Statement

Silviu the lumberjack, who lives in "The Wonderful Grove", is well known for his ability and is ready to tackle another challenging task. Winter is coming and a big tree needs to be cut. Silviu is carefully studying the structure of the tree, taking precise notes about each branch and its connections. He has labelled all the points of connection between two or more branches with numbers from 1 to N. He has opted for making a single cut (after all, every cut requires physical effort…), getting rid of the branches conjuncting there and transporting the remaining smaller pieces. The company selected for transport is going to accept a part of the tree only if it is smaller (or equal) than half of the size of the original tree. The size of a (part of a) tree is merely the number of the conjunction points in it. At which points can Silviu make his cut to satisfy the requirement from the transport company?