Empty beets and their juice into a small saucepan; add vinegar, sugar and salt and heat just until sugar dissolves. Cool to room temperature.

 

Place eggs in a bowl or a half gallon jar. Pour in beet mixture and add just enough water so that liquid cover eggs. Cover and refrigerate, allowing eggs to marinate a couple of days. Stir now and then or invert jar so that all eggs redden evenly.

 

Drain; serve eggs whole, sliced or wedged.