OME 1970 Problem 2

A plant grows in the way we describe below. has a trunk which forks into two branches; each branch of the plant can, in turn, branch off into other two branches, or end in a bud. We will call the load of a branch the total number of buds it bears, that is, the number of buds fed by the sap that passes by that branch; and we will call the distance of a bud the number of bifurcations that it sap has to go through to get from the trunk to that bud. If n is the number of bifurcations that a certain plant of that type has, it is asks a) the number of branches of the plant, b) the number of buds, c) show that the sum of the charges of all the branches is equal to the sum of the clearances of all buds.