Prepare 8 to 12 hard boiled eggs. Peel them and place the eggs in a glass bowl. Dump in the drained sliced beets and set aside. Drain beets and reserve 1 Cup of beet juice. (Discard the remaining juice.) Pour the 1 Cup of juice into a saucepan. Add the water, sugar, and vinegar to the saucepan and stir. Bring to a boil, stirring to dissolve the sugar completely. Allow the mixture to cool. Pour the juice mixture over the hard boiled eggs and refrigerate for 24 hours, stirring several time to make sure the eggs are evenly colored by the juice.