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This work is part of the Graded Ring Database project [GRDB], and is a sequelto [Altinok's 1998 PhD thesis] and [Altinok, Brown and Reid, Fano 3-folds, K3surfaces and graded rings, in SISTAG (Singapore, 2001), Contemp. Math. 314,2002, pp. 25-53]. We introduce a strategy based on Kustin-Miller unprojectionthat constructs many hundreds of Gorenstein codimension 4 ideals with 9x16resolutions (that is, 9 equations and 16 first syzygies). Our two basic gamesare called Tom and Jerry; the main application is the biregular construction ofmost of the anticanonically polarised Mori Fano 3-folds of Altinok's thesis.There are 115 cases whose numerical data (in effect, the Hilbert series) allowa Type I projection. In every case, at least one Tom and one Jerry constructionworks, providing at least two deformation families of quasismooth Fano 3-foldshaving the same numerics but different topology.

Fano 3-folds in codimension 4, Tom and Jerry, Part I