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Protein structure and function is determined by the arrangement of the linear sequence of amino acids in 3D space. We show that a deep graph neural network, ProteinSolver, can precisely design sequences that fold into a predetermined shape by phrasing this challenge as a constraint satisfaction problem (CSP), akin to Sudoku puzzles. We trained ProteinSolver on over 70,000,000 real protein sequences corresponding to over 80,000 structures. We show that our method rapidly designs new protein sequences and benchmark them in silico using ene