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Soak a clean nonabrasive cloth with warm water. Wipe the stain in a gentle counterclockwise motion. Use a clean soft cloth to dry the affected area. If warm water doesn't work, wet a cotton ball with isopropyl (rubbing) alcohol. Rub the stain in a gentle counterclockwise motion until the stain disappears. Dry the area with a clean soft cloth. Wet the magic eraser under a stream of warm water. Wring out the excess. Rub the stain in a gentle counterclockwise motion until it vanishes. This will work for spills and circular marks from glasses and goblets. Use a clean nonabrasive cloth to dry the area. Spray the affected area with Goo Gone or a similar citrus cleaner. Make sure the label states that the product is safe for quartz. Rub the area with a clean nonabrasive cloth using gentle counterclockwise strokes. Dry the area with a clean nonabrasive cloth.
Use warm water before anything else. Remove permanent marker with rubbing alcohol. Tackle wine with a magic eraser. Remove sticky messes with citrus-based cleaner.