There are a couple of things that you can do to repair the carpet. For the burns that are small and minor in damage, pick at the burned section with either a pocket knife or a pair of tweezers. After doing this for a minute or two, the fibers of the carpet sealed under the burned carpet will reappear. If the cigarette burns are larger and too damaged to repair, there is an alternative. If your wall-to-wall carpeting extends into a closet, cut a patch from the carpet there, where no one will notice a small piece missing. First, cut out the section of burned carpeting, making the piece a slightly larger than the burned area. Then cut a patch of the same size from the closet carpet. You can then glue the patch into the section that had the burn. If the carpet has a pattern or design, use the same technique but find some hidden carpet that matches the pattern of the burned area.