Problem 6. In a square room, there is a light bulb on each wall that can shine in one of the seven colors of the rainbow. There are no light bulbs in the room that shine the same color. In one move, a person can change the color of one of the light bulbs to a color that is not used by any light bulb in the room at the moment of the move, which will also change the colors to the two remaining unused colors. (After this, there are still no two light bulbs with the same color in the room). What is the minimum number of moves needed to ensure that each light bulb has shone in each of the seven colors?
Answer: 8 moves.

Solution. Each light bulb on the walls of the room must change color 6 times, and there are four walls, so the total number of color changes is at least 24. On the other hand, in one move, the color of three light bulbs changes, so the number of moves is at least 8. An example for 8 moves can be provided (see the figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_a8dcf73bc968594034d3g-2.jpg?height=197&width=1765&top_left_y=2551&top_left_x=137)