Place eggs into a saucepan, and cover with water, heat on high until the water boils, cover saucepan with a lid, and turn off the heat. Leave the saucepan with the eggs inside on the stove for 15 minutes. This will let you cook hard boiled eggs without having to worry about over cooking them. Remove pan from stove, and run cool water through the pan. When the eggs have cooled off enough to peel, peel the eggs. Place the canned beets into a bowl and add eggs. It is a great idea to use a glass bowl here, sometimes plastic bowls can stain. Place hard boiled eggs into bowl with the beets. Cover bowl, and place in the refrigerator for 24 to 36 hours.