11. At a railway station, there are $k$ traffic lights, each of which can transmit three signals: red, yellow, and green. How many different signals can be transmitted using all the traffic lights?
11. Solution. Using two semaphores, one can transmit $3 \cdot 3=3^{2}$ signals, using three $-3^{2} \cdot 3=$ $=3^{3}$ different signals, using four $-3^{3} \cdot 3=3^{4}$ signals, and so on. Using $k$ semaphores, one can transmit $3^{k}$ different signals.