How many types of tRNA are involved in protein synthesis in the cell?

At least 20 (the number of amino acids), no more than 61 (the number of semantic codons). Usually about 43 tRNA in prokaryotes. In humans, about 50 different tRNAs enable the incorporation of amino acids into a protein.
One of the properties of the genetic code is multiplicity, i.e., amino acids are encoded by several triplets (from 2 to 6). There are 64 variants of triplets, three triplets are terminating and do not encode amino acids. Therefore, there must be 61 types of tRNA in the cell.

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