Cut off the leaves from the beets leaving 1 inch of stem attached. Do not trim the taproot. Scrub the beets to remove any dirt. Put them in a large saucepan and cover with cold water by about 2 inches. Bring to a boil, lower the heat, cover, and simmer until fork tender, about 25 to 30 minutes. Drain.
When cool enough to handle, trim, and peel the beets. Slice into rounds and toss in a medium bowl with the onion.
In a small saucepan bring the sugar, vinegar, water, and salt to a boil. Stir to dissolve the sugar and salt and immediately pour over the beets and onion. Refrigerate overnight before serving.
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