Question 15
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 $R$s and $L$s 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.