RU-ALLRUSSIAN 1977 Problem 16

You are given a set of scales and a set of n different weights. R represents the state in which the right pan is heavier, L represents the state in which the left pan is heavier and B represents the state in which the pans balance. Show that given any n- letter string of Rs and Ls you can put the weights onto the scales one at a time so that the string represents the successive states of the scales. For example, if the weights were 1, 2 and 3 and the string was LRL, then you would place 1 in the left pan, then 2 in the right pan, then 3 in the left pan.