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Step 1
Place the carrot and daikons in a bowl and sprinkle with the salt and 2 teaspoons of the sugar. Use your hands to knead the vegetables for about 3 minutes, expelling the water from them. They will soften and liquid will pool at the bottom of the bowl. Stop kneading when you can bend a piece of daikon so that the ends touch but the daikon does not break. The vegetables should have lost about one-fourth of their volume. Drain in a colander and rinse under cold running water, then press gently to expel extra water. Return the vegetables to the bowl if you plan to eat them soon, or transfer them to a 1-quart jar for longer storage.
Step 2
To make the brine, in a bowl, combine the 1/2 cup sugar, the vinegar, and the water and stir to dissolve the sugar. Pour over the vegetables. The brine should cover the vegetables. Let the vegetables marinate in the brine for at least 1 hour before eating. They will keep in the refrigerator for up to 4 weeks. Beyond that point, they get tired.