point WANs such that each LAN can directly communicate with every other LAN, we need to create a fully connected (mesh) […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-21916","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21916","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=21916"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21916\/revisions"}],"predecessor-version":[{"id":21917,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/21916\/revisions\/21917"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=21916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=21916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=21916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\ud83d\udd22 Correct Answer:<\/strong><\/h3>\n\n\n\n
\n\n\n\n\u2705 Explanation (300 Words):<\/strong><\/h3>\n\n\n\n
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\n\n\n\n\ud83d\udca1 Example:<\/h3>\n\n\n\n
\n\n\n\n\ud83d\udd01 Why Not Use Fewer?<\/h3>\n\n\n\n
\n\n\n\n\u2705 Final Note:<\/h3>\n\n\n\n