Combine water, vinegar, sugar, cinnamon, salt and cloves.  Heat till boiling.  Add beets.  Cover and simmer 5 minutes.  Chill then add eggs.  Put everything in a container with a sealed lid so you can shake things so eggs are covered.  If you can find pickled beets you can use those.  But no need to cook them.  Just add them after you cook other ingredients.