The goal is to place one string of lights in each region. Each string contains one light of each color. The same is to be true of each row and column.
Consider the region that has a green bulb () at one end. Three strings have a green bulb on an end, so one of these strings must be used in this region. But using the top string there would put a purple bulb () in the middle column. That column already has a purple bulb, so you can't use that string in this region.
Use similar logic to try to find a string that must go in a particular region. Placing that string will then eliminate possibilities for other strings elsewhere.
It is possible to solve the puzzle without looking at the strings. For example, the third row (from the top) must have an orange bulb () in the far right column. Why? Because the rest of the row belongs to a region that already has an orange bulb. Similar logic will allow you to fill in all the other lights.
Information about this puzzle (a Latin Squares Puzzle)
Solution Guide (using strings) (this walks you step by step to the solution)
Solution Guide (without strings) (this walks you step by step to the solution)
What is Cubber D. Bear's middle name?
Solution (don't look if you don't want to see the solution!)