In a mixing bowl, combine the cucumber slices, salt and vinegar and toss them about with a large spoon until the cucumber is well moistened.
Marinate at room temperature for 30 minutes, then drain the cucumbers through a sieve and pat them thoroughly dry with paper towels. Place them is a large mixing bowl.
Separate the yolks from the whites of the hard-cooked eggs. Cut the whites into small strips and mix the egg whites into the cucumber.
With the back of a large spoon, rub the egg yolks through a fine sieve set over a small bowl.