We make a sequence of diagrams. The first diagram consists of a single node. The second diagram is made from the first diagram by drawing two edges of length from that node, and putting a node at the other end of each new edge. After that, we make each new diagram from the previous diagram by adding two new edges to each node, with these new edges each having half the length of the edges that were added in the previous diagram. We also attach a node to the end of each new edge. The first four diagrams are shown. Find the total length of all the edges in the fifth diagram, in cm.
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Junior Mathematical Olympiad 2024 (2024)
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