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Using a certain one-to-one correspondence, Koll\\'ar formulated the algebraic version of the Montgomery-Yang problem: every projective surface $S$ with quotient singularities such that $b_2(S) = 1$ has at most 3 singular points if its smooth locus $S^0$ is simply-connected.\n  In this paper, we prove the conjecture under the assumption that $S$ has at least one noncyclic singularity. 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