Problem 5. The Martian traffic light consists of six identical bulbs arranged in two horizontal rows (one above the other) with three bulbs in each. A rover driver in the fog can distinguish the number and relative position of the lit bulbs on the traffic light (for example, if two bulbs are lit, whether they are in the same horizontal row or in different rows, whether they are in the same vertical row, or in adjacent vertical rows, or in the two outer vertical rows). However, he cannot distinguish the unlit bulbs and the body of the traffic light. Therefore, if only one bulb is lit, it is impossible to determine which one of the six it is). How many signals of the Martian traffic light can the rover driver distinguish in the fog? If no bulb on the traffic light is lit, the driver cannot see it.
Answer: 44.

Solution. If two traffic light signals differ only by the shift of the lit bulbs, then the driver cannot distinguish them (and vice versa). Therefore, any signal can either be transformed by a shift to the left and/or up into an indistinguishable signal, which has at least one bulb lit in the top horizontal row and at least one in the left vertical row, or the signal already has this property. There are two cases.