In a class experiment, $\pu{20 mL}$ of hydrochloric acid was diluted with distilled water to $\pu{500 mL}$. $\pu{20 mL}$ of this diluted solution was added to $\pu{20 mL}$ of $\pu{0.1 M}$ sodium hydroxide in a conical flask. Potassium permanganate was added into the flask until it turned a light pink colour. $\pu{15.6 mL}$ was needed.
The information I know so far is: $$\ce{NaOH + HCl -> NaCl + H2O}$$ \begin{align} c &= \frac{n}{V}\\ n &= c \cdot V\\ c(\ce{NaOH}) &= \pu{0.1 M}\\ V(\ce{NaOH}) &= \pu{0.02 L}\\ n(\ce{NaOH}) &= \pu{0.1 M}\times \pu{0.02 L} \end{align}
I am not understanding how it is possible to work out the concentration of hydrochloric acid from the conducted experiment and the known information, and I am confused as to how the volume of potassium permanganate allows this concentration to be found.