Houston Problem Book Problem 35

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Problem 35 (HPB): Suppose $f$ is a continuous mapping of a continuum $X$ onto a continuum $Y$, $Y=H \cup K$ is a decomposition of $Y$ into subcontinua $H$ and $K$, $f \big|_{f^{-1}(H)}$ and $f\big|_{f^{-1}(K)}$ are confluent, and $H \cap K$ is a continuum which does not cut $Y$ and is an end continuum of both $H$ and $K$. Is $f$ confluent? (Asked by W.T. Ingram, 11 October 1972)

Answer: Unknown