$$\begin{gathered} 1) 4\mathrm{HCl} + {\mathrm{MnO}}_2 \to {\mathrm{MnCl}}_2 + {\mathrm{Cl}}_2 + 2{\mathrm{H}}_2\mathrm{O} \\ 1 | 2{\mathrm{Cl}}^{—1} —2\mathrm{e}\to {\mathrm{Cl}}_2^0 \\ 1 | {\mathrm{Mn}}^{+4}+2\mathrm{e}\to {\mathrm{Mn}}^{+2} \\ 2) 3{\mathrm{Cl}}_2 + 6\mathrm{KOH} \to 5\mathrm{KCl} + {\mathrm{KClO}}_3 + 3{\mathrm{H}}_2\mathrm{O} \\ 5 | {\mathrm{Cl}}_2^0 +2\mathrm{e}\to 2{\mathrm{Cl}}^{—1} \\ 1 | {\mathrm{Cl}}_2^0 —10\mathrm{e}\to 2{\mathrm{Cl}}^{+5} \end{gathered}$$