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In the book 'Quadratic algebras' by Polishchuk and Positselski [23] algebraswith a small number of generators (n=2,3) are considered. For some number r ofrelations possible Hilbert series are listed, and those appearing as series ofKoszul algebras are specified. The first case, where it was not possible to do,namely the case of three generators n=3 and six relations r=6 is formulated asan open problem. We give here a complete answer to this question, namely forquadratic algebras with dim A_1=dim A_2=3, we list all possible Hilbert series,and find out which of them can come from Koszul algebras, and which can not.  As a consequence of this classification, we found an algebra, which serves asa counterexample to another problem from the same book [23] (Chapter 7, Sec. 1,Conjecture 2), saying that Koszul algebra of finite global homologicaldimension d has dim A_1 >= d. Namely, the 3-generated algebra A given byrelations xx+yx=xz=zy=0 is Koszul and its Koszul dual algebra A^! has Hilbertseries of degree 4: H_{A^!}(t)= 1+3t+3t^2+2t^3+t^4, hence A has globalhomological dimension 4.

Two problems from the Polishchuk and Positselski book on Quadratic algebras