  The conjecture called algebraic Montgomery-Yang problem is still open for
rational $\mathbb{Q}$-homology projective planes with cyclic quotient
singularities having ample canonical divisor. All known such surfaces have a
special birational behavior called a cascade. In this note, we establish
algebraic Montgomery-Yang problem assuming the cascade conjecture, which claims
that every rational $\mathbb{Q}$-homology projective planes with quotient
singularities having ample canonical divisor admits a cascade.
