XI OBM

Let $R$ be reflection in $BC$: $(x,y)\to (3-y,3-x)$. Let $S$ be reflection in $AC$: $(x,y)\to (-x,y)$. Let $T$ be reflection in $AB$: $(x,y)\to (x,-y)$. Let $RS$ denote the reflection $R$ followed by the reflection $S$. Then we have $Q=STR$ is $(x,y)\to (y+3,x+3)$. So $Q^2$ is $(x,y)\to (x+6,y+6)$, and $Q^{10}$ is $(x,y)\to (x+30,y+30)$. $P=TRS$ is $(x,y)\to (x,-y)\to (y+3,-x+3)\to (-y-3,-x+3)$. So $P^2$ is $(x,y)\to (x-6,y+6)$. Hence $Q^{10}{P}^2$ is $(x,y)\to (x+24,y+36)$, which is the required translation.