Why do three DNA or RNA bases form a codon for one amino acid?

In genetics, a codon consists of a sequence of three adjacent nucleotides because this triplet structure provides enough combinations to encode the necessary biological information.

There are four different nitrogenous bases in RNA—adenine (A), guanine (G), cytosine (C), and uracil (U). If a single base coded for an amino acid, only four could be specified; if two bases formed a codon, there would be $4^2=16$ possible combinations. Neither is sufficient to account for the 20 amino acids required to build proteins. By using a triplet code, there are $4^3=64$ possible sequences.12

This arrangement allows 61 of these codons to specify the 20 amino acids, while the remaining three serve as stop signals to terminate translation. Because 61 codons map to only 20 amino acids, the genetic code is considered degenerate, meaning most amino acids are specified by more than one codon. Evidence suggests the code may have evolved from a more primitive system involving 16 dinucleotides.132