MathDB

In a remote island, a language in which every word can be written using only the letters

a

b

c

d

e

f

g

is spoken. Let's say two words are synonymous if we can transform one into the other according to the following rules: i) Change a letter by another two in the following way:

a \rightarrow bc,\ b \rightarrow cd,\ c \rightarrow de,\ d \rightarrow ef,\ e \rightarrow fg,\ f\rightarrow ga,\ g\rightarrow ab

ii) If a letter is between other two equal letters, these can be removed. For example,

dfd \rightarrow f

. Show that all words in this language are synonymous.

Problem Statement