Add the sugar and vinegar to your pot and cook over medium heat until the sugar is fully dissolved. Wait for the solution to cool until it won't scald.
Begin layering the cucumber in the jar. Place one layer of slices in the container and sprinkle with salt. Repeat until you've used up your cucumber. Pour in your solution.
Put the lid on the jar and refrigerate for at least one day before serving.
Notes
Serve with raw vegetables and dill dip, or as a side dish with anything you want. You can even put them on a burger.
Although this needs to be chilled before service, other than the refrigeration it only takes about 10 minutes to make. It will keep in the refrigerator for a couple of weeks if tightly sealed. Because it isn't a real pickle, you can't keep it around forever.
A wire bale jar or glass mason jar makes a nice container for this dish. It is important to have a jar that closes with a good seal. Taller, narrower containers will help create the right proportion of salt.
We use the foot-long English (or "Burpless") cucumbers for this dish, primarily because of their low seed count. Other vegetables can be pickled as well or instead, such as tiny baby carrots or daikon (which is really good in this recipe).
Note that this recipe uses normal iodized salt, not pickling salt or kosher salt. You will probably be unhappy with the saltiness if you substitute a different salt.