Dissolve yeast in warm water.
In a large bowl, combine sugar, salt, oil, eggs and mashed potatoes. Mix until smooth.
Stir in yeast mixture, followed by 4 cups of flour. Gradually add the remaining flour until a soft dough forms. You may not use all the flour.
Turn dough onto a floured surface and need for about 5 minutes.
Place dough in a greased bowl. Cover and let rise until doubled in size, about 1 hour.
Punch down dough and divide into three equal portions. Divide and shape each portion into 12 equal balls. Place in greased baking pans. Let rise in a warm place until doubled, about 30 minutes.
Preheat oven to 375 degrees.
Bake rolls for 20-25 minutes, or until golden brown. Remove from oven and brush with melted butter. Remove rolls to wire racks to cool completely.