Purple Pickled Eggs & Beets

12-18 large eggs. Hard-cook the eggs: Place in a pan large enough so that they don't overlap, and fill pan with water to 1" over eggs. Over med-high heat bring just to a rolling boil. Turn off the heat, cover the pan and let sit for 12 minutes. Rinse briefly with cold water. Shell eggs while still hot under running cold water. Drain the beets, reserving the juice, and place beets into a large Tupperware container. As the eggs are shelled, add them in and mix beets and eggs together gently. Add enough water to the beet juice to make 2 cups. Bring just to a boil and add the cider, sugar, salt and cloves. Return just to the boil. (Do not overboil! You'll lose the beautiful color!) Pour over eggs and beets. Refrigerate, shaking gently twice a day or so to rotate the eggs. In three days the whites should be completely dyed. The eggs are best served cut into quarters to show off the colors. After about a week the yolk will be purple also - not as pretty but still delicious. They keep for quite a while.