Easy. Before going down to the basement, tell somebody else in the house to flip each switch in 10-second intervals after 5 minutes (to let you have enough time to get down to the basement) and tell that person to go to the basement afterwards. Go down to the basement, wait, and watch which switch turns on which lightbulb. After your family member comes down to the basement, ask them the order of the switch they flipped (for example, left to right, right to left, etc.). Then you're done, since you know which switch corresponds to which bulb.
Am I close?