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In 1909 Borel defined normality as a notion of randomness of the digits ofthe representation of a real number over certain base (fractional expansion).If we think the representation of a number over a base as an infinite sequenceof symbols from a finite alphabet $A$, we can define normality directly forwords of symbols of $A$: A word $x$ is normal to the alphabet $A$ if everyfinite block of symbols from $A$ appears with the same asymptotic frequency in$x$ as every other block of the same length. Many examples of normal words havebeen found since its definition, being Champernowne in 1933 the first to showan explicit and simple instance. Moreover, it has been characterized how we canselect subsequences of a normal word $x$ preserving its normality, alwaysleaving the alphabet $A$ fixed. In this work we consider the dual problem whichconsists of inserting symbols in infinite positions of a given word, in such away that normality is preserved. Specifically, given a symbol $s$ that is notpresent on the original alphabet $A$ and given a word $x$ that is normal to thealphabet $A$ we solve how to insert the symbol $s$ in infinite positions of theword $x$ such that the resulting word is normal to the expanded alphabet $A\cup\{s\}$.

From randomness in two symbols to randomness in three symbols