In a small bowl, dissolve yeast in 2/3 cup warm water. In a large bowl, cream sugar and shortening until light and fluffy. Add the eggs, potatoes, salt, yeast mixture, remaining water and 2 cups flour. Beat until smooth. Add enough remaining flour to form a soft dough.
Shape into a ball; do not knead. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 hour.
Punch dough down; divide into thirds. Shape each portion into 15 balls and arrange in three greased 9-in. round baking pans. Cover and let rise until doubled, about 30 minutes.
Bake at 375° for 20-25 minutes or until golden brown. Remove from pans to cool on wire racks.