Is it possible to restore a marble floor that has small two inch granite insets without touching the granite? The granite is in good shape but the marble is worn and dull.

There are several tricks you can use to hone and polish the marble without touching the granite. The best method is to cover the granite insets with duct tape. If you use resin bond diamonds starting at a 120, the diamonds should glide over the duct tape. Do not use metal bond diamonds since they will cut through the duct tape. Another method would be to simply polish the marble floor avoiding the use of diamond abrasives. This should work if the marble is dull and not badly scratched. A third method would be to treat the entire floor as if it where granite. Use granite diamonds and proceed through every step. At the higher grits the marble will develop a polish. In this case ignore the marble and concentrate on the granite.