problem: Evaluate $\lfloor 11.1 \rfloor + 2 \cdot \lfloor 0.5 \cdot 11.1 \rfloor .$
solution: Since $11 < 11.1 < 12$ we have $\lfloor 11.1 \rfloor = 11.$  Next we have that  $2 \cdot \lfloor 0.5 \cdot 11.1 \rfloor = 2 \lfloor 5.55 \rfloor = 2 \cdot 5 = 10.$ Therefore, $\lfloor 11.1 \rfloor + 2 \cdot \lfloor 0.5 \cdot 11.1 \rfloor = \boxed{21}.$