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In a recent systematic study, C.Sandon and F.Zanello offered 30 conjectured identities for partitions.In this lecture, we provide proofs for all 30 conjectures of Sandon and Zanello.Most of our proofs depend upon known modular equations and formulas of Ramanujan for theta functions, while for the remainder of our proofs it was necessary to derive new modular equations and to employ the process of duplication to extend Ramanujans catalogue of theta function formulas.