A method for synthesizing a target double stranded (ds) polynucleotide by providing an oligonucleotide library within an array device that has a diversity of oligonucleotide library members, each of which has a different nucleotide sequence and is contained in a separate library containment in an aqueous solution. The library includes single stranded oligonucleotides and double stranded oligonucleotides with at least one overhang and covers at least 10,000 pairs of matching oligonucleotides. In a first step, transferring at least a first pair of matching oligonucleotides transferred from the library into a first reaction containment using a liquid handler and the matching oligonucleotides are assembled, thereby obtaining a first reaction product comprising at least one overhang. Further reaction products are then likewise obtained and are assembled in a predetermined workflow using an algorithm, thereby producing said target ds polynucleotide with an overhang, optionally followed by a finalization step to prepare blunt ends.